Distributed Time-Varying Optimization for High-Order Linear Multi-Agent Systems With Applications in Battery Energy Storage Systems

This paper is concerned with distributed time-varying optimization problems for heterogeneous high-order linear multiagent systems (MASs). Compared to the time-invariant case, the outputs of the agents converge to optimal trajectories rather than fixed points. Moreover, the most existing works on time-varying optimization are limited to the first- or second-order MASs. The time-varying and higher-order characteristics of the problem considered in this paper make it particularly challenging. To this end, an integrated optimization and control strategy is proposed, which consists of a novel robust distributed optimizer based on the signum function and a set of tracking controllers. The robustness of the distributed optimizer to reference-tracking errors is guaranteed by the input-to-state stability. The proposed strategy ensures that the outputs of the agents converge to the optimal trajectories with zero optimum-tracking errors. On this basis, the signum function is approximated and replaced by a continuous nonlinear function, resulting in a smooth strategy that effectively eliminates chattering at the cost of bounded optimum-tracking errors. Finally, the proposed approach is applied to the optimal balancing problem for battery energy storage systems to validate its effectiveness.