Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

Abstract

This paper considers the problem of adaptive fuzzy output-feedback tracking control for a class of switched stochastic nonlinear systems in pure-feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states.Based on these methods, an adaptive fuzzy output-feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method. KEYWORDS adaptive fuzzy control, backstepping, pure-feedback form, state observer, switched stochastic systems Int J Adapt Control Signal Process. 2019;33:1567-1582.wileyonlinelibrary.com/journal/acs

Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems

“…where x(t) = e(t), y(t) =̇e(t) and for each j ∈ M, g j ( Besides, (0, 0) is an equilibrium of system (37) according to the fact that g j (0, 0, t) = −f j (y * , 0, t) = −f j (y * , 0, 0) = 0 for all j ∈ M and all t ∈ R ≥0 . Thus, the tracking problem of the PD controlled system (6) can be changed into the problem of analyzing the global uniform asymptotic stability of system (37) with respect to (0, 0).…”

“…Second, for the convenience of demonstrating the global uniform asymptotic stability of system (37), inspired by the work of Zhao and Guo, 41 we rewrite g j (x, y, t) as g j (x, y, t) = b j (x, t)x + a j (x, y, t)y, where b j (x, t) and a j (x, y, t) are similarly defined as Equation 13. Then, system (37) can be transformed into…”

“…been extensively researched due to their significance and broad applications in engineering, [37][38][39][40] such as mechanical system, 41 neural networks, 38,42 industrial systems, 43 rigid-body spacecraft, 44 and so on. Correspondingly, numerous remarkable control methods had been addressed in the literatures, 41,[45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] for example, proportional-integral-derivative (PID) control, 41,45,46 PD control, 47,48 PI control, 49 adaptive control, [50][51][52][53] robust control, 54,55 sliding mode control, 56,57 and so on.…”

Observer‐based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances

“…In practice, the control systems always includes different faults and unknown model, which will make some problems to the control design. But the developments of fuzzy logic systems (FLSs) 7,8 and neural networks (NNs) [9][10][11] have brought effective methods to solve these problems. In the work of Wang and Wu et al, 12,13 an AFTC was considered for nonlinear nonstrict-feedback systems with actuator failures and by constructing filter to estimate unmeasured states.…”

Adaptive Dynamic Surface Control for a Class of Nonlinear Pure-Feedback Systems with Parameter Drift

“…Since nonlinear systems are different from linear systems, it is difficult to be analyzed in the way that linear systems are discussed. However, nonlinear pure-feedback systems [8,9] are more general systems compared with lower triangle nonlinear systems, which can reflect the actual physical situation while the nonaffine pure-feedback system is one of the complicated systems. According to the literature [10,11], there are two nonaffine functions in the purefeedback system: system control input and system state variables.…”