Journal
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
Volume 50, Issue 11, Pages 4009-4019Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMC.2019.2897379
Keywords
Game theory; Artificial neural networks; Games; Optimal control; Heuristic algorithms; Nonlinear systems; Adaptive critic designs; adaptive dynamic programming; approximate dynamic programming (ADP); policy iteration (PI); robust control; zero-sum game (ZSG)
Funding
- National Natural Science Foundation of China [61873300, 61722312]
- Fundamental Research Funds for the Central Universities [FRF-GF-17-B45]
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This paper establishes an approximate optimal critic learning algorithm based on single neural network (NN) policy iteration (PI) aiming at solving for continuous-time (CT) 2-player zero-sum games (ZSGs). In fact, we have to face the problem that the errors will disturb the dynamics and in turn identifying dynamics will generate errors. In order to prevent the effect of errors, in this paper, a single NN-based online PI algorithm is developed for the CT system, which is disturbed nonlinear ZSG. With plenty of online data, the Hamilton-Jacobi-Isaacs equation can be solved without complete dynamics. Then by the least-squares method, we can obtain the NN weights. Moreover, in the process of dealing with the undisturbed system, we find the way that obtains NN weights in this paper is equal to the way that obtains the optimal solution by the Gauss-Newton method. Based on the convergence of the Gauss-Newton method, we can efficiently obtain the optimal controller for the undisturbed system by utilizing online data. After getting the controller of the undisturbed system, it is time to take disturbance into consideration, so that we design a robust control pair to overcome the disturbance. In order to demonstrate the effectiveness of this algorithm, we design a set of simulations. The results verify that we can solve the disturbed nonlinear ZSG by this algorithm.
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