\r\n\tBoth diagnosis and clinical manipulation of the patient with vasospasm is a unique and challenging situation. Multi-clinical approach is extremely mandatory. The patient must be treated in a center, which requires a experienced team with both neurological surgeons, interventional radiologists, neurologists and neuroanesthesiologists. Moreover, a well-equiped, isolated neurointensive care is needed for all patients suffering form subarachnoid hemorraghe. \r\n\tIn their daily practice, both neurological surgeons, interventional radiologists, neurologists, neuroanesthesiologists, and even intensive care providers have to deal and challenge of vasospasm. Numerous studies relevant to pathophysiological mechanisms underlying vasospasm had been published, but we still know little about the exact mechanisms causing vasospasm. In the last decades of modern medical era, despite the technological developments concerning the neurological care of the patients with vasospasm, we still have no effective treatment and preventive care of this devastating entity. \r\n\tThe aim of this book project is to provide in detailed knowledge to both physicians and scientists dealing with cerebral vasospasm. This book will attract interest of both students, residents, specialists and academics of neurological sciences.
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\n\t\t\t
1. Introduction
\n\t\t\t
Rupture of anterior cruciate ligament (ACL) is a common knee trauma which leads to anterior knee instability. The ACL has long been thought to have poor capacity for healing with suture repair. ACL reconstruction is the standard of care which can restore the knee stability of ACL deficit knee. Although ACL reconstruction is an excellent operation for restoring the sagittal plane stability of the knee, significant problems remain. Studies have demonstrated that remodeling of the graft usually takes longer than expected, and many patients develop arthritis after an ACL tear, even if they have a reconstruction, with rates as high as 78% reported at 14 years post-operatively (1).
\n\t\t\t
In ACL reconstruction, inflammation and necrosis of the graft can occur immediately after transplantation. The graft then undergoes revascularization and cellular repopulation from an extrinsic origin, followed by a remodeling period. In the early phase, the properties of the grafted tendon are deteriorated and do not recover to physiological levels even at 18 months after surgery (2). Therefore, the main goals of ACL reconstruction are to prevent the deterioration of grafted tendon and accelerate mechanical restoration of the deteriorated graft. New solutions are needed to accelerate and improve remodeling of tendon grafts.
\n\t\t\t
The ACL graft remodeling process is regulated by a complex growth factor network. Many growth factors have been evaluated for their ability to stimulate tendon and ligament healing in vitro and in vivo. In enhancing ligament repair, the most interesting candidates are insulin-like growth factor-I (IGF-I), transforming growth factor β1 (TGFβ1), vascular endothelial growth factor (VEGF), epidermal growth factor (EGF), platelet derived growth factor (PDGF), and basic fibroblast growth factor (bFGF). PDGF and VEGF appear in the early stage of reconstruction, during the stage of graft maturing, the granular tissue becomes ligament-like tissue and both PDGF and VEGF are not able to be detected gradually, as the replacement, TGFβ1and other cytokines are involving in the reconstruction process to mature the ligament. TGFβ1 is the main cytokine for the maturing of ligament. Studies have demonstrated improved cellular proliferation and migration as well as increased collagen production rates with the addition of growth factors.
\n\t\t
\n\t\t
\n\t\t\t
2. VEGF
\n\t\t\t
Angiogenesis is an essential step in the process of tendon healing and tendon graft remodeling, in which neovascularization prompts delivery of inflammatory cells, fibroblasts and growth factors to the wound site. VEGF plays an essential role in angiogenesis, regulating the activation, migration, and proliferation of endothelial cells in various pathological conditions. It is well-known that angiogenesis is an essential step in the healing process of tendon and tendon graft remodeling. Two studies found that VEGF therapy can enhance revascularization in the graft, as well as promoting the infiltration of fibroblasts after ACL reconstruction; however, it did not affect the mechanical properties of the in situ freeze-thawed ACL model (3). Furthermore, it decreased the stiffness of the grafted tendon with increased knee laxity, 12 weeks after ACL reconstruction in a sheep model (4). Yoshikawa et al. examined the effects of an application of VEGF to a hamstring graft in a sheep ACL reconstruction model and demonstrated that the linear stiffness of the VEGF-treated graft was significantly lower than that of the PBS-treated group at 12 weeks (4). In this study, the stiffness of the VEGF165 group was higher than those of the control group at 12 weeks, although there was no significant difference (P > 0.05). There are two possible reasons for this difference.
\n\t\t\t
In our study, the stiffness of the VEGF165 group was higher than those of the control group at 12 weeks, although there was no significant difference (5). There are two possible reasons for this difference. One is the method of applying this factor. In our study, the method was transfer of the VEGF165 gene, rather than the gene products. The secretion time and quantity of VEGF165 may be suitable for ACL graft remolding. The other possible reason is the use of BMSCs in our experiment. BMSCs have the capacity to differentiate into various mesenchymal lineages, including ligament, tendon, muscle, bone, cartilage and adipose tissue. Kanaya et al. reported that the intra-articular injection of BMSCs could accelerate the healing of partially torn knee ACLs in a rat model (6). Our study also demonstrated that the application of BMSCs is effective in enhancing collagen deposition and changing certain structural properties for improving tendon allograft remodeling after ACL reconstruction in a rabbit model (7). The exact reasons for the better healing observed in injured ACLs using BMSCs are uncertain. One possibility is that BMSCs directly differentiated into ligament fibroblasts within the healing environment. Alternatively, another possibility is that injected mesenchymal stromal cells directly contribute as a cellular source for ligament healing. BMSCs may also secrete a variety of growth factors, which may contribute to the activation and recruitment of local fibroblast precursors or enhance extracellular matrix synthesis.
\n\t\t
\n\t\t
\n\t\t\t
3. PDGF
\n\t\t\t
Many studies have also attempted to determine the effects of PDGF-BB on a ligament engineering system. It has been demonstrated that it promoted fibroblast proliferation, matrix synthesis, neovascularization, and mechanical properties. In our studies in the gene-transfected group, more cells and blood vessels could be found at 3 weeks, and more collagen was synthesized in the ACL as compared with the control and MSCs group (7). Similar to our findings were the results of a study by Nakamuraetal, which described an increased vascularity and enhanced collagen deposition in the wound of a patellar ligament afte rPDGF-B gene transfer in rats (8).
\n\t\t\t
The mechanisms by which PDGF affects ligament healing are complex. Kuroda et al. studied immunohistochemically the presence and the level of bFGF, TGF-ß, PDGFAA and PDGF-BB expression in a model of ACL reconstruction using a free patellar tendon autograft (9). They found that all tested growth factors were upregulated with a maximum expression at 3 weeks and up to 60% of all cells were stained PDGF positive. PDGF is one of the most effective growth factors during tendon graft remodeling.
\n\t\t\t
Tendon grafts are exposed to the reduced PO2 of the intra-articular environment, Petersen et al. (10) showed that PDGF as well as hypoxia strongly enhanced VEGF secretion from tenocytes. Besides this VEGF-mediated angiogenetic effect, PDGF further more induces the synthesis of other growth factors, including IGF, and regulates the presence of other receptors (11). Therefore, it could be concluded that the expression of PDGF-BB by the small number of transfected cells may activate a cascade of PDGF-BB throughout the wound. Some researches (12) showed that there are some growth factors receptors such as PDGFR on the surface of MSCs. MSCs from bone marrow might have a better response to PDGF as compared with those from the ACL or MCL regarding proliferation and migration. Thus, it might be suggested that a tendon graft seeded with MSCs-PDGF-BB is more likely to promote MSCs or fibroblast proliferation and migration and accelerate graft tissue remodeling.
\n\t\t\t
The observations of Kuroda et al. also imply that if a growth factor is administered to the tendon graft, its tissue concentration should be highest around the third week to enhance the effect of the other intrinsical growth factors (9). In our study at 3 weeks, we found significantly higher vascularity in the PDGF-transfected grafts. The concentration of PDGF-BB inarticular fluid from gene-transfected rabbit increased at 3 week, got to the highest point at 6 week and then dropped down. This rapid reduction in the level of their localization indicates that once the extrinsic cells infiltrate to the graft and revascularization is complete, these growth factors may have less significance for subsequent remodeling. Therefore, it is very important to find the appropriate time point for the administration of growth factors to promote healing.
\n\t\t\t
In vivo study by Hildebrand et al. demonstrated that the improvements in the MCL structural properties were dose-dependent to PDGF-BB (13).That is, a higher dose of PDGF-BB improved more structural properties of the femur–MCL–tibia complex than a lower dose of PDGF-BB did. In both the MSCs group and gene-transfected group, although there are much more differences in morphology at the early stages, the structure of the ACL in the two groups have less significant differences at the later stages, especially at 12 weeks. For an ACL reconstruction model, we don’t know if the dosage we used was appropriate to maximally enhance graft remodeling, or this indicates that the growth fact or PDGF may have early effect on the ACL reconstruction and have less significance for subsequent remodeling. It is essential to find an appropriate dosage for ACL reconstruction.
\n\t\t
\n\t\t
\n\t\t\t
4. TGFβ1
\n\t\t\t
Many studies indicate that TGFβ1 plays a key role in the healing process of ligaments. TGFβ1 increased both collagen and non-collagenous protein synthesis by the introduction of ACL fibroblasts (14, 15). Furthermore, it has also been shown to increase ACL fibroblast proliferation. TGFβ1 enhanced graft remolding in ACL reconstruction by inhibiting mechanical deterioration (16).
\n\t\t\t
In situ freeze-thawed ACL tissues, which were established as an autograft model, transfected with TGFβ1 and EGF, significantly reduced the increase in water content and cross-sectional area and reduced the deterioration of the ACL (17). However, the results were dose- and time-dependent, and of high cost. Furthermore, the clinical application of growth factors is hampered by delivery problems. Amiel et al. reported that a high dose of TGFβ1 inhibits proliferation of rabbit ACL fibroblasts (18). One study reported that an application of low-dose TGFβ1 mixed with fibrin sealant enhanced the remodeling process of the in situ freeze-thawed ACL, whereas a high dose of TGFβ1 had no effect (17). We demonstrated that TGFβ1 gene-modified BMSCs implanted within the Achilles allograft in ACL reconstruction significantly affects the biomechanical properties of the graft. Our results suggest that the transfer of the TGFβ1 gene, rather than the gene products, may be the most expeditious method of harnessing this factor for the purposes of accelerating ACL graft remolding (5).
\n\t\t\t
Our results showed that the ultimate failure load and the stiffness of the grafted tendon were significantly increased in the TGFβ1 treatment group compared with the VEGF165 and control groups at 6, 12 and 24 weeks after surgery. Meanwhile toluidine blue staining of the grafts appeared positive only in the TGFβ1 group at 12 weeks. ACL has different histological characteristics from medical collateral ligament (MCL), which is more cartilage-like in nature. The normal ACL is positive to toluidine blue staining, so we hypothesized that TGFβ1 may promote early maturation of the graft. Histological examination and immunohistochemistry showed significantly enhanced cell infiltration and revascularization at 3, 6, and 12 weeks in the VEGF165 and the TGFβ1/VEGF165 groups. However, VEGF165 cDNA-transduced BMSCs exhibited no significant effects on the mechanical properties of the ACL graft, while TGFβ1/VEGF165 cDNA-transduced BMSCs showed the best biomechanical properties of the ACL graft at 24 weeks after surgery. This work shows that the use of TGFβ1 and the co-expression of TGFβ1/VEGF165 of gene therapy may be useful for accelerating the remolding of the graft after ACL reconstruction.
\n\t\t\t
Previous study by Lee et al. demonstrated that VEGF and TGFβ1 were both expressed in ACL healing (18). We demonstrate here that the combination of TGFβ1 and VEGF165 gene has a synergistic effect on accelerating the remolding of the ACL graft, but few studies have defined the exact regulating mechanisms of these two growth factors during ligament healing. Several studies have demonstrated that together VEGF and TGFβ1 can enhance each the synthesis of one another (19, 20). These studies revealed that the mechanism of synergy is probably mediated through Smad3, HIF-1α/β, Smad3/4, PI3K/Akt or ERK1/2 signaling pathways.
\n\t\t
\n\t\t
\n\t\t\t
5. The Effects of TGF-β1, VEGF165 transfer on achilles tendon healing
\n\t\t\t
The Achilles tendon itself is a dense, regular connective tissue consisting primarily of type I collagen and interspersed specializedmesenchymal cells (tenocytes) responsible for the maintenance of collagen structure. With respect to reconstruction of the tendon, there are three key factors which must be addressed: the cell, the fiber, and their arrangement. The properties of the tendon matrix and its regulation by growth factors are largely uncharacterized. We examined the effects of implantation of BMSCs transduced with either the TGF-β1, VEGF165, or both on experimentally injured Achilles tendons in a rabbit model in vivo (21).
\n\t\t\t
The maximum failure load, the tendon stiffness, and the elastic modular of the healing tendons were significantly increased in the TGF-β1 and the co-expression treatment groups compared with the other treatment groups at one, two, four, and eight weeks after surgery. Moreover, there was evidence of accelerated remodeling of the lesion in response to TGF-β1 and co-expression TGF-β1/VEGF165 treatment, while the size of the ruptured callus was increased in the presence of VEGF165. Histological examination showed a much more organized and homogeneous pattern of collagen fibers at all time points in the lesions of the TGF-β1 and the co-expression treatment groups. Both single fibrils and the collagen fibers had a greater diameter, with a higher degree of collagen crimp than the collagen of the other treatment groups. This was confirmed by Sirius red staining in conjunction with polarized light microscopy, which showed a higher shift of small yellow-green fibers to strong yellow-orange fibers after two, four, and eight weeks in the TGF-β1 and the co-expression treatment groups. Immunohistochemistry showed more vessels after one, two, four, and eight weeks in the VEGF165 treatment group, but only a few vessels in the co-expression treatment group. There was also an earlier shift from fibroblasts to fibrocytes within the healing tendon, with fewer fat cells present in the tendons of the TGF-β1 and the co-expression treatment groups compared with intact tendon. Thus treatment with TGF-β1 transduced BMSCs resulted in a promising acceleration and improvement of tendon healing, particularly influencing early tissue regeneration, leading to quicker recovery and improved biomechanical properties of the Achilles tendon. However, VEGF165 transduced BMSCs exhibited a negative role. The angiogenesis effects of VEGF165 were diminished by TGF-β1, while the collagen synthesis effects of TGF-β1 were only slightly affected by VEGF165. The TGF-β1 and VEGF165 synthesized of BMSCs with gene transfer were evaluated by ELISA. However, the stimulation effect is very weak with heterologous gene transfer in contrast with homologous gene transfer. In terms of the fibroblasts, the mRNA expression of Collagen type I, type III and Fibronectin were evaluated. All showed significant increasing under the stimulation of TGF-β1 or TGF-β1/VEGF165 co-existing. Nevertheless, the fibroblasts stimulated by VEGF165 showed no difference with control.
\n\t\t\t
We demonstrated that gene modified BMSCs implanted within the tendon-repair site contributed to early tendon-healing following primary repair, and that growth factor signaling can regulate the mechanical properties of the tendon matrix by affecting tendon mass and architecture. These data provide a basis for future application of supplementary therapy of surgery for tendon and ligaments. Future studies determining the optimal growth factor(s), dose, and timing and site of administration are required, along with the interactions between different growth factors.
\n\t\t
\n\t\t
\n\t\t\t
6. Summary
\n\t\t\t
The effects of TGF-β1, VEGF and PDGF on the remodeling of anterior cruciate ligament graft are different. PDGF, VEGF and TGFβ1transfected MSCs accelerated cellular infiltration and enhanced collagen deposition in the graft. PDGF and VEGF promoted the angiogenesis of the graft, but did not show any improvement of the biomechanical nature of the graft. Only TGFβ1accerated the maturing of graft and improved the biomehchanical nature. TGFβ1 co–expression with VEGF165 in gene-transfected BMSCs could accelerate the remodeling of the reconstructed ligament. The cross-talk between TGFβ1 and VEGF165 has positive consequences, with TGFβ1/VEGF165-gene-transfected BMSCs could significantly promote angiogenesis of the reconstructed ligament, while achieving the best mechanical properties of the reconstructed ligament. However, the molecular mechanism that regulates these two growth factors during ligament healing still needs to be fully elucidated. The effects of other growth factors on the remodeling of ACL graft, such as IGF-1, bFGF, need further study.
\n\t\t
\n\t\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/17934.pdf",chapterXML:"https://mts.intechopen.com/source/xml/17934.xml",downloadPdfUrl:"/chapter/pdf-download/17934",previewPdfUrl:"/chapter/pdf-preview/17934",totalDownloads:1162,totalViews:104,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"October 26th 2010",dateReviewed:"March 31st 2011",datePrePublished:null,datePublished:"August 23rd 2011",readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/17934",risUrl:"/chapter/ris/17934",book:{slug:"targets-in-gene-therapy"},signatures:"Changlong Yu, Lin Lin and Xuelei Wei",authors:[{id:"30513",title:"Prof.",name:"Changlong",middleName:null,surname:"Yu",fullName:"Changlong Yu",slug:"changlong-yu",email:"ycl123@vip.sina.com",position:null,institution:null},{id:"45877",title:"Dr.",name:"Lin",middleName:null,surname:"Lin",fullName:"Lin Lin",slug:"lin-lin",email:"simon.lin2003@163.com",position:null,institution:null},{id:"45878",title:"Dr.",name:"Xuelei",middleName:null,surname:"Wei",fullName:"Xuelei Wei",slug:"xuelei-wei",email:"xueleiwei@163.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. VEGF",level:"1"},{id:"sec_3",title:"3. PDGF",level:"1"},{id:"sec_4",title:"4. TGFβ1",level:"1"},{id:"sec_5",title:"5. The Effects of TGF-β1, VEGF165 transfer on achilles tendon healing",level:"1"},{id:"sec_6",title:"6. Summary",level:"1"}],chapterReferences:[{id:"B1",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tVon\n\t\t\t\t\t\t\tPorat. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRoos\n\t\t\t\t\t\t\tE. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRoos\n\t\t\t\t\t\t\tH.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004High prevalence of osteoarthritis 14 years after an anterior cruciate ligament tear in male soccer players: a study of radiographic and patient relevant outcomes.Br J Sports Med.; 38: 263.\n\t\t\t'},{id:"B2",body:'\n\t\t\t\t\n\t\t\t\t\tDelay BS, McGrath BE, Mindell ER,\n\t\t\t\t\t2002Observation on a retrieved patellar tendon autograft used to reconstruct the anterior cruciate ligament. A case report. 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Matrix Biol.;28(6):324\n\t\t\t\t\t35\n\t\t\t\t\n\t\t\t'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Yu Changlong",address:null,affiliation:'
Institute of Sports Medicine, Peking University Third Hospital, No.49, North Garden Road, Haidian District, P.R.China
Institute of Sports Medicine, Peking University Third Hospital, No.49, North Garden Road, Haidian District, P.R.China
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Chen",authors:[{id:"62462",title:"Prof.",name:"Clark",middleName:null,surname:"Chen",fullName:"Clark Chen",slug:"clark-chen"},{id:"85623",title:"Prof.",name:"Kimberly",middleName:null,surname:"Ng",fullName:"Kimberly Ng",slug:"kimberly-ng"},{id:"86785",title:"Dr.",name:"Joshua",middleName:null,surname:"Lawson",fullName:"Joshua Lawson",slug:"joshua-lawson"},{id:"86788",title:"Dr.",name:"Santosh",middleName:null,surname:"Kesari",fullName:"Santosh Kesari",slug:"santosh-kesari"},{id:"86789",title:"Dr.",name:"Bob",middleName:null,surname:"Carter",fullName:"Bob Carter",slug:"bob-carter"},{id:"86790",title:"Dr.",name:"Kirstopher",middleName:null,surname:"Kahle",fullName:"Kirstopher Kahle",slug:"kirstopher-kahle"}]},{id:"22730",title:"The Botanical Extract Feverfew PFE Reduces DNA Damage and Induces DNA Repair Processes",slug:"the-botanical-extract-feverfew-pfe-reduces-dna-damage-and-induces-dna-repair-processes",signatures:"Michael D. Southall, Simarna Kaur and Khalid Mahmood",authors:[{id:"42297",title:"Dr.",name:"Michael",middleName:null,surname:"Southall",fullName:"Michael Southall",slug:"michael-southall"},{id:"54272",title:"Dr.",name:"Simarna",middleName:null,surname:"Kaur",fullName:"Simarna Kaur",slug:"simarna-kaur"},{id:"54559",title:"Dr.",name:"Khalid",middleName:null,surname:"Mahmood",fullName:"Khalid Mahmood",slug:"khalid-mahmood"}]},{id:"22731",title:"Food Factors and Oxidative DNA Damage / DNA Repair Systems",slug:"food-factors-and-oxidative-dna-damage-dna-repair-systems",signatures:"Takeshi Hirano and Kazuyoshi Tamae",authors:[{id:"41165",title:"Prof.",name:"Takeshi",middleName:null,surname:"Hirano",fullName:"Takeshi Hirano",slug:"takeshi-hirano"},{id:"41284",title:"Dr.",name:"Kazuyoshi",middleName:null,surname:"Tamae",fullName:"Kazuyoshi Tamae",slug:"kazuyoshi-tamae"}]},{id:"22732",title:"Enhancing DNA Repair by Combining only Dietary Supplement Ingredients that do not Metabolically Compete in Order to Achieve Synergism",slug:"enhancing-dna-repair-by-combining-only-dietary-supplement-ingredients-that-do-not-metabolically-comp",signatures:"Ronald W. Pero",authors:[{id:"56402",title:"Prof.",name:"Ronald",middleName:null,surname:"Pero",fullName:"Ronald Pero",slug:"ronald-pero"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"68778",title:"Secure State Estimation and Attack Reconstruction in Cyber-Physical Systems: Sliding Mode Observer Approach",doi:"10.5772/intechopen.88669",slug:"secure-state-estimation-and-attack-reconstruction-in-cyber-physical-systems-sliding-mode-observer-ap",body:'\n
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1. Introduction
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Cyber-physical systems (CPS) are the integration of the cyber-world of computing and communications with the physical world. In many systems, control of a physical plant is integrated with a wireless communication network, for example, transportation networks, electric power networks, integrated biological systems, industrial automation systems, and economic systems [1, 2]. Since CPSs use open computation and communication platform architectures, they are vulnerable to suffering adversarial physical faults or cyber-attacks. Faults and cyber-attacks are referred to as attacks throughout this chapter.
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Recent real-world cyber-attacks, including multiple power blackouts in Brazil [3], and the Stuxnet attack [4] in 2010, showed the importance of providing security to CPSs. Identification and modeling process as [5, 6] which are based on data can be seriously affected by corrupted data. As a result, information security techniques [7] may be not sufficient for protecting systems from sophisticated cyber-attacks. It is suggested in [8] that information security mechanisms have to be complemented by specially designed resilient control systems. Controlling CPS with sensors and actuators, who are hijacked/corrupted remotely or physically by the attackers, is a challenge. The use of novel control/observation algorithms is proposed in this chapter for recovering CPS performance online if an attacker penetrates the information security mechanisms.
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Cyber security of CPS must provide three main security goals: availability, confidentiality, and integrity [7]. This means that the CPS is to be accessible and usable upon demand, the information has to be kept secret from unauthorized users, and the trustworthiness of data has to be guaranteed. Lack of availability, confidentiality, and integrity yields denial of service, disclosure, and deception, respectively. A specific kind of deception attack called a replay attack has been investigated when the system model is unknown to the attackers but they have access to the all sensors [9, 10]. Replay attacks are carried out by “hijacking” the sensors, recording the readings for a certain time, and repeating such readings while injecting them together with an exogenous signal into the system’s sensors. It is shown that these attacks can be detected by injecting a random signal, unknown to the attacker, into the system. In the case when the system’s dynamic model is known to the attacker, another kind of deception attack, called a cover attack, has been studied in [11], and the proposed algorithm allows cancelling out the effect of this attack on the system dynamics. In systems with unstable modes, false data injection attacks are applied to make some unstable modes unobservable [12]. Denial of service attacks assaults data availability through blocking information flows between different components of the CPS. The attacker can jam the communication channels, modify devices, and prevent them from sending data, violate the routing protocols, etc. [13]. In a stealth attack, the attacker modifies some sensor readings by physically tampering with the individual meters or by getting access to some communication channels [14, 15]. As a result, detecting and isolating of cyber-attacks in CPSs has received immense attention [16]. However, how to ensure the CPS can continue functioning properly if a cyber-attack has happened is another serious problem that should be investigated; therefore, the focus of this chapter is on resilient control of CPS.
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In [17], new adaptive control architectures that can foil malicious sensor and actuator attacks are developed without reconstructing the attacks, by means of feedback control only. A sparse recovery algorithm is applied to reconstruct online the cyber-attacks in [18]. Sliding mode control with advantages of quick response and strong robustness is one of the best approaches to control CPS [19, 20, 21, 22]. In [23], a finite-time convergent higher-order sliding mode (HOSM) observer, based on a HOSM differentiator and a sparse recovery algorithm, are used to reconstruct online the cyber-attack in a nonlinear system. Detection and observation of a scalar attack by a sliding mode observer (SMO) has been accomplished for a linearized differential-algebraic model of an electric power network when plant and sensor attacks do not occur simultaneously [24]. Cyber-attacks against phasor measurement unit (PMU) networks are considered in [25], where a risk mitigation technique determines whether a certain PMU should be kept connected to network or removed. In [26] a sliding mode-based observation algorithm is used to reconstruct the attacks asymptotically. This reconstruction is approximate only, since pseudo-inverse techniques are used.
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In this chapter, CPSs controlled by a control input subject to sensor attacks and state/plant attacks are considered. The corrupted measurements propagate the attack signals to the CPS through the control signals causing CPS performance degradation. The main challenge that is addressed in the chapter is online exact reconstruction of the sensor and state attacks with an application to an electric power network. The contribution of this chapter is:
Novel fixed and adaptive-gain SMO for the linearized/linear CPS under attack are proposed for the online reconstruction of sensor attacks. The time-varying attacks are reconstructed via the proposed SMO that includes a newly designed dynamic filter. Note that the well-known SMO proposed in [27] reconstructs the slow-varying perturbations only.
A super twisting SMO is applied to reconstruct the state/plant time-varying attacks of the linearized/linear CPS under attack.
For online state/plant attack reconstruction in nonlinear CPS under attack, a higher-order sliding mode disturbance observer [28] is used.
An algorithm that use sliding mode differentiation techniques [29] in concert with the finite-time convergent observer for the sparse signal recovery is applied to online reconstruction of time-varying attack in nonlinear CPS under attack when we have limited measurements and more possible sources of attack [30].
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2. Motivation example: electric power network under attack
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In a real-world power network, only a small group of generator rotor angles and rates is directly measured, and typical attacks aim at injecting disturbance signals that mainly affect the sensorless generators [24].
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The small-signal version of the classic structure-preserving power network model is adopted to describe the dynamics of a power network. Consider a connected power network consisting of \n\n\nn\n1\n\n\n generators \n\n\n\ng\n1\n\n…\n\ng\n\nn\n1\n\n\n\n\n and \n\n\nn\n2\n\n\n load buses \n\n\n\nb\n\n\nn\n1\n\n+\n1\n\n\n…\n\nb\n\n\nn\n1\n\n+\n\nn\n2\n\n\n\n\n\n. The interconnection structure of the power network is encoded by a connected susceptance-weighted graph G. The vertices of G are the generators \n\n\ng\ni\n\n\n and the buses \n\n\nb\ni\n\n\n. The edges of G are the transmission lines \n\n\n\nb\ni\n\n\nb\nj\n\n\n\n and the connections \n\n\n\ng\ni\n\n\nb\ni\n\n\n\n weighted by their susceptance values. The Laplacian associated with the susceptance-weighted graph is the symmetric susceptance matrix \n\nL\n∈\n\nR\n\n\n\n\nn\n1\n\n+\n\nn\n2\n\n\n\n×\n\n\n\nn\n1\n\n+\n\nn\n2\n\n\n\n\n\n\n defined by \n\n\nL\nθ\n\n=\n\n\n\n\n\nL\n\ng\n,\ng\n\nθ\n\n\n\n\nL\n\ng\n,\nl\n\nθ\n\n\n\n\n\n\nL\n\nl\n,\ng\n\nθ\n\n\n\n\nL\n\nl\n,\nl\n\nθ\n\n\n\n\n\n\n [8].
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The CPS that motivates the results presented in this work is the US Western Electricity Coordinating Council (WECC) power system [8] under attack with three generators and six buses, whose electrical schematic is presented in Figure 1. The mathematical model of the power network in Figure 1 under sensor stealth attack and deception attack can be represented as the following descriptor equations that consist of differential and algebraic equations [8]:
where the state vector \n\nx\n=\n\n\n\n\n\n\nδ\nT\n\n\n\n\nω\nT\n\n\n\n\nθ\nT\n\n\n\n\n\nT\n\n\n includes the vector of rotor angles \n\nδ\n∈\n\nR\n3\n\n\n, the vector of generator speed deviations from synchronicity \n\nω\n∈\n\nR\n3\n\n\n, as well as the vector of voltage angles at the buses \n\nθ\n∈\n\nR\n6\n\n\n. The \n\ny\n∈\n\nR\np\n\n\n is the measurement vector, \n\n\nd\nx\n\n∈\n\nR\n\nm\n1\n\n\n\n is the Deception attack corrupting the states, and \n\n\nd\ny\n\n∈\n\nR\n\nm\n−\n\nm\n1\n\n\n\n\n is the stealth attack vector spoofing the measurements. Note that the states of the plant are under attack even if they are not attacked directly but via propagation.
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The measurement corruption attacks through an output control feedback. The matrices \n\n\nE\ng\n\n,\n\nM\ng\n\n∈\n\nR\n\n3\n×\n3\n\n\n\n are diagonal whose nonzero entries consist of the damping coefficients and the normalized inertias of the generators, respectively:
The inputs \n\n\nP\nω\n\n\n and \n\n\nP\nθ\n\n\n are due to known changes in the mechanical input power to the generators and real power demands at the loads. The matrices \n\nB\n∈\n\nR\n\n12\n×\n\nm\n1\n\n\n\n\n and \n\nD\n∈\n\nR\n\np\n×\n\n\nm\n−\n\nm\n1\n\n\n\n\n\n\n are the attack distribution matrices, and \n\nC\n∈\n\nR\n\np\n×\n12\n\n\n\n is the output gain matrix. The \n\n\nL\nθ\n\n∈\n\nR\n\n9\n×\n9\n\n\n\n with\n\n\n\n\n\nL\n\ng\n,\ng\n\nθ\n\n∈\n\nR\n\n3\n×\n3\n\n\n,\n\nL\n\ng\n,\nl\n\nθ\n\n∈\n\nR\n\n3\n×\n6\n\n\n,\n\nL\n\nl\n,\ng\n\nθ\n\n∈\n\nR\n\n6\n×\n3\n\n\n,\n\nL\n\nl\n,\nl\n\nθ\n\n∈\n\nR\n\n6\n×\n6\n\n\n\n\n\n\n is giving by
Note that \n\n\nω\ni\n\n→\n0\n\n∀\n\ni\n=\n1\n,\n2\n,\n3\n\n in a case of the nominal performance of the studied network. Consider the case when the outputs of system, which are the measurement sensors \n\n\nω\n1\n\n,\n\nω\n2\n\n,\n\nω\n3\n\n\n, are corrupted by the following stealth attacks.
The system (1) was simulated with and without above attacks. Based on the simulation results shown in Figures 2 and 3, the stealth attack in (4) yields inappropriate degradation of the power network performance.
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Figure 2.
Comparing corrupted sensor measurements (\n\n\nω\n1\n\n,\n\nω\n2\n\n,\n\nω\n3\n\n\n under attack) and sensor measurements when there is no attack.
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Figure 3.
Comparing corrupted states (\n\n\nδ\n1\n\n,\n\nδ\n2\n\n,\n\nδ\n3\n\n\n under attack) and stats when there is no attack.
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This motivates why online reconstruction of the attacks followed by cleanup of the measurements prior to using them in control signal is of prime importance for retaining the performance of the power network (as it will be shown in Section VI where the proposed SMO is applied to achieve this goal). The case study of the power network (1) will be further discussed in details in Section 6.
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3. Cyber-physical system dynamics
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Consider the following completely observable and asymptotically stable system
where \n\nx\n∈\n\nR\nn\n\n\n is the state vector, \n\nf\n\nx\n\n∈\n\nR\nn\n\n\n is a smooth vector field, \n\nd\n\nt\n\n∈\n\nR\nm\n\n\n denotes the attack/fault vector which is additive and matched to the control signal, \n\ny\n∈\n\nR\np\n\n\n is the measurement vector, \n\np\n≥\nm\n\n, \n\nC\n\nx\n\n∈\n\nR\np\n\n\n is the output smooth vector field, \n\nB\n\nx\n\n∈\n\nR\n\nn\n×\nm\n\n\n\n and \n\nD\n∈\n\nR\n\np\n×\nm\n\n\n\n denote the attack/fault distribution matrices. For notational convenience, and without affecting generality, the input distribution matrices can be partitioned as
where \n\n\nB\n1\n\n\nx\n\n∈\n\nR\n\nn\n×\n\nm\n1\n\n\n\n,\n\n\nD\n1\n\n∈\n\nR\n\np\n×\n\n\nm\n−\n\nm\n1\n\n\n\n\n\n,\n\n\n0\n1\n\n∈\n\nR\n\nn\n×\n\n\nm\n−\n\nm\n1\n\n\n\n\n\n,\n\n\n0\n2\n\n∈\n\nR\n\np\n×\n\nm\n1\n\n\n\n\n where \n\n\nm\n1\n\n≤\nm\n\n.
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Assumption (A1):\n\n\nB\n1\n\n\nx\n\n,\n\nD\n1\n\n\n are of full rank.
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The attack/fault vector is partitioned accordingly as
where \n\n\nd\nx\n\n\nt\n\n\n, \n\n\nd\ny\n\n\nt\n\n\n represent the state and the sensor attack vectors, respectively. Different attack strategies are shown in Table 1 and discussed in Section 1.
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Attack plan
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\n\n\n\nd\nx\n\n\nt\n\n≠\n0\n\n\n
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\n\n\n\nd\ny\n\n\nt\n\n≠\n0\n\n\n
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Access to all sensors
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Need to know the system model
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Stealth attack
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√
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Deception attack
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√
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Reply attack
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√
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√
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√
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Covert attack
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√
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√
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√
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False data injection attack
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√
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√
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Table 1.
Cyber-attack strategies.
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Since \n\np\n≥\nm\n−\n\nm\n1\n\n\n, the system (8) can be partitioned using a nonsingular transformation \n\nM\n∈\n\nR\n\np\n×\np\n\n\n\n
where \n\n\n\ny\n¯\n\n1\n\n∈\n\nR\n\np\n1\n\n\n\n with \n\n\np\n1\n\n=\np\n−\n\n\nm\n−\n\nm\n1\n\n\n\n\n and \n\n\n\ny\n¯\n\n2\n\n∈\n\nR\n\np\n2\n\n\n\n where \n\n\np\n2\n\n=\nm\n−\n\nm\n1\n\n\n. Note that the state attack vector \n\n\nd\nx\n\n\nt\n\n\n is additive and matched to the control input that is embedded in system Eq. (11) already.
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4. Problem formulation
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Assumption (A2): Attacks are detectable, i.e., the invariant zeros of Eq. (11) are stable.
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The problem is to protect the closed loop system (11) from the sensor attack \n\n\nd\ny\n\n∈\n\nR\n\nm\n−\n\nm\n1\n\n\n\n\n and state/plant attack \n\n\nd\nx\n\n\nt\n\n∈\n\nR\n\nm\n1\n\n\n\n by means of designing fixed-gain and adaptive-gain SMOs that allow: (a) reconstructing online the sensor attack \n\n\nd\ny\n\n\n, the state/plant attack \n\n\nd\nx\n\n\nt\n\n\n, and the plant states \n\nx\n\n so that
Note that Eq. (13) represents the compensated CPS that converges to CPS without attack as time increases.
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5. Results: secure state estimation
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In this chapter, for the linearized case of the system in Eq. (5), two SMOs for state estimation and attack reconstruction are discussed. Two other SMO strategies for nonlinear system (5) are also proposed and investigated.
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5.1 Attack reconstruction in linear system via filtering by adaptive sliding mode observer
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Consider the linearized system in Eq. (5) with \n\nC\n\nx\n\n=\nCx\n\n and \n\nB\n\nx\n\n=\nB\n\n
Considering system Eq. (14) and assuming assumption (A1) holds, then as show in [29] there exists a matrix \n\nN\n∈\n\nR\n\n\n\nn\n−\np\n\n\n×\nn\n\n\n\n such that the square matrix
is nonsingular and the change of coordinates \n\nx\n↦\n\nT\nc\n\nx\n\n creates, without loss of generality, a new state-space representation \n\n\n\nA\n′\n\n\n\nB\n′\n\n\n\n\nC\n′\n\n\nD\n\n\n where
with \n\n\n\n\n\nx\n1\n\n∈\n\nR\n\nn\n−\np\n\n\n,\n\n\n\nx\n2\n\n∈\n\nR\np\n\n\n\n\n\n, \n\n\nB\n1\n\n∈\n\nR\n\n\n\nn\n−\np\n\n\n×\nm\n\n\n\n, \n\n\nB\n2\n\n∈\n\nR\n\np\n×\nm\n\n\n\n, \n\n\nA\n11\n\n∈\n\nR\n\n\n\nn\n−\np\n\n\n×\n\n\nn\n−\np\n\n\n\n\n\n, \n\n\nA\n12\n\n∈\n\nR\n\n\n\nn\n−\np\n\n\n×\np\n\n\n\n, \n\n\nA\n21\n\n∈\n\nR\n\np\n×\n\n\nn\n−\np\n\n\n\n\n,\n\nA\n22\n\n∈\n\nR\n\np\n×\np\n\n\n\n. It is well known that \n\n\nA\nC\n\n\n is observable if and only if \n\n\n\nA\n11\n\n\nA\n21\n\n\n\n is observable [31].
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Defining a further change of coordinates \n\n\n\nx\n¯\n\n1\n\n=\n\nx\n1\n\n+\n\nLx\n2\n\n\n where \n\nL\n∈\n\nR\n\n\n\nn\n−\np\n\n\n×\np\n\n\n\n is the design matrix, then the system Eq. (17) can be rewritten as
where \n\n\n\n\n\n\nA\n˜\n\n11\n\n=\n\nA\n11\n\n+\n\nLA\n21\n\n,\n\n\n\n\nA\n˜\n\n12\n\n=\n−\n\nA\n11\n\nL\n+\n\nA\n12\n\n−\n\nLA\n21\n\nL\n+\n\nLA\n22\n\n\n\n\n\n, \n\n\n\nB\n˜\n\n1\n\n=\n\nB\n1\n\n+\n\nLB\n2\n\n\n, \n\n\n\nA\n˜\n\n21\n\n=\n\nA\n21\n\n\n, \n\n\n\nA\n˜\n\n22\n\n=\n\nA\n22\n\n−\n\nA\n21\n\nL\n\n, \n\n\n\nB\n˜\n\n2\n\n=\n\nB\n2\n\n\n. Since \n\n\n\nA\n11\n\n\nA\n21\n\n\n\n is observable, there exist choices of the matrix \n\nL\n\n so that the matrix \n\n\n\nA\n˜\n\n11\n\n=\n\nA\n11\n\n+\n\nLA\n21\n\n\n is Hurwitz.
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Assumption (A3): The attack \n\nd\n\nt\n\n\n and its derivative are norm bounded, i.e.,
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\n\n\n\nd\n\n<\n\nk\nd\n\n\n and \n\n\n\nd\ṅ\n\n\n<\n\nl\nd\n\n\n where \n\n\nk\nd\n\n,\n\nl\nd\n\n>\n0\n\n and are known.
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Since \n\np\n>\nm\n\n, there exists a nonsingular scaling matrix \n\nQ\n∈\n\nR\n\np\n×\np\n\n\n\n such that
where \n\n\nD\n2\n\n∈\n\nR\n\nm\n×\nm\n\n\n\n is nonsingular. Define \n\n\ny\n¯\n\n\n as the scaling of the measured outputs \n\ny\n\n according to \n\n\ny\n¯\n\n=\nQy\n\n. Partition the output of the CPS into unpolluted measurements \n\n\n\ny\n¯\n\n1\n\n∈\n\nR\n\np\n−\nm\n\n\n\n and polluted measurements \n\n\n\ny\n¯\n\n2\n\n∈\n\nR\nm\n\n\n as
where \n\n\n\nA\n¯\n\n11\n\n=\n\n\nA\n˜\n\n11\n\n\n, \n\n\n\nA\n¯\n\n12\n\n=\n\n\nA\n˜\n\n12\n\n\nQ\n\n−\n1\n\n\n\n, \n\n\n\nB\n¯\n\n1\n\n=\n\n\nB\n˜\n\n1\n\n\n, \n\n\n\nA\n¯\n\n21\n\n=\nQ\n\n\nA\n˜\n\n21\n\n\n, \n\n\n\nA\n¯\n\n22\n\n=\nQ\n\n\nA\n˜\n\n22\n\n\nQ\n\n−\n1\n\n\n\n, and \n\n\n\nB\n¯\n\n2\n\n=\nQ\n\n\nB\n˜\n\n2\n\n\n. Define \n\n\n\nx\n¯\n\n2\n\n=\ncol\n\n\n\nx\n¯\n\n21\n\n\n\nx\n¯\n\n22\n\n\n\n, where \n\n\n\nx\n¯\n\n21\n\n∈\n\nR\n\np\n−\nm\n\n\n\n and \n\n\n\nx\n¯\n\n22\n\n∈\n\nR\nm\n\n\n. Consequently the system in Eq. (21) can be written in partitioned form as
where \n\n\n\nA\n¯\n\n11\n\n\n is Hurwitz and the virtual measurement \n\n\n\ny\n¯\n\n1\n\n\n presents the protected measurements and \n\n\n\ny\n¯\n\n2\n\n\n shows the attacked/corrupted measurements.
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5.1.2 Attack observation
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A SMO is proposed to reconstruct the attack in order to clean up the measurements and states and to allow the use of clean measurement in the control signal.
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Define a (sliding mode) observer for the system Eq. (22) as
where \n\n\nz\n¯\n\n=\ncol\n\n\n\nz\n¯\n\n1\n\n\n\nz\n¯\n\n21\n\n\n\nz\n¯\n\n22\n\n\n\n is conformal with the partition of \n\n\nx\n¯\n\n\n in Eq. (22). In Eq. (23), \n\nυ\n\n is a nonlinear injection signal that depends on \n\n\n\n\n\ny\n¯\n\n2\n\n−\n\n\nz\n¯\n\n22\n\n\n\n\n and is used to induce a sliding motion in the estimation error space, and
are the gain matrices where \n\n\n\nA\n¯\n\n\n12\na\n\n\n∈\n\nR\n\n\n\nn\n−\np\n\n\n×\n\n\np\n−\nm\n\n\n\n\n\n, \n\n\n\nA\n¯\n\n\n22\na\n\n\n∈\n\nR\n\n\n\np\n−\nm\n\n\n×\n\n\np\n−\nm\n\n\n\n\n\n, \n\n\n\nA\n¯\n\n\n12\nb\n\n\n∈\n\nR\n\n\n\nn\n−\np\n\n\n×\nm\n\n\n\n, \n\n\n\nA\n¯\n\n\n22\nb\n\n\n∈\n\nR\n\n\n\np\n−\nm\n\n\n×\nm\n\n\n\n, \n\n\n\nA\n¯\n\n\n22\nd\n\n\n∈\n\nR\n\nm\n×\nm\n\n\n\n, and the matrices \n\n\nA\n22\ns\n\n∈\n\nR\n\n\n\np\n−\nm\n\n\n×\n\n\np\n−\nm\n\n\n\n\n\n and \n\n\nA\n33\ns\n\n∈\n\nR\n\nm\n×\nm\n\n\n\n are user-selected Hurwitz matrices, while \n\n\nA\n33\ns\n\n\n is symmetric negative definite. The injection signal \n\nυ\n∈\n\nR\nm\n\n\n is defined as
where scalar gain \n\nρ\n\n will be defined in the sequel, and \n\nη\n\n is a positive design scalar.
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Assumption (A4): Matrix \n\n\n\nsI\n−\n\nA\n∗\n\n\n\n\n is invertible, where \n\n\nA\n∗\n\n=\n\nA\n¯\n\n−\n\nB\n¯\n\n\nD\n2\n\n−\n1\n\n\n\n\nC\n¯\n\n2\n\n−\n\n\nG\n¯\n\n1\n\n\n\nC\n¯\n\n1\n\n\n.
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Defining \n\n\ne\n¯\n\n=\n\nx\n¯\n\n−\n\nz\n¯\n\n\n, then it follows \n\n\ne\n¯\n\n=\ncol\n\n\n\ne\n¯\n\n1\n\n\n\ne\n¯\n\n21\n\n\n\ne\n¯\n\n22\n\n\n\n where \n\n\n\ne\n¯\n\n1\n\n=\n\n\nx\n¯\n\n1\n\n−\n\n\nz\n¯\n\n1\n\n\n, \n\n\n\ne\n¯\n\n21\n\n=\n\n\nx\n¯\n\n21\n\n−\n\n\nz\n¯\n\n21\n\n\n, \n\n\n\ne\n¯\n\n22\n\n=\n\n\nx\n¯\n\n22\n\n−\n\n\nz\n¯\n\n22\n\n\n. It follows
Then, as soon as the sliding mode is established in finite time in Eq. (27) on the sliding surface Eq. (28) by means of the injection term Eq. (25) with \n\nρ\n=\n\nm\n0\n\n\nk\nd\n\n+\n\n\n\nD\n2\n\n\n∞\n\n\nl\nd\n\n\n, the attack \n\nd\n\n is asymptotically estimated as
where \n\n\nυ\neq\n\n\n is the equivalent injection term [31] and a close approximation and \n\n\n\nυ\n¯\n\neq\n\n\n can be obtained in real time by low-pass filtering of the switching signal Eq. (25) [29]. Replacing \n\n\nυ\neq\n\n\n by \n\n\n\nυ\n¯\n\neq\n\n\n in Eq. (30) gives
Remark 1: The SMO (31) is a dynamic filter that allows reconstructing the time-varying attack \n\nd\n\nt\n\n\n. This filter is the main novel feature of the proposed observer.
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5.1.3 Adaptive-gain attack observer design
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In Eq. (29), it was assumed that the perturbation term \n\nφ\n\n is locally norm-bounded and \n\nρ\n>\n0\n\n in Eq. (25) is known. In many practical cases, the boundary of attacks is unknown, and the gain of the sliding mode injection term Eq. (25) in the fixed-gain observer in Eq. (23) can be overestimated. The gain overestimation could increase chattering that is difficult to attenuate.
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The constant gain \n\nρ\n>\n0\n\n can be replaced by an adaptive-gain \n\nρ\n\nt\n\n\n by applying the dual layer nested adaptive sliding mode observation algorithm [32], i.e.,
and assume that \n\n\n\na\n\nt\n\n\n\n<\n\na\n0\n\n,\n\n\n\na\ṅ\n\n\nt\n\n\n\n<\n\na\n1\n\n\n, where \n\n\na\n0\n\n\n and \n\n\na\n1\n\n\n are finite but unknown. A SMO is designed as in Eq. (23) with the adaptive injection term in Eqs. (32)–(37). If \n\nε\n>\n0\n\n in (34) is chosen to satisfy
for any given \n\n\nσ\n0\n\n\n, \n\nq\n>\n1\n\n, and, \n\n0\n<\nα\n<\n1\n\n, then the injection term (32) exploiting the dual layer adaptive scheme given by Eqs. (35)–(37) drives \n\nσ\n\nt\n\n\n to a domain \n\n\n\nσ\n\nt\n\n\n\n<\nε\n/\n2\n\n in finite time and consequently ensures a sliding motion \n\n\ne\ny\n\n=\n0\n\n can be reached in finite time and sustained thereafter. The gains \n\nr\n\nt\n\n\n and \n\nρ\n\nt\n\n\n remain bounded. The sensor attack signal \n\nd\n\nt\n\n\n is reconstructed as in Eq. (30) with the equivalent adaptive injection term \n\n\nυ\neq\n\n\n or \n\n\n\nυ\n¯\n\neq\n\n\n.
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Proof of Theorem 2 is based on the results in [32] and is omitted for brevity.
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Remark 2: The proposed unit vector injection gain-adaptation algorithm in Eqs. (32)–(37) does not require the knowledge of the boundaries \n\n\nk\nd\n\n,\n\nl\nd\n\n>\n0\n\n in \n\n\nd\n\n<\n\nk\nd\n\n\n and \n\n\n\nd\ṅ\n\n\n<\n\nl\nd\n\n\n.
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5.2 State estimation and attack reconstruction in linear systems by using super twisting SMO
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Consider the completely observable linearized system Eq. (11) with \n\n\nC\n1\n\n\nx\n\n=\n\nC\n1\n\nx\n\n, \n\n\nC\n2\n\n\nx\n\n=\n\nC\n2\n\nx\n\n, \n\n\nB\n1\n\n\nx\n\n=\nB\n\n, that is,
where \n\n\nB\n1\n\n∈\n\nR\n\nn\n×\n\nm\n1\n\n\n\n\n, \n\n\nC\n1\n\n∈\n\nR\n\n\n\np\n−\n\n\nm\n−\n\nm\n1\n\n\n\n\n\n×\nn\n\n\n\n, \n\n\nC\n2\n\n∈\n\nR\n\n\n\nm\n−\n\nm\n1\n\n\n\n×\nn\n\n\n\n.
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Assumption (A5): The number of uncorrupted/protected measurements is equal or larger than the number of state/plant attack, i.e., \n\n\np\n1\n\n=\np\n−\n\n\nm\n−\n\nm\n1\n\n\n\n≥\n\nm\n1\n\n\n.
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The system Eq. (40) is assumed to have an input-output vector relative degree \n\nr\n=\n\n\nr\n1\n\n\nr\n2\n\n…\n\nr\n\np\n1\n\n\n\n\n, where relative degree\n\n\nr\ni\n\n\n for \n\ni\n=\n1\n,\n2\n,\n…\n,\n\np\n1\n\n\n is defined as follows:
where integers \n\n1\n≤\n\nr\n\nα\ni\n\n\n≤\n\nr\ni\n\n\n are such that \n\nrank\n\n\n\nC\na\n\nB\n\n\n=\nrank\n\nB\n\n\n and \n\n\nr\n\nα\ni\n\n\n\n are chosen such that \n\n\n∑\n\ni\n=\n1\n\n\np\n1\n\n\n\nr\n\nα\ni\n\n\n\n is minimal.
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The following SMO [33] is used to estimate the states of system Eq. (40):
where the matrices of appropriate dimensions \n\n\nG\nl\n\n\n and \n\n\nG\nn\n\n\n are to be designed, and \n\n\nυ\nc\n\n\n.\n\n\n is an injection vector
Proof: Defining the state estimation error as \n\ne\n=\nx\n−\n\nx\n̂\n\n\n and the augmented output estimation error \n\n\ne\ny\n\n=\n\nC\na\n\nx\n−\n\ny\n¯\n\n\n with
Since \n\nrank\n\n\n\nC\na\n\n\n\nB\n¯\n\n1\n\n\n\n=\nrank\n\n\n\nB\n¯\n\n1\n\n\n\n and by assumption the invariant zeros of the triple \n\n\nA\nB\n\nC\na\n\n\n\n lie in the left half plane, based on the design methodologies in [35], It follows that \n\ne\n=\n0\n\n is an asymptotically stable equilibrium point of Eq. (52) and dynamics are independent of \n\n\nd\nx\n\n\nt\n\n\n once a sliding motion on the sliding manifold \n\ns\n=\n\nC\na\n\ne\n=\n0\n\n has been attained. During the sliding mode \n\n\ns\ṅ\n\n=\ns\n=\n0\n\n, it is
where \n\n\n\n\nυ\nc\n\n\neq\n\n\n is the equivalent output error injection required to maintain the system on the sliding manifold. Since \n\n\nC\na\n\n\n\nB\n¯\n\n1\n\n\n is full rank, the attack reconstruction is obtained as (50).
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According to (A1), \n\n\n\nD\n¯\n\n1\n\n\n is full rank; then sensor attacks in Eq. (40) are reconstructed
5.3 The state and disturbance observer for nonlinear systems using higher-order sliding mode differentiator
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Consider the locally stable system Eq. (11) where \n\n\n\ny\n¯\n\n1\n\n\n and \n\n\nB\n1\n\n\nx\n\n\n are \n\n\n\ny\n¯\n\n1\n\n=\n\n\n\n\n\n\ny\n1\n\n\n\n\ny\n2\n\n\n\n,\n…\n,\n\n\n\ny\n\np\n1\n\n\n\n\n\n\nT\n\n\n, \n\nB\n=\n\n\nb\n1\n\n\nb\n2\n\n…\n\nb\n\nm\n1\n\n\n\n∈\n\nR\n\nn\n×\n\nm\n1\n\n\n\n\n, \n\n\nb\ni\n\n∈\n\nR\nn\n\n,\n\n∀\ni\n=\n1\n,\n…\n,\n\nm\n1\n\n\n are smooth vector fields defined on an open \n\nΩ\n⊂\n\nR\nn\n\n\n. According to (A5), we consider \n\n\np\n1\n\n=\n\nm\n1\n\n\n here. The following properties introduced by Isidori [36] are assumed for \n\nx\n∈\nΩ\n\n.
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Assumption (A7): The system in Eq. (11) is assumed to have vector relative degree \n\nr\n=\n\n\nr\n1\n\n\nr\n2\n\n…\n\nr\n\nm\n1\n\n\n\n\n and total relative degree \n\n\nr\nt\n\n=\n\n∑\n\ni\n=\n1\n\n\nm\n1\n\n\n\nr\ni\n\n,\n\n\nr\nt\n\n≤\nn\n\n, i.e.,
With an involutive distribution \n\nΓ\n\n as defined in (A9), it is always possible to identify the variables \n\n\nη\n\nr\n+\n1\n\n\n\nx\n\n,\n…\n,\n\nη\nn\n\n\nx\n\n\n which satisfy
Assumption (A10): The norm-bounded solution of the internal dynamics \n\n\nγ\ṅ\n\n=\ng\n\nδ\nγ\n\n\n is assumed to be locally asymptotically stable [29].
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If assumption (A9) is satisfied, then it is always possible to find \n\nn\n−\nr\n\n functions \n\n\nη\n\nr\n+\n1\n\n\n\nx\n\n,\n…\n,\n\nη\nn\n\n\nx\n\n\n such that
Since the finite-time exact estimates \n\n\n\n\nδ\ṅ\n\n̂\n\n\nir\ni\n\n\n\n of \n\n\n\nδ\ṅ\n\n\nir\ni\n\n\n\n, \n\n∀\ni\n=\n1\n,\n…\n,\n\nm\n1\n\n\n are available via the higher-order sliding mode differentiator, and using the estimates \n\n\n\n\n\nδ\n̂\n\n,\n\nγ\n̂\n\n\n\n\n\n for \n\nδ\n,\nγ\n\n, an asymptotic estimate \n\n\nd\n̂\n\n\nt\n\n\n of disturbance \n\nd\n\nt\n\n\n in Eq. (11) is identified as [28].
where \n\nL\n\n\n\nΨ\n\n−\n1\n\n\n\n\nδ\n̂\n\n\nγ\n̂\n\n\n\n\n=\n\n∑\n\nj\n=\n1\n\n\nm\n1\n\n\n\nL\n\nb\nj\n\n\n\n\nL\nf\n\n\n\nr\ni\n\n−\n1\n\n\n\ny\n\n1\ni\n\n\n\nx\n\n\n. Finally, \n\n\nx\n̂\n\n\nt\n\n\n and \n\n\nd\n̂\n\n\nt\n\n\n are obtained.
Remark 3: The convergence \n\n\nd\n̂\n\n→\nd\n\n can be achieved only locally and as time increases due to the local asymptotic stability of the norm-bounded solution of the internal dynamics \n\n\nγ\ṅ\n\n=\ng\n\nδ\nγ\n\n\n. However convergence will be achieved in finite time if the total relative degree \n\nr\n=\nn\n\n and no internal dynamics exist.
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Considering Eq. (11) and \n\n\n\nD\n¯\n\n1\n\n\n is full rank, sensor attack can be reconstructed as
5.4 Attack reconstruction in nonlinear system by sparse recovery algorithm
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In some applications, there are a limited number of measurements, \n\np\n\n, and more sources of attack, \n\nm\n\n. Previously, we investigated the cases where \n\np\n>\nm\n\n. Now, consider system (5) with more attacks than measurements, \n\nm\n>\np\n\n.
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Notice that a more general format of (5) is considered here where matrix \n\nD\n\n is a function of \n\nx\n\n as well.
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Assumption (A11): Assume that the attack vector \n\nd\n\nt\n\n\n is sparse, meaning that numerous attacks are possible, but the attacks are not coordinated, and only few nonzero attacks happen at the same time.
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5.4.1 Sparse recovering algorithm
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The problem of recovering an unknown input signal from measurements is well known, as a left invertibility problem, as seen in several works [30, 37], but this problem was only treated in the case where the number of measurements is equal or greater than the number of unknown inputs. The left invertibility problem in the case of fewer measurements than unknown inputs has no solution or more exactly has an infinity of solutions.
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In particular, the objective of exact recovery under sparse assumptions denoted for the sake of simplicity as “sparse recovery” (SR) is to find a concise representation of a signal using a few atoms from some specified (over-complete) dictionary,
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\n\nξ\n=\nΦ\n\ns\n¯\n\n+\n\nε\n0\n\n\nE74
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where \n\n\ns\n¯\n\n∈\n\nR\nN\n\n\n are the unknown inputs with no more than \n\nj\n\n nonzero entries, \n\nξ\n∈\n\nR\nM\n\n\n are the measurements, \n\n\nε\n0\n\n\n is a measurement noise, and \n\nΦ\n∈\n\nR\n\nM\n×\nN\n\n\n\n is the dictionary where \n\nM\n≪\nN\n\n.
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Definition 1: The Restricted Isometry Property (RIP) condition of \n\nj\n\n-order with constant \n\n\nς\nj\n\n∈\n\n0\n1\n\n\n (\n\n\nς\nj\n\n\n is as small as possible for computational reasons) of the matrix \n\nΦ\n\n yields
for any \n\nj\n\n sparse of signal \n\n\ns\n¯\n\n\n. Considering \n\n\nΦ\nΓ\n\n\n as the index set of nonzero elements of \n\n\ns\n¯\n\n\n, then Eq. (75) is equivalent to [23]:
where \n\n\nΦ\nΓ\n\n\n is the sub-matrix of \n\nΦ\n\n with active nodes.
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The problem of SR is often cast as an optimization problem that minimizes a cost function constructed by leveraging the observation error term and the sparsity inducing term [37], i.e.,
In Eq. (77) the original sparsity term is the quasi norm \n\n\n\n\ns\n¯\n\n\n0\n\n\n; but as long as the RIP conditions hold, it can be replaced by \n\nΘ\n\n\ns\n¯\n\n\n=\n\n\n\ns\n¯\n\n\n1\n\n≜\n\n∑\ni\n\n\n\n\ns\n¯\n\ni\n\n\n\n. Note that \n\nλ\n>\n0\n\n in Eq. (77) is the balancing parameter and \n\n\n\ns\n¯\n\n∗\n\n\n is the critical point, i.e., the solution of Eq. (74). Typically, for sparse vectors \n\n\ns\n¯\n\n\n with j-sparsity, where \n\nj\n\n must be equal or smaller than \n\n\n\nM\n−\n1\n\n2\n\n\n [37], the solution to the SR problem is unique and coincides with the critical point of Eq. (74) providing that RIP condition for \n\nΦ\n\n with order \n\n2\nj\n\n is verified. In other words, in order to guarantee the existence of a unique solution to the optimization problem Eq. (74), \n\nΦ\n\n should satisfy restricted isometry property [37].
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Under the sparse assumption of \n\n\ns\n¯\n\n\n and the fulfillment of the j-RIP condition of the matrix \n\nΦ\n\n, the estimation algorithm proposed in [37] is
where \n\nv\n∈\n\nR\nN\n\n\n is the state vector, \n\n\n\ns\n¯\n\n̂\n\n\nt\n\n\n represents the estimate of the sparse signal \n\n\ns\n¯\n\n\n of (74), and \n\nμ\n>\n0\n\n is a time-constant determined by the physical properties of the implementing system. \n\n\n\n\n.\n\n\nβ\n\n=\n\n\n\n\n\n\n.\n\nβ\n\nsign\n\n.\n\n\n and \n\na\n\nt\n\n=\n\nH\nλ\n\n\nv\n\n\n where \n\n\nH\nλ\n\n\n.\n\n\n is a continuous soft thresholding function:
where \n\nλ\n>\n0\n\n is chosen with respect to the noise and the minimum absolute value of the nonzero terms.
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Under Definition 1, the state \n\nv\n\n of Eq. (78) converges in finite time to its equilibrium point \n\n\nv\n∗\n\n\n, and \n\n\n\ns\n¯\n\n̂\n\n\nt\n\n\n in Eq.(78) converges in finite time to \n\n\ns\n̂\n\n∗\n\n of Eq. (77).
\n
\n
\n
5.4.2 Attack reconstruction
\n
The measured output under attack \n\ny\n\n of the system Eq. (5) is fed to the input of the low-pass filter that facilitates filtering out the possible measurement noise
If assumption (A2), (A7), and (A9) hold for system Eq. (81), i.e., the relative degree vector of Eq. (81) is \n\nr\n=\n\n\nr\n1\n\n\nr\n2\n\n…\n\nr\np\n\n\n\n, the distribution \n\nΓ\n=\nspan\n\n\nΩ\n1\n\n\nΩ\n2\n\n…\n\nΩ\nm\n\n\n\n is involutive, and if zero dynamics exist, they are assumed asymptotically stable and may be left alone. Here it is assumed that there are no zero dynamics in system Eq. (81) and it is presented as
Finally, filtered system Eq. (5), as it is rewritten in Eq. (85), is in the same form of Eq. (74). Then, sparse recovery algorithm discussed in Section 5.4.1 is applied to Eq. (85) to reconstruct \n\nd\n\nt\n\n\n.
\n
Remark 4: The derivatives \n\n\n\nϒ\ṅ\n\n\nr\n1\n\n1\n\n,\n…\n,\n\n\nϒ\ṅ\n\n\nr\np\n\np\n\n\n are computed exactly in finite time using higher-order sliding mode differentiators [28] discussed in Eqs. (65) and (66).
\n
\n
\n
\n
\n
6. Case study
\n
Consider the mathematical models (1)–(4) of the US Western Electricity Coordinating Council (WECC) power system [8] with three generators and six buses (Figure 1) when the sensors of the generator speed deviations from synchronicity are under stealth attack and plant is under deception attack.
\n
Assumption (A12): The matrix \n\n\nL\n\nl\n,\nl\n\nθ\n\n\n in (3) is nonsingular.
\n
If (A12) holds, then the variable \n\nθ\n\n can be rewritten as
The three sensors of rotor angles, \n\nδ\n∈\n\nR\n3\n\n\n, are assumed protected from attack, but the three sensors of the generator speed deviations from synchronicity, \n\nω\n∈\n\nR\n3\n\n\n, are assumed to be attacked.
The \n\n\nB\n\n1\nω\n\n\n=\n\nI\n3\n\n,\n\nB\n\n1\nθ\n\n\n=\n\n0\n\n6\n×\n3\n\n\n,\n\nD\nδ\n\n=\n\n0\n\n3\n×\n6\n\n\n\n are given, and then Eq. (88) is reduced to
Remark 5:\n\n\nD\n\n1\nω\n\n\n\n satisfies RIP condition defined in Eq. (75).
\n
In the first step of attack reconstruction, \n\n\nd\nx\n\n\nt\n\n\n is estimated by using protected measurements \n\n\ny\n1\n\n\n and the SMO described in Section 5.2. It is easy to verify that
where \n\n\n\nC\n¯\n\nδi\n\n\n is the ith row of \n\n\n\nC\n¯\n\nδ\n\n\n. The states of the system, \n\n\nδ\n̂\n\n,\n\nω\n̂\n\n\n, and plant attacks \n\n\n\nd\n̂\n\nx\n\n\nt\n\n\n are reconstructed using Eqs. (43) and (50). Then, \n\n\nω\n̂\n\n\n is used in Eq. (89) to find
There are six sources \n\n\nd\n\ny\n1\n\n\n,\n…\n,\n\nd\n\ny\n6\n\n\n\n attacking three measurements \n\n\nω\n1\n\n,\n\nω\n2\n\n,\n\nω\n3\n\n\n, and at any time, just one out of six attack signals is nonzero. The SR algorithm in Section 5.2 is applied to find \n\n\n\nd\n̂\n\ny\n\n\nt\n\n\n. The following attacks are considered for simulation.
Deception attacks \n\n\nd\n\nx\n1\n\n\n\n, \n\n\nd\n\nx\n2\n\n\n\n, and \n\n\nd\n\nx\n3\n\n\n\n are reconstructed very accurately as shown in Figures 4, Figures 5, 6. The only nonzero sensor attack is detected and accurately estimated by using the SR algorithm as shown in Figure 7. In Figure 8a and 8b, the corrupted system outputs (which are system states in our case) are compared to the “cleaned” outputs that are computed by subtracting the estimated attacks from the corrupted sensors and actuators and to the system outputs when the system is not under attack.
\n
Figure 4.
Plant attack \n\n\nd\n\nx\n1\n\n\n\n compared to estimated \n\n\n\nd\n̂\n\n\nx\n1\n\n\n\n.
\n
Figure 5.
Plant attack \n\n\nd\n\nx\n2\n\n\n\n compared to estimated \n\n\n\nd\n̂\n\n\nx\n2\n\n\n\n.
\n
Figure 6.
Plant attack \n\n\nd\n\nx\n3\n\n\n\n compared to estimated \n\n\n\nd\n̂\n\n\nx\n3\n\n\n\n.
\n
Figure 7.
Sensor attack \n\n\nd\ny\n\n\n reconstruction.
\n
Figure 8.
(a) Corrupted output \n\n\ny\n1\n\n,\n\ny\n2\n\n,\n\ny\n3\n\n\n compared with compensated and without any attack output and (b) corrupted output \n\n\ny\n4\n\n,\n\ny\n5\n\n,\n\ny\n6\n\n\n compared with compensated and without any attack output.
\n
\n
\n
\n
7. Conclusion
\n
The critical infrastructures like power grid, water resources, etc. are large interconnected cyber-physical systems whose reliable operation depends critically on their cyber substructure. In this chapter, cyber-physical systems when their sensors and/or states are under attack or experiencing faults are investigated. The sensor and states/plant attacks are reconstructed online by using a fixed-gain and adaptive-gain sliding mode observers. As soon as the attacks are reconstructed, corrupted measurements and states are cleaned from attacks, and the control signal that uses cleaned measurements provides cyber-physical system performance close to the one without attack. The effectiveness of the proposed approach is shown by simulation results of a real electrical power network with sensors under stealth attack and states under deception attacks.
\n
\n\n',keywords:"cyber-physical systems, sensor attack, state attack, sliding mode observers",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/68778.pdf",chapterXML:"https://mts.intechopen.com/source/xml/68778.xml",downloadPdfUrl:"/chapter/pdf-download/68778",previewPdfUrl:"/chapter/pdf-preview/68778",totalDownloads:120,totalViews:0,totalCrossrefCites:0,dateSubmitted:"May 7th 2019",dateReviewed:"July 18th 2019",datePrePublished:"September 18th 2019",datePublished:null,readingETA:"0",abstract:"A cyber-physical system (CPS) is a tight coupling of computational resources, network communication, and physical processes. They are composed of a set of networked components, including sensors, actuators, control processing units, and communication agents that instrument the physical world to make “smarter.” However, cyber components are also the source of new, unprecedented vulnerabilities to malicious attacks. In order to protect a CPS from attacks, three security levels of protection, detection, and identification are considered. In this chapter, we will discuss the identification level, i.e., secure state estimation and attack reconstruction of CPS with corrupted states and measurements. Considering different attack plans that may assault the states, sensors, or both of them, different online attack reconstruction approaches are discussed. Fixed-gain and adaptive-gain finite-time convergent observation algorithms, specifically sliding mode observers, are applied to online reconstruction of sensor and state attacks. Next, the corrupted measurements and states are to be cleaned up online in order to stop the attack propagation to the CPS via the control signal. The proposed methodologies are applied to an electric power network, whose states and sensors are under attack. Simulation results illustrate the efficacy of the proposed observers.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/68778",risUrl:"/chapter/ris/68778",signatures:"Shamila Nateghi, Yuri Shtessel, Christopher Edwards and Jean-Pierre Barbot",book:{id:"9287",title:"Control Theory in Engineering",subtitle:null,fullTitle:"Control Theory in Engineering",slug:null,publishedDate:null,bookSignature:"Prof. Constantin Volosencu and Dr. Xian Du",coverURL:"https://cdn.intechopen.com/books/images_new/9287.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"1063",title:"Prof.",name:"Constantin",middleName:null,surname:"Volosencu",slug:"constantin-volosencu",fullName:"Constantin Volosencu"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Motivation example: electric power network under attack",level:"1"},{id:"sec_3",title:"3. Cyber-physical system dynamics",level:"1"},{id:"sec_4",title:"4. Problem formulation",level:"1"},{id:"sec_5",title:"5. Results: secure state estimation",level:"1"},{id:"sec_5_2",title:"5.1 Attack reconstruction in linear system via filtering by adaptive sliding mode observer",level:"2"},{id:"sec_5_3",title:"5.1.1 System’s transformation",level:"3"},{id:"sec_6_3",title:"5.1.2 Attack observation",level:"3"},{id:"sec_7_3",title:"5.1.3 Adaptive-gain attack observer design",level:"3"},{id:"sec_9_2",title:"5.2 State estimation and attack reconstruction in linear systems by using super twisting SMO",level:"2"},{id:"sec_9_3",title:"5.2.1 Attack observation",level:"3"},{id:"sec_11_2",title:"5.3 The state and disturbance observer for nonlinear systems using higher-order sliding mode differentiator",level:"2"},{id:"sec_12_2",title:"5.4 Attack reconstruction in nonlinear system by sparse recovery algorithm",level:"2"},{id:"sec_12_3",title:"5.4.1 Sparse recovering algorithm",level:"3"},{id:"sec_13_3",title:"5.4.2 Attack reconstruction",level:"3"},{id:"sec_16",title:"6. Case study",level:"1"},{id:"sec_16_2",title:"6.1 Simulation setup",level:"2"},{id:"sec_18",title:"7. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Antsaklis P. Goals and challenges in cyber-physical systems research. IEEE Transactions on Automatic Control. 2014;59:3117-3119. DOI: 10.1109/TAC.2014.2363897'},{id:"B2",body:'Baheti R, Gill H. Cyber-physical systems. The Impact of Control Technology. 2011;12:161-166'},{id:"B3",body:'Conti JP. The day the samba stopped. Engineering and Technology. 2010;5:46-47. DOI: 10.1049/et.2010.0410'},{id:"B4",body:'Karnouskos S. Stuxnet worm impact on industrial cyber-physical system security. In: 37th Annual Conference of the IEEE Industrial Electronics Society 7-10 November 2011; Melbourne: VIC, Australia. 2011. pp. 4490-4494'},{id:"B5",body:'Farhat A, Cheok CK. Improving adaptive network fuzzy inference system with Levenberg-Marquardt algorithm. 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Automatica. 2016;65:183-190. DOI: 10.1016/j.automatica.2015.11.038'},{id:"B33",body:'Floquet T, Edwards C, Spurgeon SK. On sliding mode observers for systems with unknown inputs. International Journal of Adaptive Control and Signal Processing. 2007;21:638-656. DOI: 10.1109/VSS.2006.1644520'},{id:"B34",body:'Levant A. Sliding order and sliding accuracy in sliding mode control. International Journal of Control. 1993;58:1247-1263. DOI: 10.1080/00207179308923053'},{id:"B35",body:'Edwards C, Spurgeon SK. Sliding Mode Control: Theory and Applications. London: Taylor and Francis; 1998. DOI: 10.1201/9781498701822'},{id:"B36",body:'Isidori A. Nonlinear Control Systems. 3rd ed. Berlin: Springer; 1995. pp. 219-290'},{id:"B37",body:'Candes E, Tao T. The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics. 2007;35:2313-2351. DOI: 10.1214/009053606000001523'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Shamila Nateghi",address:"shamila.nateghi.b@gmail.com",affiliation:'
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