Neural-network-based online optimal control for uncertain non-linear continuous-time systems with control constraints

In this study, an online adaptive optimal control scheme is developed for solving the infinite-horizon optimal control problem of uncertain non-linear continuous-time systems with the control policy having saturation constraints. A novel identifier-critic architecture is presented to approximate the Hamilton-Jacobi-Bellman equation using two neural networks (NNs): an identifier NN is used to estimate the uncertain system dynamics and a critic NN is utilised to derive the optimal control instead of typical action-critic dual networks employed in reinforcement learning. Based on the developed architecture, the identifier NN and the critic NN are tuned simultaneously. Meanwhile, unlike initial stabilising control indispensable in policy iteration, there is no special requirement imposed on the initial control. Moreover, by using Lyapunov´s direct method, the weights of the identifier NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. Finally, an example is provided to demonstrate the effectiveness of the present approach.