Attack-Resilient Feedback Control Systems: Secure State Estimation under Sensor Attacks

Abstract

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.