Neural network-based safe optimal robust control for affine nonlinear systems with unmatched disturbances

In this paper, for the safety–critical systems with unmatched disturbances, a safe optimal robust control method based on neural network is proposed to ensure that the safety–critical system operates within its safe region and learns the optimal control strategy. The cost function which is the goal of the designers is augmented by a control barrier function (CBF) to achieve both safety and optimality. This method does not directly regard security as a constraint on the system state, but influences the cost function through a security penalty mechanism. An additional function is used to approximate the effect of the unmatched disturbances on the safety–critical systems. On the premise of satisfying the security and robustness, the neural network approximation method is used to learn the optimal control strategy. Based on Lyapunov stability theory, it is shown that the neural network-based safe optimal robust controller can guarantee all the signals of the resulting closed-loop systems to be uniformly ultimately bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed method.