Controller Synthesis for Linear Time-varying Systems with Adversaries

We present a controller synthesis algorithm for a discrete time reach-avoid problem in the presence of adversaries. Our model of the adversary captures typical malicious attacks en- visioned on cyber-physical systems such as sensor spoofing, controller corruption, and actuator intrusion. After formu- lating the problem in a general setting, we present a sound and complete algorithm for the case with linear dynamics and an adversary with a budget on the total L2-norm of its actions. The algorithm relies on a result from linear control theory that enables us to decompose and precisely compute the reachable states of the system in terms of a symbolic simulation of the adversary-free dynamics and the total uncertainty induced by the adversary. With this de- composition, the synthesis problem eliminates the universal quantifier on the adversary's choices and the symbolic con- troller actions can be effectively solved using an SMT solver. The constraints induced by the adversary are computed by solving second-order cone programmings. The algorithm is later extended to synthesize state-dependent controller and to generate attacks for the adversary. We present prelimi- nary experimental results that show the effectiveness of this approach on several example problems.