Decentralized Event-Driven Reliability Control Using Reinforcement Learning: A Homomorphic Encryption Scheme

This article investigates the decentralized adaptive event-driven (AED) reliability control problem for nonlinear interconnected systems (NISs) with privacy-preserving. The decentralized optimal control strategy for the whole system is formulated by the optimal control for nominal subsystems, where an AED homomorphic cryptosystem is implemented for each subsystem to alleviate network burden while achieving security by encrypting transmitted signals. The Paillier cryptosystem with additive homomorphic properties is introduced to conceal the original data. Therefore, the transformed Hamilton–Jacobi–Bellman equations (HJBE) are constructed to facilitate cooperative optimization across subsystems within the framework of reinforcement learning. Subsequently, we leverage single critic networks to derive solutions to the HJBE, utilizing the experience replay approach for weight updates. Furthermore, by virtue of the Lyapunov function, the derived decentralized control law can force the whole NIS to be uniformly ultimately bounded stable. Eventually, numerical examples of NISs are provided to illustrate the effectiveness of the proposed optimization algorithm.