Novel single-loop policy iteration for linear zero-sum games

Abstract

The infinite-horizon zero-sum game of a linear system can be resorted to solve a Game algebraic Riccati equation (GARE) with indefinite quadratic term. Double-loop policy iteration algorithm is often used to find the solution of such GARE, but its calculation is usually time-consuming. In this work, we propose a novel model-based single-loop policy iteration algorithm to solve GARE and the convergence of the algorithm is guaranteed by the boundness of the iterative sequence and the comparison result. Furthermore, we devise a data-driven single-loop policy iteration algorithm for solving linear zero-sum games, without requiring the knowledge of system dynamics. Compared to the existing Newton’s single-loop methods, the initialization of our algorithms is significantly relaxed and easier to implement. Two numerical examples are included to illustrate the proposed algorithms.