Secure estimation and control for cyber-physical systems under adversarial attacks (1205.5073v1)

Abstract: The vast majority of today's critical infrastructure is supported by numerous feedback control loops and an attack on these control loops can have disastrous consequences. This is a major concern since modern control systems are becoming large and decentralized and thus more vulnerable to attacks. This paper is concerned with the estimation and control of linear systems when some of the sensors or actuators are corrupted by an attacker. In the first part we look at the estimation problem where we characterize the resilience of a system to attacks and study the possibility of increasing its resilience by a change of parameters. We then propose an efficient algorithm to estimate the state despite the attacks and we characterize its performance. Our approach is inspired from the areas of error-correction over the reals and compressed sensing. In the second part we consider the problem of designing output-feedback controllers that stabilize the system despite attacks. We show that a principle of separation between estimation and control holds and that the design of resilient output feedback controllers can be reduced to the design of resilient state estimators.

• The paper introduces a novel ℓ1/ℓr decoding algorithm for secure state estimation, establishing conditions for maximal resilience at ⌈p/2 - 1⌉ errors.
• It demonstrates that separating estimation from state-feedback control enables resilient system stabilization despite adversarial sensor and actuator attacks.
• Numerical simulations on synthetic models and an IEEE 14-bus power network confirm the practical viability of the proposed robust algorithms.

Secure Estimation and Control for Cyber-Physical Systems under Adversarial Attacks

The paper "Secure estimation and control for cyber-physical systems under adversarial attacks" by Hamza Fawzi, Paulo Tabuada, and Suhas Diggavi addresses critical issues related to the resilience of control systems in the presence of sensor and actuator attacks. In the landscape of modern, increasingly decentralized control systems, the susceptibility to adversarial attacks is a significant concern, necessitating robust methodologies for secure estimation and control.

Estimation Problem

The initial focus of this paper is on characterizing and enhancing the resilience of linear systems against attacks on sensors. The estimation problem is framed within the context of determining the maximum number of sensor attacks that a system can withstand while still enabling accurate state estimation. A key contribution in this regard is the introduction of a novel decoding algorithm inspired by error-correction over the reals and compressed sensing techniques.

The paper rigorously characterizes the resilience of the system by defining resilience conditions and establishing bounds on the number of correctable errors. Proposition 2 presents a necessary and sufficient condition: for all nonzero vectors $z$, the union of the supports of $Cz, CAz, \ldots, CA^{T-1}z$ must be sufficiently large to tolerate the given number of attacks. Notably, the paper asserts that for almost all systems (i.e., for a full-measure set of system parameterizations), the resilience is maximized at $\lceil p/2 - 1 \rceil$ errors, highlighting the robustness of the proposed decoding method.

Control under State Feedback

Beyond secure estimation, the paper extends its scope to address the design of state-feedback controllers that can stabilize the system despite sensor attacks. It demonstrates that a key principle of separation between estimation and control holds; specifically, the design of resilient output-feedback controllers can be reduced to that of resilient state estimators. This principle is substantiated by a detailed analysis culminating in Proposition 7, which asserts that it's feasible to design state-feedback laws that ensure the maximum possible correctability of errors without sacrificing system performance, provided the eigenvalues of $A+BK$ can be chosen with distinct amplitudes.

Actuator Attacks

Incorporating actuator attacks further enriches the analysis. The extended system model considers both sensor and actuator attacks, and defines resilience in this expanded scenario. Proposition 12 generalizes previous results by providing necessary and sufficient conditions for the correctability of the total number of attacks on both sensors and actuators. This is achieved through an injectivity condition on the mapping from the initial state and attack vectors to the observed outputs. The theoretical upper bound on resilience remains at $\lceil p/2 - 1 \rceil$, supporting the assertion with a proof of almost-sure maximality.

Practical and Theoretical Implications

The practical relevance is underscored through numerical simulations on random systems and on a model of the IEEE 14-bus power network. These simulations validate the efficacy of the proposed $\ell_1/\ell_r$ decoding algorithm in both synthetic and real-world scenarios. The results show robust performance, where the $\ell_1/\ell_r$ decoder is observed to correctly recover the state of the system even in the face of multiple sensor and actuator attacks.

The separation of estimation and control has profound implications for the design of resilient control systems. Theoretically, it establishes that resilient state estimation frameworks are fundamentally linked to resilient control strategies, enabling the use of standard control techniques once resilient state estimation is ensured.

Future Directions

Potential future developments could include the formulation of iterative estimation algorithms, which might offer computational advantages over the one-shot $\ell_1$ estimators proposed. Additionally, a deeper investigation into the performance under stochastic noise could be instructive. Applying the methodologies proposed here to more complex and specific applications while considering structural vulnerabilities could provide tailored solutions enhancing their practical applicability.

In summary, this paper presents a comprehensive paper on the resilience of cyber-physical control systems under adversarial conditions, offering both theoretical insights and practical algorithms. It effectively bridges the gap between robust state estimation and resilient control, thereby contributing significantly to the field of secure cyber-physical systems.