Adaptive dynamic programming for optimal control of discrete‐time nonlinear system with state constraints based on control barrier function

Adaptive dynamic programming (ADP) methods have demonstrated their efficiency. However, many of the applications for which ADP offers great potential, are also safety‐critical and need to meet safety specifications in the presence of physical constraints. In this article, an optimal controller for solving discrete‐time nonlinear systems with state constraints is proposed. By introducing the control barrier function into the utility function, the problem with state constraints is transformed into an unconstrained optimal control problem, addressing state constraints which are difficult to handle by traditional ADP methods. The constructed sequence of value function is shown to be monotonically non‐increasing and converges to the optimal value. Besides, this article gives the stability proof of the developed algorithm, as well as the conditions for satisfying the state constraints. To implement and approximate the control barrier function based adaptive dynamic programming algorithm, an actor‐critic network structure is built. During the training process, two neural networks are used for approximation separately. The performance of the proposed method is validated by testing it on a simulation example.