Adaptive backstepping for stabilization of switched nonlinear systems

Tamba, Tua A.; Leksono, Edi

doi:10.1109/cdc.2010.5717241

Cited by 16 publications

(26 citation statements)

References 16 publications

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“…Such a method not only reduces the computational burden, but also is a need to achieve adaptive arbitrary switching control for the switched system in this paper. And the inappropriate expression of adaptive laws being related to the switching signal proposed in [14] under arbitrary switching is righted simultaneously.…”

Section: Observer-based Fuzzy Errors Switched Systemsmentioning

confidence: 99%

“…Moreover, all signals , xˆ, xˆ, φ u are SGUUB by virtue of the relationships (6), (14), (15), (19), (22), (23) and the choices of the virtual control law…”

Section: Observer-based Fuzzy Errors Switched Systemsmentioning

confidence: 99%

“…It overcomes the structural restrictions on functions of [12] in obtaining the common virtual control. Also under arbitrary switching, a systemic adaptive recursive control method was further proposed in [13] to design a common adaptive state feedback controller for nonlinearly parameterized switched systems in lower-triangular forms, which is concerned essentially with drawbacks of lacking the detailed forms of common virtual control laws and relating to the switching signal for the given adaptive laws in [14]. The discontinuity of the designed adaptive controller in [15] was also defeated at the same time.…”

Section: Introductionmentioning

confidence: 98%

“…Around the key issue of how to design a controller independent of the switching signal to achieve the arbitrarily switching control, great efforts have been made by researchers for a class of switched lower triangular systems, see ref. [10][11][12][13][14][15]. Among them, ref.…”

Section: Introductionmentioning

confidence: 98%

See 3 more Smart Citations

Observer-based adaptive arbitrary switching fuzzy tracking control for a class of switched nonlinear systems

Wang

Jiao

2015

Int. J. Control Autom. Syst.

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This paper focuses on the output tracking problem for a class of uncertain switched nonlinear systems with arbitrary switching signal and unavailable states. By designing a proper reducedorder observer and introducing fuzzy approximation, a systematic adaptive domination recursive method is presented to explicitly construct a common smooth dynamic output feedback controller, such that under arbitrary switching, all error variables of the corresponding closed-loop switched systems are semi-globally, uniformly, and ultimately bounded (SGUUB), as well as the tracking error may be adjusted to a small neighborhood of the origin. Compared with the existing results, the proposed control scheme overcomes the restrictions on nonlinear functions of systems only relating to the output variable and switching signal subjecting to certain dwell time. Its effectiveness and feasibility are demonstrated by both a numerical example and a chemical system.

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Section: Observer-based Fuzzy Errors Switched Systemsmentioning

confidence: 99%

“…Moreover, all signals , xˆ, xˆ, φ u are SGUUB by virtue of the relationships (6), (14), (15), (19), (22), (23) and the choices of the virtual control law…”

Section: Observer-based Fuzzy Errors Switched Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Observer-based adaptive arbitrary switching fuzzy tracking control for a class of switched nonlinear systems

Wang

Jiao

2015

Int. J. Control Autom. Syst.

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“…Based on the common control Lyapunov function approach presented in Moulay, Bourdais, and Perruquetti (2007) and Wu (2008), the stabilisation for switched systems under arbitrary switchings has been studied. Based on the combination of CLF concept and the nonlinear adaptive stabilisation technique, Tamba and Leksono (2010) studied the problem of adaptive control of a class of switched nonlinear systems. The main deficiency of the common control Lyapunov function method is that there is no systematic method to construct such a common control Lyapunov function for general nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Backstepping design for global robust stabilisation of switched nonlinear systems in lower triangular form

Zhao

Dimirovski

2013

International Journal of Systems Science

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This article deals with the global robust stabilisation for a class of switched nonlinear systems under arbitrary switchings. The system under consideration is in lower triangular form and contains uncertainty. Both common Lyapunov function and state feedback controller are simultaneously constructed by backstepping such that the closed-loop system is globally robustly asymptotically stable under arbitrary switchings. Lastly, the design method proposed is extended to the uncertain switched nonlinear systems in nested lower triangular form to solve the global robust stabilisation problem under arbitrary switchings. Two examples are given to show the effectiveness of the proposed methods

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Switched adaptive stabilization of switched nonlinearly parameterized cascade systems and its application to a two inverted pendulums

Long

Zhao

2014

Adaptive Control & Signal

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This paper studies adaptive control of switched nonlinearly parameterized cascade systems. No solvability of the adaptive control problem for subsystems is required. By exploiting the multiple Lyapunov functions method and the parameter separation technique and the tool of adding a power integrator, we develop a new switched adaptive control approach for the explicit construction of adaptive controllers of subsystems and a proper switching law that solves the adaptive stabilization problem. A key feature of the proposed adaptive controllers is its switched property, namely, each subsystem has its individual update law. A two-inverted pendulum as a practical example is also provided to demonstrate the effectiveness of the proposed design method.On the other hand, uncertainties extensively exist in real world systems. For example, such uncertainties often appear in control systems such as those in electrical, friction dynamics, dynamics of magnetic bearing, mechanical, chemical, aeronautical, and biomedical engineering [19][20][21][22]. Adaptive control is an effective methodology, which provides adaptation mechanisms to adjust controllers for systems with parametric, structural, and environmental uncertainties to achieve desired system performance [23][24][25]. For about two decades, hence, adaptive control of non-switched nonlinear systems with parametric uncertainty has been one of the most active subjects in the field of nonlinear control [26,27]. In particular, adaptive control has proven its great capability in compensating for non-switched nonlinearly parameterized systems involving inherent nonlinearity on the basic of a parameter separation technique [28].For switched systems, adaptive control was not studied until recently focusing on switched linear systems [29-32] and piecewise affine systems [33,34]. For switched nonlinear systems with parametric uncertainty, however, few results on adaptive control have appeared by now. In [35], an adaptive neural networks (NN) control scheme for strict-feedback switched nonlinear systems is proposed. By using the CLF method and backstepping, adaptive stabilization for strict-feedback switched nonlinear systems under arbitrary switchings is achieved [36]. On the basis of the MLFs technique, an adaptive disturbance rejection problem for switched nonlinear systems in strictfeedback form with unknown exosystem is studied in [37]. Tamba and Leksono and Long and Zhao [36,37] present some effective methods of the adaptive control problem for switched nonlinear systems in strict-feedback form. It should be observed that the literature mentioned earlier has focused on adaptive control of switched nonlinear systems with linear parameterization, and a common update law is used to estimate all the vector parameters in different subsystems. Most switched nonlinear systems in practice, however, do not possess linear parameterization and a common update law for all subsystems. In addition, nonlinear parameterization can be found in various practical control systems such as machine...

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Adaptive backstepping for stabilization of switched nonlinear systems

Cited by 16 publications

References 16 publications

Observer-based adaptive arbitrary switching fuzzy tracking control for a class of switched nonlinear systems

Observer-based adaptive arbitrary switching fuzzy tracking control for a class of switched nonlinear systems

Backstepping design for global robust stabilisation of switched nonlinear systems in lower triangular form

Switched adaptive stabilization of switched nonlinearly parameterized cascade systems and its application to a two inverted pendulums

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