Adaptive critic learning for event-triggered safe control of nonlinear safety-critical systems

In this paper, an event-triggered safe control method based on adaptive critic learning (ACL) is proposed for a class of nonlinear safety-critical systems. First, a safe cost function is constructed by adding a control barrier function (CBF) to the traditional quadratic cost function; the optimization problem with safety constraints that is difficult to deal with by classical ACL methods is solved. Subsequently, the event-triggered scheme is introduced to reduce the amount of computation. Further, combining the properties of CBF with the ACL-based event-triggering mechanism, the event-triggered safe Hamilton–Jacobi–Bellman (HJB) equation is derived, and a single critic neural network (NN) framework is constructed to approximate the solution of the event-triggered safe HJB equation. In addition, the concurrent learning method is applied to the NN learning process, so that the persistence of excitation (PE) condition is not required. The weight approximation error of the NN and the states of the system are proven to be uniformly ultimately bounded (UUB) in the safe set with the Lyapunov theory. Finally, the availability of the presented method can be validated through the simulation.