Abstract
This paper presents a decentralized composite suboptimal control strategy to solve the optimal control problem for a class of two-time-scale networks, which consist of m lower-level subsystems interconnected through an upper-level main system with unknown dynamics. Firstly, the original optimal control problem is reformulated into the optimal control problems of separated subsystems on different time-scales by means of singular perturbation theory. Secondly, a decentralized composite suboptimal control is designed by combing model-based fast controller and data-based slow controller. Thirdly, the asymptotic stability of the closed-loop overall system and the sub-optimality of the proposed scheme are rigorously proved. As a consequence, the ill-conditioned numerical issues and high dimensionality associated with the full-order model are eliminated in controller design. Finally, a numerical simulation is provided to illustrate the effectiveness of the theoretical developments.
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