Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 46, Issue 3, Pages 854-865Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2015.2488680
Keywords
Adaptive dynamic programming (ADP); experience replay; nonzero-sum (NZS) games; optimal control; unknown dynamics
Categories
Funding
- National Natural Science Foundation of China [61273136, 61573353, 61533017, 61304086]
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In this paper, an approximate online equilibrium solution is developed for an N-player nonzero-sum (NZS) game systems with completely unknown dynamics. First, a model identifier based on a three-layer neural network (NN) is established to reconstruct the unknown NZS games systems. Moreover, the identifier weight vector is updated based on experience replay technique which can relax the traditional persistence of excitation condition to a simplified condition on recorded data. Then, the single-network adaptive dynamic programming (ADP) with experience replay algorithm is proposed for each player to solve the coupled nonlinear Hamilton-Jacobi (HJ) equations, where only the critic NN weight vectors are required to tune for each player. The feedback Nash equilibrium is provided by the solution of the coupled HJ equations. Based on the experience replay technique, a novel critic NN weights tuning law is proposed to guarantee the stability of the closed-loop system and the convergence of the value functions. Furthermore, a Lyapunov-based stability analysis shows that the uniform ultimate boundedness of the closed-loop system is achieved. Finally, two simulation examples are given to verify the effectiveness of the proposed control scheme.
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