A New Nussbaum-Type Function and its Application in the Control of Uncertain Strict-Feedback Systems
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A New Nussbaum-Type Function and its Application in the Control of Uncertain Strict-Feedback Systems Ning Li1 • Heng Liu2 • Yaguang Li3 • Wei Xiang1 • Jin Xu1
Received: 18 December 2019 / Revised: 16 May 2020 / Accepted: 16 June 2020 Ó Taiwan Fuzzy Systems Association 2020
Abstract In this study, an adaptive fuzzy output tracking control scheme is proposed for uncertain strict-feedback systems with unknown control directions. Nussbaum-type functions are designed, with which the effects of multiple unknown control directions can be handled. Compared with the existing Nussbaum-type functions dealing with the same problem, the proposed Nussbaum-type functions have smaller amplitudes that are more conducive to the design of the controller. Fuzzy functions are used to estimate the unknown terms by combining adaptive laws with backstepping procedure. Adaptive fuzzy controller is constructed to guarantee that the output tracking error system is asymptotically stable and all states in the closed-loop system are bounded. Finally, numerical simulation studies are presented to illustrate the effectiveness of the proposed criteria. Keywords Nussbaum-type function Adaptive fuzzy control Unknown control direction Backstepping
& Yaguang Li [email protected] 1
Department of Applied Mathematics, Huainan Normal University, Huainan 232038, China
2
School of Science, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China
3
School of Management, Hefei University of Technology, Hefei 230002, China
1 Introduction Adaptive fuzzy control has been an active research area in the past decades, given its powerful approximation ability in handling unknown nonlinear functions [1–8]. In [9], the adaptive fuzzy tracking control problem for a class of perturbed nonlinear systems with backlash nonlinearity is presented. Using proposed parameter adaptation laws, the high-gain phenomenon can be avoided. In [10], the fuzzy fault-tolerant control problem for multi-agent systems is considered. A fuzzy adaptive fault-tolerant control method for agents to achieve bipartite consensus is proposed in the presence of actuator bias faults and unknown nonlinear functions. The dimensions of the input and output vectors can be unequal. The adaptive backstepping method is well-known to be efficient for designing controllers for strict-feedback systems. Wang et al. investigate the problem of adaptive funnel control for strict-feedback nonlinear systems with non-modelled dynamics. An adaptive fuzzy funnel controller is constructed via backstepping in [11]. In [12], Pade approximation, backstepping and nonlinear disturbance observers strategies can be combined together. The problem of adaptive fuzzy control based on disturbance observer is studied for nonlinear systems with full state constraints, input constraints and unknown external disturbance. In [13], the problem of adaptive fuzzy tracking control is studied for a class of multi-input and multi-output (MIMO) nonlinear sy
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