Non-zero sum Nash Q-learning for unknown deterministic continuous-time linear systems

• Kyriakos G. Vamvoudakis ^[1]
  1. [1] University of California, Santa Barbara

     University of California, Santa Barbara

     Estados Unidos

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 61, 2015, págs. 274-281
• Idioma: inglés
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• Resumen

  • This work proposes a novel Q-learning algorithm to solve the problem of non-zero sum Nash games of linear time invariant systems with NN-players (control inputs) and centralized uncertain/unknown dynamics. We first formulate the Q-function of each player as a parametrization of the state and all other the control inputs or players. An integral reinforcement learning approach is used to develop a model-free structure of NN-actors/NN-critics to estimate the parameters of the NN-coupled Q-functions online while also guaranteeing closed-loop stability and convergence of the control policies to a Nash equilibrium. A 4th order, simulation example with five players is presented to show the efficacy of the proposed approach.