Numerical Computation of Pareto Optimal Strategy for General Multiparameter Singularly Perturbed Systems

Authors:	Mukaidani Hiroaki, Hiroshima University, Japan Xu Hua, The University of Tsukuba, Japan Mizukami Koich, Hiroshima Kokusai Gakuin University, Japan
Topic:	2.4 Optimal Control
Session:	Specific Problems in Optimal Control
Keywords:	Numerical algorithms, Singular perturbations, Differential games, Optimal control

Abstract

In this paper, Pareto optimal strategy for general multiparameter singularly perturbed systems is investigated. The main contribution is to propose a new computational method for obtaining the high-order Pareto near-optimal strategy. Newton's method and two fixed point algorithms are combined. As a result, the new iterative algorithm achieves the quadratic convergence property and succeeds in reducing the computing workspace dramatically. It is newly shown that the resulting optimal strategy achieves the near-optimal cost.