Finite-Time Control of Nonlinear Systems Using Constrained Reinforcement Learning

This paper presents a constrained reinforcement learning (RL) framework for training a controller for nonlinear systems with guaranteed finite-time stability. The scheme is based on the deep deterministic policy gradient (DDPG) algorithm, integrated with a constrained optimization technique. The controller architecture is formulated as a convex combination of multiple neural networks (NNs), each utilizing fractional power functions as activation functions to facilitate the derivation of a finite-time stability condition. This condition is rigorously derived based on Lyapunov stability theory and imposed as a constraint during training to ensure the finite-time stability of the control system while simultaneously optimizing a cumulative reward function. Simulation results are presented to demonstrate the effectiveness of the proposed framework.