Adaptive Approximation-Based Control for Uncertain Nonlinear Systems With Unknown Dead-Zone Using Minimal Learning Parameter Algorithm

Abstract

This paper proposes an adaptive approximation-based controller for uncertain strict-feedback nonlinear systems with unknown dead-zone nonlinearity. Dead-zone constraint is represented as a combination of a linear system with a disturbance-like term. This work invokes neural networks (NNs) as a linear-in-parameter approximator to model uncertain nonlinear functions that appear in virtual and actual control laws. Minimal learning parameter (MLP) algorithm is proposed to decrease the computational load, the number of adjustable parameters, and to avoid the “explosion of learning parameters” problem. An adaptive TSK-type fuzzy system is proposed to estimate the disturbance-like term in the dead-zone description which further will be used to compensate the effect of the dead-zone, and it does not require the availability of the dead-zone input. Then, the proposed method based on the dynamic surface control (DSC) method is designed which avoids the “explosion of complexity” problem. Proposed scheme deals with dead-zone nonlinearity and uncertain dynamics without requiring the availability of any knowledge about them, and it develops a control input without singularity concern. Stability analysis shows that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to the vicinity of the origin. Simulation and comparison results verify the acceptable performance of the presented controller.

Keywords

• Dead-Zone Nonlinearity
• Minimal Learning Parameter Algorithm
• Adaptive Fuzzy Approach
• Neural Networks.