Recursive computation of pareto optimal strategy for multiparameter singularly perturbed systems

摘要

In this paper, we study the Pareto optimal strategy for multiparameter singularly perturbed system (MSPS). In order to obtain the solution, we must solve the multiparameter algebraic Riccati equations (MARE). The main results in this paper are to propose a new recursive algorithm for solving the MARE and to find sufficient conditions regarding the convergence of our proposed algorithm. Using the recursive algorithm, we show that the solution of the MARE converges to a positive semi-definite stabilizing solution with the rate of convergence of O(‖μ‖~(i+1)) under the sufficient conditions. Furthermore, we also show that the near-optimal strategy achieves the cost functional J_j~* + O(‖μ‖~(i+1)).