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Iterative algorithms for computing the feedback Nash equilibrium point for positive systems. (English) Zbl 1362.49022
Summary: The paper studies \(N\)-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilizing solution of a set of generalized algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

49N75 Pursuit and evasion games
49N10 Linear-quadratic optimal control problems
91A06 \(n\)-person games, \(n>2\)
91A23 Differential games (aspects of game theory)
49M15 Newton-type methods
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