Safe reinforcement learning for fixed-time stability of a class of nonlinear systems

This paper presents novel safe reinforcement-learning-based, fixed-time control framework for a class of discrete time uncertain nonlinear systems which guarantees fixed-time stability (FxTS). This framework is developed to ensure fixed-time convergence for nonlinear systems in the absence of exact model. The main contribution is to present a unified framework by integration of fixed-time Lyapunov-based constraints and Gaussian process-based uncertainty modeling into the safe reinforcement learning loop in a manner that each candidate policy must ensure the fixed-time Lyapunov decrement condition within a uniform bounded convergence time in the entire learning process. The Lyapunov function for the nominal fixed-time stable closed loop system is used for enlarging the safe set for FxTS with accumulation of system data through refining the traditional Gaussian process model for uncertain system dynamics Gaussian process model is used to learn the unknown system dynamics online and to provide probabilistic confidence bounds. These bounds are directly incorporated into the fixed-time Lyapunov condition, leading to safety guarantees and monotonic expansion of the Lyapunov certified safe set. The control policy is then optimized for the enlarged safe set through exploration while ensuring FxTS. The proposed approach is validated through simulated results of inverted pendulum and reduced-order vehicle dynamic model for lateral vehicle dynamics. The validation for both nonlinear systems confirms fixed-time convergence, certified expansion of safe operating region, and improved control performance under safety and Lyapunov constraints.