Dissipativity-Based Verification for Autonomous Systems in Adversarial Environments

In this chapter, we investigate the problem of verifying desired properties of large-scale cyber-physical systems that operate in uncertain, adversarial environments. We focus on properties relating to dissipativity and we propose approaches to achieve verification with minimum knowledge of the system dynamics. In order to achieve compositionality in large-scale models, we distribute the verification process among individual subsystems, which utilize limited information received locally from their immediate neighbors. The need for knowledge of the subsystem parameters is avoided via a novel reinforcement learning-inspired approach that enables decentralized evaluation of appropriate storage functions that can be used to verify dissipativity. Our method allows the addition of learning-enabled subsystems to the cyber-physical network while dissipativity is ensured. We show how different learning rules can be used to guarantee different properties, such as \(L_2\)-gain stability or losslessness. Finally, the need for verification of complex properties is addressed and we propose new directions for this problem.