Dynamic Surface Control Approach to Adaptive Robust Control of Nonlinear Systems in Semi-Strict Feedback Form

Yang, Zi Jiang; Nagai, Takashi; Kanae, Shunshoku; Wada, Kiyoshi

doi:10.3182/20050703-6-cz-1902.00849

Cited by 10 publications

(26 citation statements)

References 4 publications

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“…Choose an intermediate stabilizing function α j,i j for x j,i j +1 in (25) and the update laws as follows:…”

Section: Controller Designmentioning

confidence: 99%

“…Wang et al [19] extended the DSC approach to neural networks based adaptive tracking control for a class of strict-feedback SISO systems with arbitrary uncertain non-linearities and constant gain coefficient. Recently, the authors in [25,28] extended the method in [19] to a wider class of SISO systems with more general form. However, these works are only limited to SISO systems, and still suffer from the problem of "explosion of learning parameters".…”

Section: Introductionmentioning

confidence: 99%

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Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms

Wang

Chen

2010

Nonlinear Dyn

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Adaptive control of a class of uncertain multi-input/multi-output (MIMO) non-linear systems in block-triangular forms is considered in this paper. By incorporating dynamic surface approach and "minimal learning parameters" algorithm, a systematic procedure for the synthesis of stable adaptive fuzzy tracking controllers with less tuning parameters is developed. Takagi-Sugeno (T-S) fuzzy logic systems (FLSs) are used to approximate those unstructured system functions rather than the unknown virtual control gain functions. Consequently, the potential controller singularity problem can be overcome. Moreover, both problems of "explosion of learning parameters" and "explosion of complexity" are avoided. The computational burden has thus been greatly reduced. T. Li ( ) Navigation College,The stability in the sense of semi-globally uniform ultimate boundedness (SGUUB) of the closed-loop MIMO systems is established via Lyapunov stability theorem. Finally, simulation results are presented to demonstrate the effectiveness and the advantages of the proposed control approach.

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“…Choose an intermediate stabilizing function α j,i j for x j,i j +1 in (25) and the update laws as follows:…”

Section: Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms

Wang

Chen

2010

Nonlinear Dyn

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“…Theorem 1: Consider the closed-loop system composed of (26)∼(28), the controllers (9), (16) and (23), and the adaptive laws (10), (17) and (24). Given any positive number p i , for all initial conditions satisfying…”

Section: Stability Analysismentioning

confidence: 99%

“…Fortunately, for a class of parametric uncertain SISO nonlinear systems, a dynamic surface control (DSC) technique was proposed recently to eliminate this problem in [14] [15] by introducing a first-order filtering of the synthetic input at each step of the traditional backstepping approach. Soon after, the DSC method was then extended to adaptive tracking control via neural networks for a class of strict-feedback SISO systems with arbitrary uncertain nonlinearities in [16] and [17].…”

Section: Introductionmentioning

confidence: 99%

A simple adaptive fuzzy control for a class of strict-feedback SISO systems

2009

2009 IEEE International Conference on Fuzzy Systems

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A simple adaptive fuzzy control (SAFC) is proposed for a class of strict-feedback uncertain nonlinear systems with both unknown system nonlinearities and unknown virtual control gain nonlinearities. Combining the dynamic surface control(DSC) technique with minimal-learning-parameters(MLP) algorithm, a systematic procedure for synthesis of SAFC is developed base on the universal approximation of TakagiSugeno(T-S) fuzzy system. An important feature of the proposed algorithm is that the number of parameters updated on line for each subsystem is reduced dramatically to one, both problems of "explosion of complexity" and "curse of dimension" are avoided, such that the computation load is reduced drastically. It is shown that all closed-loop signals are semi-global uniform ultimate bound(SGUUB) via Lyapunov stability theory and the tracking error can be made arbitrary small. Finally, simulation results are presented to demonstrate the effectiveness and performance of the proposed scheme.Index Terms-Uncertain nonlinear systems, TakagiSugeno(T-S) fuzzy system, adaptive control, dynamic surface, minimal-learning parameters.

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“…The DSC approach replaces the derivatives at each step of the traditional backstepping design by some first order filters. Because of its convenience, the DSC technique has been used in adaptive controller design [11], [12] and state feedback ARC design [13]. In this paper, we use DSC technique to simplify the design of an observer-based ARC, which is more complicated than the adaptive controller and state feedback ARC when synthesized by integrator backstepping approach.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Robust Control for Servo Mechanisms With Partially Unknown States via Dynamic Surface Control Approach

Zhang

Chen

Lee

2010

IEEE Trans. Contr. Syst. Technol.

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In order to achieve high performance control for servo mechanisms with electrical dynamics and unmeasurable states, an observer-based adaptive robust controller (ARC) is developed via dynamic surface control (DSC) technique. To represent electrical dynamics, a third-order model is used to describe the servo mechanism. However, the third-order model brings some difficulties to observer construction and recursive controller design. To solve this problem, we first transform the model into a particular form suitable for observer design, and then construct a parameterized observer to estimate the unmeasurable states. The state estimation is based on the output and its derivatives, which can be acquired by an output differential observer. Subsequently, an observer-based ARC can be developed through DSC technique, with which the problem of "explosion of complexity" caused by backstepping method in the traditional ARC design can be overcome. A stability analysis is given, showing that our control law can guarantee uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small. This scheme is implemented on a precision two-axis turntable. Experimental results are presented to illustrate the effectiveness and the achievable control performance of the proposed scheme.Index Terms-Adaptive robust control (ARC), dynamic surface control (DSC), servo mechanism, state observer, two-axis turntable.

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Dynamic Surface Control Approach to Adaptive Robust Control of Nonlinear Systems in Semi-Strict Feedback Form

Cited by 10 publications

References 4 publications

Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms

Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms

A simple adaptive fuzzy control for a class of strict-feedback SISO systems

Adaptive Robust Control for Servo Mechanisms With Partially Unknown States via Dynamic Surface Control Approach

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