ABSTRACT
This paper investigates the problem of safety-critical optimal control for discrete-time non-linear systems. A safety-critical control algorithm is developed based on Q-learning and an iterative adaptive dynamic programming, that is, policy iteration. Discrete-time control barrier functions (CBFs) are introduced into the utility function for guaranteeing safety, in which a novel definition of the safe set and its boundary with multiple discrete-time CBFs are given. Also, for discrete-time systems, by using multiple discrete-time CBFs, the safety-critical optimal control problem of multiple safety objectives is addressed. Meanwhile, safety, convergence, and stability of the developed algorithm are rigorously demonstrated. An effective method to obtain an initial safety-admissible control law is established. Also, the developed algorithm is implemented by building an actor-critic structure with neural networks. Finally, the effectiveness of the proposed algorithm is illustrated by three simulation examples.
International Journal of Robust and Nonlinear Control, Volume 35, Issue 8, Page 2863-2881, 25 May 2025. Read More
