Minimum Violation Control Synthesis on Cyber-Physical Systems under Attacks

TL;DR

This paper introduces a novel approach for synthesizing controllers for cyber-physical systems that optimally balance task satisfaction and violations under adversarial attacks, using a game-theoretic framework and heuristic algorithms.

Contribution

It formulates the minimum violation control synthesis problem under LTL constraints as a Stackelberg game and provides an efficient heuristic solution method.

Findings

Effective control strategies under attack scenarios

Reduced computational complexity with heuristic algorithm

Successful demonstration through a numerical case study

Abstract

Cyber-physical systems are conducting increasingly complex tasks, which are often modeled using formal languages such as temporal logic. The system's ability to perform the required tasks can be curtailed by malicious adversaries that mount intelligent attacks. At present, however, synthesis in the presence of such attacks has received limited research attention. In particular, the problem of synthesizing a controller when the required specifications cannot be satisfied completely due to adversarial attacks has not been studied. In this paper, we focus on the minimum violation control synthesis problem under linear temporal logic constraints of a stochastic finite state discrete-time system with the presence of an adversary. A minimum violation control strategy is one that satisfies the most important tasks defined by the user while violating the less important ones. We model the interaction between the controller and adversary using a concurrent Stackelberg game and present a nonlinear programming problem to formulate and solve for the optimal control policy. To reduce the computation effort, we develop a heuristic algorithm that solves the problem efficiently and demonstrate our proposed approach using a numerical case study.