Off-Policy Learning $H_{\infty }$ Cooperative Optimal Output Regulation for Unknown Multiagent Systems Without Initial Stabilizing Gains

In this article, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> cooperative optimal output regulation (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula>COOR) method based on policy iteration is proposed for unknown multiagent systems (MASs). First, the dynamics matrix and states of the unknown leader are estimated by designing a data-driven distributed observer. Then, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula>COOR problem is decomposed into a static constrained optimization problem and a zero-sum game dynamic optimization problem. Optimal feedback gains are obtained by designing a model-free three-phases off-policy learning algorithm for solving the zero-sum game optimization problem. In two initialization phases, the stabilizing gains are obtained via iterating the poles of the closed-loop system into the stabilization region without a priori knowledge of the MASs. The feedforward control policy is obtained by solving the static constrained optimization problem. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula>COOR is realized by means of a data-based distributed feed-forward feedback controller. For the proposed method, we prove that even if state estimation errors are present, stabilizing gains can still be obtained and that optimal solutions to GAREs can be obtained as the estimation errors asymptotically converge to zero. Finally, the effectiveness of the algorithm is verified by simulation.