A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

Abstract

In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.

A Fast Adaptive Artificial Neural Network Controller for Flexible Link Manipulators

“…On other hand, much research effort has been put into the design of artificial neural network and fuzzy logic-based controllers as they reduce the complexity and allow a faster computation of the command [20][21][22][23][24][25][26][27][28][29][30][31][32].…”

On the Active Disturbance Rejection of SWATH Ship based on Terminal Sliding Mode Control

“…Most previous researches on SWATH are mainly carried out based on nominal parameters, whereas the influence on control performance caused by system uncertainties is usually neglected [1][2][3][4]. Several strategies have been investigated for system uncertainties, such as adaptive control [5], neural networks [6], fuzzy systems [7], and nonlinear disturbance observer [8]. However, the analysis and description of all the strategies mentioned above are based on time domain, whereas the frequency domain performance is rarely concerned.…”

Affine-TS-Based Fuzzy Tracking Design

“…Optimal fuzzy control techniques were proposed to minimize a performance index from local-concept and global-concept approach, respectively (13), (14), (15). Yang and coworkers used an input-free T-S fuzzy system to approximate a uncertain nonlinear state function, and adopted hybrid sliding-mode, adaptive and back-stepping control techniques to control a strick-feedback uncertainty-included nonlinear system (16). Via a fuzzy-static-output-feedback technique, Lo and Lin transformed a robust H ∞ quadratic tracking problem into a bilinear-matrix inequality (17).…”