Hamza Fawzi

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

The vast majority of todays 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. We give a new simple characterization of the maximum number of attacks that can be detected and corrected as a function of the pair (A,C) of the system and we show in particular that it is impossible to accurately reconstruct the state of a system if more than half the sensors are attacked. In addition, we show how the design of a secure local control loop can improve the resilience of the system. When the number of attacks is smaller than a threshold, we propose an efficient algorithm inspired from techniques in compressed sensing to estimate the state of the plant despite attacks. We give a theoretical characterization of the performance of this algorithm and we show on numerical simulations that the method is promising and allows to reconstruct the state accurately despite attacks. Finally, we consider the problem of designing output-feedback controllers that stabilize the system despite sensor 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.

Secure state-estimation for dynamical systems under active adversaries

We consider the problem of state-estimation of a linear dynamical system when some of the sensor measurements are corrupted by an adversarial attacker. The errors injected by the attacker in the sensor measurements can be arbitrary and are not assumed to follow a specific model (in particular they can be of arbitrary magnitude). We first characterize the number of attacked sensors that can be tolerated so that the state of the system can still be correctly recovered by any decoding algorithm. We then propose a specific computationally feasible decoding algorithm and we give a characterization of the number of errors this decoder can correct. For this we use ideas from compressed sensing and error correction over the reals and we exploit the dynamical nature of the problem. We show using numerical simulations that this decoder performs very well in practice and allows to correct a large number of errors.

Security for control systems under sensor and actuator attacks

We consider the problem of estimation and control of a linear system when some of the sensors or actuators are attacked by a malicious agent. In our previous work [1] we studied systems with no control inputs and we formulated the estimation problem as a dynamic error correction problem with sparse attack vectors. In this paper we extend our study and look at the role of inputs and control. We first show that it is possible to increase the resilience of the system to attacks by changing the dynamics of the system using state-feedback while having (almost) total freedom in placing the new poles of the system. We then look at the problem of stabilizing a plant using output-feedback despite attacks on sensors, and we show that a principle of separation of estimation and control holds. Finally we look at the effect of attacks on actuators in addition to attacks on sensors: we characterize the resilience of the system with respect to actuator and sensor attacks and we formulate an efficient optimization-based decoder to estimate the state of the system despite attacks on actuators and sensors.

Positive semidefinite rank

Let

Sparse sum-of-squares certificates on finite abelian groups

M \in \mathbb {R}^{p \times q}

Lower bounds on nonnegative rank via nonnegative nuclear norms

M∈Rp×q be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices

Equivariant Semidefinite Lifts of Regular Polygons

A_i, B_j