Search

In this paper, an adjustable Q-learning scheme is developed to solve the discrete-time nonlinear zero-sum game problem, which can accelerate the convergence rate of the iterative Q-function sequence. First, the monotonicity and convergence of the iterative Q-function sequence are analyzed under some conditions. Moreover, by employing neural networks, the model-free tracking control problem can be overcome for zero-sum games. Second, two practical algorithms are designed to guarantee the convergence with accelerated learning. In one algorithm, an adjustable acceleration phase is added to the iteration process of Q-learning, which can be adaptively terminated with convergence guarantee. In another algorithm, a novel acceleration function is developed, which can adjust the relaxation factor to ensure the convergence. Finally, through a simulation example with the practical physical background, the fantastic performance of the developed algorithm is demonstrated with neural networks. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we solve the zero-sum game problems for discrete-time affine nonlinear systems with known dynamics via iterative adaptive dynamic programming algorithm. First, a greedy heuristic dynamic programming iteration algorithm is developed to solve the zero-sum game problems, which can be used to solve the Hamilton–Jacobi–Isaacs equation associated with optimal regulation control problems. The convergence analysis in terms of value function and control policy is provided. To facilitate the implementation of the algorithm, three neural networks are used to approximate the control policy, the disturbance policy, and the value function, respectively. Then, we extend the algorithm to optimal tracking control problems through system transformation. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed scheme. [Copyright &y& Elsevier]