Fuzzy Adaptive Control Design and Discretization for a Class of Nonlinear Uncertain Systems

Abstract

In this paper, tracking control problems are investigated for a class of uncertain nonlinear systems in lower triangular form. First, a state-feedback controller is designed by using adaptive backstepping technique and the universal approximation ability of fuzzy logic systems. During the design procedure, a developed method with less computation is proposed by constructing one maximum adaptive parameter. Furthermore, adaptive controllers with nonsymmetric dead-zone are also designed for the systems. Then, a sampled-data control scheme is presented to discretize the obtained continuous-time controller by using the forward Euler method. It is shown that both proposed continuous and discrete controllers can ensure that the system output tracks the target signal with a small bounded error and the other closed-loop signals remain bounded. Two simulation examples are presented to verify the effectiveness and applicability of the proposed new design techniques.

Output‐feedback adaptive tracking control of stochastic nonlinear systems using multi‐dimensional Taylor network

“…During the past decade, for highly uncertain, nonlinear, and complex systems, many approximations based on adaptive control approaches have been developed via fuzzy logic systems (FLSs) or neural networks (NNs), and many significant results have been reported, eg, Zhao et al 20 proposed a fuzzy adaptive control design method for strict-feedback systems. A novel adaptive neural tracking control scheme was presented in the work of Wang et al 21 for nonlinear time-delay systems.…”

Adaptive neural tracking control for nonstrict‐feedback nonlinear systems with unknown backlash‐like hysteresis and unknown control directions

“…Recently, great attention and developments have been gained in adaptive control design for nonlinear systems due to the important fact that almost all practical systems have a common nonlinear characteristic, such as the aircraft control system and the beam system, and many significant results were proposed in the literature. [1][2][3][4][5][6][7][8][9][10] A variety of different types of nonlinear systems have been explored by using neural networks (NNs) or the fuzzy logic system-based adaptive backstepping technique, where NNs (or fuzzy logic systems) are used to deal with unknown nonlinearities. In the works of Zhang et al 11 and Ge et al, 12 an adaptive controller was designed on the basis of NNs for nonlinear systems with unknown virtual control coefficient functions.…”

Adaptive Composite Fuzzy Dynamic Surface Control for Electro‐Hydraulic‐System, with Variable‐Supply‐Pressure

“…However, due to the application of the backstepping method, the control algorithm recommended by most of the previous literatures needs analytic calculation of the partial derivatives of the virtual controllers, which would inevitably suffer the "explosion of complexity" problem [12]. It is well documented that the calculation of these partial derivatives can be difficult in applications when the order of the nonlinear systems increases, such as equations (34)(35)(36) and (39) in [4], equations (19)(20)(21) and (25) in [13], and equations 26 and 31 in [14]. Therefore, the dynamic surface control (DSC) technique has been considered as a better option to construct the nonlinear controller of the EHS, which was formed by introducing the first-order filters [15,16].…”