Optimal bounded policy for nonlinear tracking control of unknown constrained-input systems

Abstract

This paper introduces a novel algorithm that seamlessly integrates type-2 fuzzy systems with a sliding mode controller, aiming to create an optimal bounded control policy for tracking nonlinear problems that are plagued with uncertain or incomplete system dynamics and control input constraints. Proving its efficacy in navigating uncertainties, the proposed approach maintains effectiveness even when such encounters are sporadic or infrequent. The algorithm tactically employs three type-2 fuzzy systems. Among these, the actor and critic fuzzy systems are specifically tasked to resolve the optimal control tracking problem, while the third fuzzy system is designated to approximate the system’s unknown dynamics. The sliding mode controller’s role is instrumental in this setup. It dynamically adjusts to ensure the system’s convergence, enabling precise tracking of the desired trajectory, undeterred by the prevalent uncertainties. We validate the stability of the entire amalgamation, consisting of the actor, critic, identifier and controller. The robustness and efficiency of this innovative method are confirmed through rigorous simulation testing on a nonlinear system. Our results substantiate that the proposed solution excels in optimal tracking control, particularly in situations where system dynamics are uncertain or incomplete and where control input constraints are a critical factor.