학위논문 (박사)-- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2018. 2. 심형보.Recent advances in computer and communication technologies make control systems more connected thanks to the developments in networked actuation and sensing devices. As this connectivity increases, the resulting large scale networked control systems, or the cyber-physical systems (CPS), are exposed and can be vulnerable to malicious attacks. In response to the crisis by the malicious adversaries, this dissertation presents sophisticated control algorithms which are more reliable even when some components of the feedback control systems are corrupted. Focusing especially on sensor attacks, security related problems on CPS are carefully analyzed and an attack-resilient state estimation scheme is proposed. First, the notion of redundant observability is introduced that explains in a unified manner existing security notions such as dynamic security index, attack detectability, and observability under attacks. The redundant observability is a key concept in this dissertation, and a system is said to be q-redundant observable if it is observable even after eliminating any q measurements. It has been shown that any q-sparse sensor attack is detectable if and only if the given linear time invariant (LTI) system is q-redundant observable. It is also equivalent to the condition that the system is observable under ⌊q/2⌋-sparse sensor attacks. Moreover, the dynamic security index, which is defined by the minimum number of attacks to be undetectable, can be computed as q + 1. In addition, the redundant detectability (or, asymptotic redundant observability), which is a weaker notion than the redundant observability, is also introduced. While the redundant observability does not care about the magnitudes of sensor attacks and does not mind whether the attacks are disruptive or not, the redundant detectability only deals with attacks that do not converge to zero as time goes on, so that it is more practical in the sense that it can only detect and correct the attacks that are actually harmful to the system. Next, a resilient state estimation scheme is proposed under two assumptions: ⌊q/2⌋-sparsity of attack vector and q-redundant detectability of the system. The proposed estimator consists of a bank of partial observers operating based on Kalman detectability decomposition and a decoder exploiting error correction techniques. The partial observers are either constructed by Luenberger observers or Kalman filters. The Luenberger observer guarantees the robustness with bounded disturbances/noises, while the Kalman filter shows the suboptimality in the sense of minimum variance with Garussian disturbances/noises. In terms of time complexity, an ℓ0 minimization problem in the decoder alleviates the computational efforts by reducing the search space to a finite set and by combining a detection algorithm to the optimization process. On the other hand, in terms of space complexity, the required memory is linear with the number of sensors by means of the decomposition used for constructing a bank of partial observers. This resilient state estimation scheme proposed for LTI systems, is further extended for a class of uniformly observable nonlinear systems. Based on the uniform observability decomposition, a high gain observer is constructed for each single measurement to estimate the observable sub-state and it constitutes the partial observer. Finally, the decoder solves a nonlinear error correcting problem by collecting all the information from the high gain observers and by exploiting redundancy.1 Introduction 1
1.1 Background 1
1.2 Research Objective and Contributions 5
1.3 Outline of the Dissertation 8
2 Error Correction over Reals and its Extensions 11
2.1 Error Correction over Reals and Compressed Sensing 11
2.2 Extension to Stacked Vector Case 16
2.2.1 Error Detectability and Error Correctability 16
2.2.2 Error Detection and Correction Scheme for Noiseless Case 20
2.2.3 Error Detection and Correction Scheme for Noisy Case 23
3 On Redundant Observability 41
3.1 Redundant Observability 42
3.1.1 Definition and Characterization 42
3.1.2 Relationship with Strong Observability 45
3.1.3 Redundant Unobservable Subspace 47
3.1.4 Asymptotic Redundant Observability 49
3.2 Attack Detectability and Dynamic Security Index 56
3.3 Observability under Sparse Sensor Attacks 65
4 Attack-Resilient State Estimation for Linear Systems 69
4.1 Problem Formulation 70
4.2 Components of Attack-Resilient Estimator and Their Functions 73
4.2.1 Partial Observer: Kalman Detectability Decomposition 73
4.2.2 Decoder: Error Correction for Stacked Vector 77
4.3 Design of Attack-Resilient State Estimator 78
4.3.1 Deterministic Estimator with Bounded Disturbance and Noise 79
4.3.2 Suboptimal Estimator with Gaussian Disturbance and Noise 85
4.4 Remarks on Proposed Attack-Resilient Estimator 93
4.4.1 Comparison with Fault Detection and Isolation 93
4.4.2 Analysis of Time and Space Complexity 95
4.5 Simulation Results: Three-Inertia System 96
5 Attack-Resilient State Estimation for Nonlinear Systems 101
5.1 Problem Formulation and Preliminaries 102
5.1.1 Problem Formulation 102
5.1.2 Bi-Lipschitz Function and Lipschitz Left Inverse 103
5.1.3 Nonlinear Error Detectability and Error Correctability 105
5.2 Uniformly Observable Nonlinear Systems for Any Input 108
5.2.1 Uniform Observability Decomposition 108
5.2.2 Design of High Gain Observer 111
5.3 Redundant Observability for Nonlinear Systems 112
5.4 Attack Detection and Resilient Estimation for Nonlinear Systems 115
5.4.1 Detection of Sensor Attacks 115
5.4.2 Attack-Resilient State Estimation 119
5.5 Simulation Results: Numerical Example 121
6 Conclusion 125
6.1 Summary 125
6.2 Future Works 127
Bibliography 129
국문초록 141Docto
