Cooperative Optimal Output Tracking for Discrete-Time Multiagent Systems: Stabilizing Policy Iteration Frameworks

This paper proposes two cooperative optimal output tracking (COOT) algorithms based on policy iteration (PI) for discrete-time multi-agent systems with unknown model parameters. First, we establish a stabilizing PI framework that can start from any initial control policy, relaxing the dependence of traditional PI on the initial stabilizing control policy. Then, another efficient and equivalent$Q$-learning framework is developed, which is shown to require only less system data to get the same results as the stabilizing PI. In the two frameworks, the stabilizing control policy is obtained by gradually iterating the stabilizing virtual system to the actual feedback closed-loop system. Two explicit schemes for adjusting the iteration step-size/coefficient are designed and their stability is analyzed. Finally, the COOT is realized by a distributed feedforward-feedback controller with learned optimal gains. The proposed algorithms are validated by simulation.