Distributed Optimal State Consensus for Multiple Circuit Systems with Disturbance Rejection

This paper investigates the distributed optimal state consensus problem for an electronic system with a group of circuit units, where the dynamics of each unit is modeled by a Chua's circuit in the presence of disturbance generated by an external system. By means of the internal model approach and feedback control, a compensator-based continuous-time algorithm is proposed to minimize the sum of all cost functions associated with each individual unit in a cooperative manner. Supported by convex analysis, graph theory and Lyapunov theory, it is proved that the proposed algorithm is exponentially convergent. Compared with the centralized algorithms, the proposed protocol possesses remarkable superiority in improving scalability and reliability of multiple circuit systems. Moreover, we also study the distributed uncertain optimal state consensus problem and a linear regret bound is obtained in this case. Finally, a state synchronization example is provided to validate the effectiveness of the proposed algorithms.