Neural Network-Based Model-Free Learning Approach for Approximate Optimal Control of Nonlinear Systems

This paper studies the infinite time horizon optimal control problem for continuous-time nonlinear systems. A completely model-free approximate optimal control design method is proposed, which only makes use of the real-time measured data from trajectories instead of a dynamical model of the system. This approach is based on the actor-critic structure, where the weights of the critic neural network and the actor neural network are updated sequentially by the method of weighted residuals. It should be noted that an external input is introduced to replace the input-to-state dynamics to improve the control policy. Moreover, strict proof of convergence to the optimal solution along with the stability of the closed-loop system is given. Finally, a numerical example is given to show the efficiency of the method.