Data-based on-line optimal control for unknown nonlinear systems via adaptive dynamic programming approach

In this paper, the data-based optimal control problem for unknown nonlinear system is solved on line by using adaptive dynamic programming (ADP) approach. Three neural network (NN) are used to design the optimal controller, which are a recurrent neural network (RNN), a critic NN and an action NN. The RNN as the on-line data-based model is used to reconstruct the unknown system dynamics. The available input-output data is required to instead of the known system dynamics. The critic NN is designed to approximate the performance index function, and the action NN is designed to approximate the optimal controller. Novel update laws for tuning the unknown weights of the NNs on line are derived. Lyapunov techniques are used to show that all signal are uniformly ultimately bounded. The weights of the three NNs are tuned on line. Moreover, the three NNs implement simultaneously. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.