Robust Fuzzy Adaptive Finite-Time Control for High-Order Nonlinear Systems With Unmodeled Dynamics

This article studies the problem of the robust fuzzy adaptive finite-time control design for a class of single-input single-output high-order nonlinear systems. The considered plants contain unknown nonlinear functions, unmodeled dynamics, and dynamical disturbances. In this control design, fuzzy logic systems are utilized to approximate unknown nonlinear functions, and dynamical signal functions are introduced to solve unmodeled dynamics and dynamical disturbances. Under the framework of an adaptive backstepping control and adding a power integrator control design technique, a robust fuzzy adaptive finite-time control scheme is developed, which can not only guarantee the controlled system to be semiglobal practical finite-time stable, but also have the robustness to unmodeled dynamics and dynamical disturbances. Both numerical and practical simulation examples are provided to check the effectiveness of the proposed control method.

I. Introduction

High-order nonlinear systems are an important class of nonlinear systems. Unlike the strict-feedback nonlinear systems [1], the subsystem can be expressed as , where the exponentials of the virtual and actual control inputs are the ratios of two positive odd integers, instead of 1 in the high-order nonlinear systems. Therefore, the traditional backstepping control design technique cannot be applied to high-order nonlinear systems. [2] first proposed a control design approach for a class of high-order nonlinear systems. [3] and [4] studied the control problems of global robust stabilization for high-order nonlinear systems by designing novel iterative-type Lyapunov functions, referred to as adding a power integrator technique. By using this technique, [5] and [6] proposed using adaptive state-feedback stabilization and output tracking control design schemes for stochastic high-order systems, respectively. In addition, [6] applied the proposed control algorithm to benchmark a mechanical system. By adopting a homogeneous domination algorithm, [7] solved the problem of state-feedback stabilization control for stochastic high-order nonlinear systems with time-varying delay. It should be pointed out that the aforementioned control schemes are all designed under the framework of asymptotic stability. Therefore, their convergence time is arbitrary or tends to be infinite.