Safe Adaptive Dynamic Programming Method for Nonlinear Safety-Critical Systems with Disturbance

Abstract

In this paper, a safe adaptive dynamic programming (SADP) method based on the barrier function (BF) is proposed for the optimal control problem of nonlinear safety-critical systems with the safety constraints and external disturbance. Firstly, the barrier function is used to transform the nonlinear system with the security constraints into a transformed system without the security constraints. Secondly, based on the transformed system, a new barrier-disturbance-related term is proposed to approximate the effect of the external disturbance. On the premise of satisfying the security constraints and stability, the neural network (NN) approximation method is used to approximate the optimal cost function and optimal control strategy of the system online. Finally, the simulation results show that the proposed method can make the system state convergence well and does not violate the security constraints.