Secure-by-Construction Controller Synthesis for Stochastic Systems under Linear Temporal Logic Specifications

In this paper, we investigate the problem of synthesizing optimal control policies for stochastic control systems to achieve high-level temporal logic specifications under security constraints. Specifically, we consider a stochastic control system modeled by a finite labeled Markov Decision Process (MDP). We consider a passive intruder (an eavesdropper) that can observe the external output behavior of the system. We assume the system has a secret, modeled as visiting of some secret states, that does not want to be revealed to the intruder. The security constraint is that the intruder can never determine for sure that the system is/was at a secret state for any specific instant of time. The overall objective is to maximize the probability of achieving the temporal logic task while ensuring the information-flow security of the system. An effective algorithm is proposed to solve this problem. Specifically, we show that the security constraints can be handled as a safety requirement over the information-state-space and the optimal control problem can be solved by leveraging existing results from probabilistic model checking. The proposed approach is also illustrated by a case study for robot task planning.