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Iterative solution of algebraic matrix Riccati equations in open loop Nash games
Author(s) -
AzevedoPerdicoúlis Teresa Paula,
Jank Gerhard
Publication year - 2004
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.966
Subject(s) - algebraic riccati equation , mathematics , uniqueness , riccati equation , algebraic number , nash equilibrium , matrix (chemical analysis) , linear quadratic regulator , algebraic equation , iterative method , optimal control , differential equation , mathematical optimization , mathematical analysis , nonlinear system , materials science , physics , quantum mechanics , composite material
In this note we study a fixed point iteration approach to solve algebraic Riccati equations as they appear in general two player Nash differential games on an infinite time horizon, where the information structure is of open loop type. We obtain conditions for existence and uniqueness of non‐negative solutions. The performance of the numerical algorithm is shown in an example. Copyright © 2005 John Wiley & Sons, Ltd.