Adaptive Optimal Output Regulation for Unknown Linear Systems via Internal Model Principle and Policy Iteration

The data-driven output regulation problem via internal model principle has been studied by both policy-iteration method and value-iteration method. But the results were limited to single-input single-output linear systems with zero input-output transmission matrix. Recently, we have extended the existing results to multi-input multi-output linear systems with nonzero input-output transmission matrix and improved the algorithm by value-iteration method. Since the policy-iteration method is simpler and has a much faster convergence speed than the value-iteration method, in this paper, we further establish the results parallel to the value-iteration work by the policy-iteration method. Compared with the existing policy-iteration results, we are able to handle multi-input multi-output linear systems with nonzero input-output transmission matrix. Moreover, we further improve the existing policy-iteration algorithm by significantly reducing the computational cost and weakening the solvability conditions. A numerical example is used to illustrate the advantages of the improved algorithm.