Closed-loop Stackelberg strategies for singularly perturbed systems: the recursive approach

Abstract

Abstract The recursive reduced order algorithm in the context of linear closed-loop Stackelberg strategies for singularly perturbed systems is presented. Motivated by previous results for the weakly coupled linear quadratic Nash games, it is shown that a similar algorithm can be produced for singularly perturbed linear quadratic Stackelberg games and the fixed point method is very effective in this case also. It is shown that the proposed recursive algorithm improves the accuracy of the sought solution, that is, the singularly perturbed recursive algorithm converges with the rate of convergence of accuracy O(e). Since all results on linear closed-loop Stackelberg game problem for the singularly perturbed systems can be obtained as far with an accuracy O( e) only, that represents a significant improvement. In order to demonstrate the effectiveness of the proposed algorithm and the failure of the O( e) theory, a numerical example is shown.