Reinforcement learning for robust stabilization of nonlinear systems with asymmetric saturating actuators

We study the robust stabilization problem of a class of nonlinear systems with asymmetric saturating actuators and mismatched disturbances. Initially, we convert such a robust stabilization problem into a nonlinear-constrained optimal control problem by constructing a discounted cost function for the auxiliary system. Then, for the purpose of solving the nonlinear-constrained optimal control problem, we develop a simultaneous policy iteration (PI) in the reinforcement learning framework. The implementation of the simultaneous PI relies on an actor-critic architecture, which employs actor and critic neural networks (NNs) to separately approximate the control policy and the value function. To determine the actor and critic NNs' weights, we use the approach of weighted residuals together with the typical Monte-Carlo integration technique. Finally, we perform simulations of two nonlinear plants to validate the established theoretical claims.