Adaptive optimal control of affine nonlinear systems via identifier–critic neural network approximation with relaxed PE conditions

This paper considers an optimal control of an affine nonlinear system with unknown system dynamics. A new identifier–critic framework is proposed to solve the optimal control problem. Firstly, a neural network identifier is built to estimate the unknown system dynamics, and a critic NN is constructed to solve the Hamiltonian–Jacobi–Bellman equation associated with the optimal control problem. A dynamic regressor extension and mixing technique is applied to design the weight update laws with relaxed persistence of excitation conditions for the two classes of neural networks. The parameter estimation of the update laws and the stability of the closed-loop system under the adaptive optimal control are analyzed using a Lyapunov function method. Numerical simulation results are presented to demonstrate the effectiveness of the proposed IC learning based optimal control algorithm for the affine nonlinear system.