# THE RECURSIVE ALGOFITHM FOR OPTIMAL REGULATOR OF NONSTANCARD SINGULARLY PERTURVED SYSTEMS

• Mukaidani, Hiroaki (Graduate School of Engineering, Hiroshima Univ.) ;
• Xu, Hau (Faculty of Integrated Arts and Science, Hiroshima University) ;
• Mizukami, Koichi (Faculty of Integrated Arts and Science, Hiroshima University)
• Published : 1995.10.01

#### Abstract

This paper considers the linear-quadratic optimal regulator problem for nonstandard singularly perturbed systems making use of the recursive technique. We first derive a generalized Riccati differential equation by the Hamilton-Jacobi equation. In order to obtain the feedback gain, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(.epsilon.). The existence of a bounded solution of error term can be proved by the implicit function theorem. It is enough to show that the corresponding Jacobian matrix is nonsingular at .epsilon. = 0. As a result, the solution of optimal regulator problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(.epsilon.$^{k}$ ). The proposed technique represents a significant improvement since the existing method for the standard singularly perturbed systems can not be applied to the nonstandard singularly perturbed systems.