Title :
Numerical solutions of soft constrained nash games for multiparameter singularly perturbed systems
Author :
Mukaidani, Hiroaki ; Kurokawa, Taku ; Yamamoto, Seiji ; Yamamoto, Toru
Author_Institution :
Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi, 739-8524 Japan
Abstract :
In this paper, the soft constrained Nash games for multiparameter singularly perturbed systems (MSPS) are discussed. After establishing the asymptotic structure and local uniqueness of the solution for the cross-coupled sign-indefinite multiparameter algebraic Riccati equations (CSMARE), a new algorithm that is based on Newton’s method for solving the CSMARE is established. As a result, it is shown that the proposed algorithm attains quadratic convergence. Moreover, in order to solve the cross-coupled multiparameter algebraic Lyapunov equation (CMALE) that appears in Newton’s method, a new gradient-based iterative algorithm is proposed.
Keywords :
Game theory; Iterative algorithms; Newton method; Noise robustness; Riccati equations; Stochastic processes; Stochastic resonance; Uncertainty; White noise; Working environment noise;
Conference_Titel :
Systems, Man and Cybernetics, 2007. ISIC. IEEE International Conference on
Conference_Location :
Montreal, QC, Canada
Print_ISBN :
978-1-4244-0990-7
Electronic_ISBN :
978-1-4244-0991-4
DOI :
10.1109/ICSMC.2007.4414242
