Title :
Numerical algorithm for solving cross-coupled algebraic Riccati equations related to Nash games of multimodeling systems
Author :
Mukaidani, Hiroaki ; Shimomura, Tetsu ; Xu, Hua
Author_Institution :
Graduate Sch. of Educ., Hiroshima Univ., Japan
Abstract :
In this paper, the numerical design of a Nash equilibrium for infinite horizon multiparameter singularly perturbed systems (MSPS) is analyzed. A new algorithm which is based on the Newton method for solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE), is proposed. It is proven that the proposed algorithm guarantees the quadratic convergence. As a result, it is shown the proposed algorithm succeed in improving the convergence rate dramatically compared with the existing results.
Keywords :
Newton method; Riccati equations; convergence of numerical methods; infinite horizon; linear quadratic control; singularly perturbed systems; Nash equilibrium; Nash games; Newtons method; convergence rate; generalized cross coupled multiparameter algebraic Riccati equations; infinite horizon; multimodeling systems; multiparameter singularly perturbed systems; numerical algorithm; quadratic convergence; Control systems; Convergence of numerical methods; Filtering; Infinite horizon; Iterative algorithms; Large-scale systems; Nash equilibrium; Newton method; Riccati equations; Stability;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1185023
