An Improved Method for Approximating the Infinite-horizon Value Function of the Discrete-time Switched LQR Problem

This paper considers the problem of approximating the infinite-horizon value function of the discrete-time switched LQR problem. In particular, we propose a new value iteration method to generate a sequence of monotonically decreasing functions that converges exponentially to the value function. This method facilitates us to use coarse approximations resulting from faster but less accurate algorithms for further value iteration, and thus, our method is capable of achieving a better approximation for a given computation time compared with the existing methods. Two numerical examples are presented in this paper to illustrate the effectiveness of our method.