Securing state reconstruction under sensor and actuator attacks: Theory and design

This paper discusses the problem of reconstructing the state of a linear time invariant system when some of its actuators and sensors are compromised by an adversarial agent. In the model considered in this paper, the adversarial agent attacks an input (output) by manipulating its value arbitrarily, i.e., we impose no constraints (statistical or otherwise) on how control commands (sensor measurements) are changed by the adversary other than a bound on the number of attacked actuators and sensors In the first part of this paper, we introduce the notion of sparse strong observability and we show that is a necessary and sufficient condition for correctly reconstructing the state despite the considered attacks. In the second half of this work, we propose an observer to harness the complexity of this intrinsically combinatorial problem, by leveraging satisfiability modulo theory solving. Numerical simulations illustrate the effectiveness and scalability of our observer.