Sliding Mode Learning Control of Uncertain Nonlinear Systems with Lyapunov Stability Analysis

TL;DR

This paper introduces a novel sliding mode learning control approach for uncertain nonlinear systems, combining a conventional control term with a Type-2 Neuro-Fuzzy Controller, and proves system stability with simulations demonstrating robustness under noise.

Contribution

It proposes a new control structure with a novel sliding surface and proves stability for nth-order uncertain nonlinear systems, enhancing learning and robustness capabilities.

Findings

The SMLC algorithm learns system behavior without mathematical models.

The control scheme exhibits robustness against external disturbances.

Simulation results confirm rapid learning and stability under noisy conditions.

Abstract

This paper addresses to Sliding Mode Learning Control (SMLC) of uncertain nonlinear systems with Lyapunov stability analysis. In the control scheme, a conventional control term is used to provide the system stability in compact space while a Type-2 Neuro-Fuzzy Controller (T2NFC) learns system behavior so that the T2NFC takes the overall control of the system completely in a very short time period. The stability of the sliding mode learning algorithm was proven in literature; however, it is so restrictive for systems without the overall system stability. To address this shortcoming, a novel control structure with a novel sliding surface is proposed in this paper and the stability of the overall system is proven for nth-order uncertain nonlinear systems. To investigate the capability and effectiveness of the proposed learning and control algorithms, the simulation studies have been achieved under noisy conditions. The simulation results confirm that the developed SMLC algorithm can learn the system behavior in the absence of any mathematical model knowledge and exhibit robust control performance against external disturbances.