Adaptive Dynamic Programming and Decentralized Optimal Output Regulation of Two-Time-Scale Interconnected Systems.

In this paper, we address the decentralized optimal output regulation problem for two-time-scale (TTS) interconnected systems with unknown slow dynamics through adaptive dynamic programming (ADP). Firstly, singular perturbation theory is leveraged to decompose the TTS interconnected system into a slow subsystem and several interconnected fast time-scale subsystems. Secondly, we develop a decentralized optimal control scheme for the fast time-scale subsystems with interconnections. Also, we devise an off-policy ADP algorithm to learn the optimal control strategy for the slow time-scale subsystem with unknown dynamics. Moreover, we combine the slow and fast control strategies to design the composite decentralized optimal output regulator. Both optimality and stability of the closed-loop system are rigorously analyzed. Finally, simulation results are provided to validate the effectiveness of the proposed methodology.