Neural-network-based optimal control for discrete-time nonlinear systems using general value iteration

In this paper, we propose a novel adaptive dynamic programming (ADP) scheme based on general value iteration to obtain near optimal control for discrete-time nonlinear systems with continuous state and control space. First, the selection of initial value function is different from the traditional value iteration, and a new method is introduced to demonstrate the convergence property and convergence speed of the value function. Then, the control law obtained at each iteration can stabilize the system under some conditions. At last, three neural networks with Levenberg-Marquardt training algorithm are used to approximate the unknown nonlinear system, the value function and the optimal control law. One simulation example is presented to demonstrate the effectiveness of the present scheme.