Optimal neuro-control strategy for nonlinear systems with asymmetric input constraints

In this paper, we present an optimal neuro-control scheme for continuous-time ( CT ) nonlinear systems with asymmetric input constraints. Initially, we introduce a discounted cost function for the CT nonlinear systems in order to handle the asymmetric input constraints. Then, we develop a Hamilton-Jacobi-Bellman equation ( HJBE ) , which arises in the discounted cost optimal control problem. To obtain the optimal neurocontroller, we utilize a critic neural network ( CNN ) to solve the HJBE under the framework of reinforcement learning. The CNN ʼ s weight vector is tuned via the gradient descent approach. Based on the Lyapunov method, we prove that uniform ultimate boundedness of the CNNʼ s weight vector and the closed-loop system is guaranteed. Finally, we verify the effectiveness of the present optimal neuro-control strategy through performing simulations of two examples.