Gaussian mixture model based adaptive control for uncertain nonlinear systems with complex state constraints

This paper addresses an uncertain nonlinear control system problem with complex state constraints and mismatched uncertainties. A novel Gaussian Mixture Model (GMM) based adaptive PID-Nonsingular Terminal Sliding Mode Control (NTSMC) (GMM-adaptive-PID-NTSMC) method is proposed. It is achieved by combining a GMM based adaptive potential function with a novel switching surface of PID-NTSMC. Next, the stability of the closed-loop system is proved. The main contribution of this paper is that the GMM method is applied to obtain the analytic description of the complex bounded state constraints, ensuring that the states’ constraints are not violated with GMM-based adaptive potential function. The developed potential function can consider the influence of uncertainties. More importantly, the GMM-adaptive-PID-NTSMC can be generalized to control a more representative class of uncertain nonlinear systems with constrained states and mismatched uncertainties. In addition, the proposed controller enhances the robustness, and requires less control cost and reduces the steady state error with respect to the Artificial Potential Function based Nonsingular Terminal Sliding Mode Control (APF-NTSMC), GMM-NTSMC and GMM-adaptive-NTSMC. At last, numerical simulation is performed to validate the superior performance of the proposed controller.