Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

This article is concerned with the problem of prescribed performance event-triggered tracking control for a class of strict-feedback switched uncertain nonlinear systems. A prescribed performance event-triggered adaptive fuzzy control approach for solving the problem is set up by exploiting backstepping and the average dwell time (ADT) technique. Compared with the existing prescribed performance control designed in the continuous-time context, the proposed approach constructs a prescribed performance event-triggered adaptive fuzzy controller for each subsystem and a switching event-triggered mechanism (ETM), which can largely save communication resources. Meanwhile, the issue of asynchronous switching between candidate subsystems and candidate controllers is dealt with, and transient and steady-state performance of tracking error is ensured under a class of switching signals with ADT. Moreover, the result above is extended to switched uncertain nonlinear systems with vanishing control gains at some points by developing a hysteresis-type switching signal. Also, Zeno phenomenon is excluded for the switching ETM and the hysteresis-type switching signal. Finally, two examples are given to verify the effectiveness of the obtained two results, respectively.

Section: A Hysteresis-type Switching Law and Prescribed Performance E...mentioning

confidence: 99%

“…In this case, in order to solve the corresponding control problem of the switched system, inspired by Xie et al, 32 one designs a hysteresis‐type switching law as

\begin{array}{ll}& \sigma (t)=k,\kern0.3em \mathrm{if}\kern0.3em \sigma \left({t}^{-}\right)=k\kern0.3em \mathrm{and}\kern0.3em x\in \operatorname{int}\kern0.3em {\Omega}_k,\\ {}& \sigma (t)=l,\kern0.3em \hspace{2.56804pt}\mathrm{if}\kern0.3em \sigma \left({t}^{-}\right)=k\kern0.3em \mathrm{and}\kern0.3em x\in {\tilde{\Omega}}_{kl},\end{array}

where

{\Omega}_k=\left\{x|{g}_{n,k}^2\left({\overline{x}}_n\right)-{g}_{n,l}^2\left({\overline{x}}_n\right)+h{g}_{n,k}^2\left({\overline{x}}_n\right)\ge 0,\forall l\in M\right\}

{\overset{normalΩ}{true}}_{k l} = false{x false| g_{n, k}^{2} false({\overset{x}{true}}_{n} false) prefix- g_{n, l<...}

…”

Section: Extensionmentioning

confidence: 99%

Prescribed performance event‐triggered control for strict‐feedback switched nonlinear systems

Fan

Wang

Long

2022

“…Due to some inherently jumping characteristics in man-made or many practical systems, switched systems have drawn widely attention. Thus, many control problems have generated for switched systems, such as stability problem, [1][2][3][4] H ∞ control, [5][6][7] adaptive control, [8][9][10] and so on. Meanwhile, a lot of control strategies have been proposed to deal with such problems.…”

Section: Introductionmentioning

confidence: 99%

Global stabilization of switched nonlinear systems with vanishing control vector fields and its application

Xie

Yang

2021

Self Cite

The global stabilization problem for a more extensive class of switched nonlinear systems is studied, in which control vector fields are allowed to vanish at some point, even for all the subsystems at the same time. The main work of this article is to design a control vector fields-dependent switching law and a bounded switching controller to stabilize the switched nonlinear systems. First, a sufficient condition ensuring the global stabilization of such a class of switched nonlinear systems is developed by the dual design of controllers and a switching law. In some special cases, the designed switching law can rule out Zeno behavior. Then, as a verification of the proposed control design method, the global stabilization of switched strict-feedback nonlinear systems with g k (x) vanishing at some points is obtained by the codesign of the control vector fields-dependent switching law and the bounded switching controller. Finally, a switched RCL circuit system example is also provided to demonstrate the effectiveness of the developed method.

“…The study of switched systems has received a great attention for their ability in describing a wide range of physical and engineering systems and for the existence of control systems that cannot be asymptotically stabilized by a single smooth feedback control law 1,2 . Recently, more and more results for stability analysis and control synthesis of switched nonlinear systems have been proposed 3‐22 . For switched nonlinear systems in some particular forms (canonical form, strict‐feedback form, etc), the design of asymptotically stabilizing controllers has been studied in some literature 4,5,7‐9,14‐18 .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, more and more results for stability analysis and control synthesis of switched nonlinear systems have been proposed 3‐22 . For switched nonlinear systems in some particular forms (canonical form, strict‐feedback form, etc), the design of asymptotically stabilizing controllers has been studied in some literature 4,5,7‐9,14‐18 . Moreover, the L 2 ‐gain control problem of switched nonlinear systems in particular forms has also been considered in several studies 10,12,19 .…”

Section: Introductionmentioning

confidence: 99%

Singular L₂‐gain control for switched nonlinear control systems under arbitrary switching

2020

This article concerns with the synthesis of L 2 -gain state feedback controllers, without the standard regular assumption, for multi-input switched nonlinear control-affine systems under arbitrary switching. A common control storage function approach is developed for deriving sufficient conditions for the existence of uniform L 2 -gain controllers. Moreover, an explicit formula for constructing L 2 -gain controllers is presented. A numerical example is given for illustration. K E Y W O R D S arbitrary switching, L 2 -gain control, nonlinear control systems, state feedback, storage function, switched control systems 1 Int J Robust Nonlinear Control. 2020;30:4149-4163. wileyonlinelibrary.com/journal/rnc