Robust Stability Analysis of TS-Fuzzy-Model-Based Control Systems with Both Elemental Parametric Uncertainties and Norm-Bounded Approximation Error

Hsieh, Chen-Huei; Chou, Jyh–Horng

doi:10.1299/jsmec.47.686

Cited by 16 publications

(6 citation statements)

References 20 publications

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“…In many interesting problems, we only have a small number of uncertain parameters, but these uncertain parameters may enter into many entries of the system and input matrices . Therefore, in this paper, we suppose that the time‐varying parametric uncertain matrices Δ A i ( t ) and Δ B i ( t ) take the forms

Δ A_{i} (t) MathClass-rel= {falsefalse}_{MathClass-op\sum}^{k MathClass-rel= 1} ϵ_{ik} (t) E_{ik} and Δ B_{i} (t) MathClass-rel= {falsefalse}_{MathClass-op\sum}^{k MathClass-rel= 1} η_{ik} (t) V_{ik} MathClass-punc,

where ϵ ik ( t ) (

{\underset{ϵ}{falsemml-underline}}_{ik} \leq ϵ_{ik} (t) \leq {\overset{ϵ}{true}}_{ik}

, for i = 1,2, … , N and k = 1,2, … , a ) and η ik ( t ) (

{\underset{η}{falsemml-underline}}_{ik} \leq η_{ik} (t) \leq {\overset{η}{true}}_{ik}, for i MathClass-rel= 1 MathClass-punc, 2 MathClass-punc, MathClass-op\dots MathClass-punc, N and k MathClass-rel= 1 MathClass-punc, 2 MathClass-punc, MathClass-op\dots MathClass-punc, a

) are the time‐varying elemental parametric uncertainties, and E ik and V ik ( i = 1,2, … , N and k = 1,2, … , a ) are, respectively, the given n × n and n × p constant matrices which are prescribed a priori to denote the linearly dependent information on the time‐varying elemental parametric uncertainties ϵ ik ( t )'s and η ik ( t )'s, respectively.…”

Section: Problem Statementmentioning

confidence: 99%

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

Chen

Chou

et al. 2011

Optim Control Appl Methods

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SUMMARYBy integrating the robust stabilizability condition, the orthogonal-function approach (OFA) and the Taguchi-sliding-based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust-optimal fuzzy parallel-distributed-compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi-Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite-horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI-based robust stabilizability condition, the robust-optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrainedoptimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition; thus, greatly simplifying the robust-optimal PDC control design problem. Then, for the static constrained-optimization problem, the TSBDEA has been employed to find the robust-optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach.

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Δ A_{i} (t) MathClass-rel= {falsefalse}_{MathClass-op\sum}^{k MathClass-rel= 1} ϵ_{ik} (t) E_{ik} and Δ B_{i} (t) MathClass-rel= {falsefalse}_{MathClass-op\sum}^{k MathClass-rel= 1} η_{ik} (t) V_{ik} MathClass-punc,

where ϵ ik ( t ) (

{\underset{ϵ}{falsemml-underline}}_{ik} \leq ϵ_{ik} (t) \leq {\overset{ϵ}{true}}_{ik}

, for i = 1,2, … , N and k = 1,2, … , a ) and η ik ( t ) (

{\underset{η}{falsemml-underline}}_{ik} \leq η_{ik} (t) \leq {\overset{η}{true}}_{ik}, for i MathClass-rel= 1 MathClass-punc, 2 MathClass-punc, MathClass-op\dots MathClass-punc, N and k MathClass-rel= 1 MathClass-punc, 2 MathClass-punc, MathClass-op\dots MathClass-punc, a

Section: Problem Statementmentioning

confidence: 99%

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

Chen

Chou

et al. 2011

Optim Control Appl Methods

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“…In many interesting problems, we have only a small number of uncertain parameters, but these uncertain parameters may enter into many entries of the system and input matrices [12], [13]. Therefore, in this paper, we suppose that the structured parametric uncertain matrices The resulting TS fuzzy descriptor system with structured parametric uncertainties inferred from Eq.…”

Section: Robust Controllability Analysismentioning

confidence: 99%

Robust controllability of TS fuzzy descriptor systems with structured parametric uncertainties

Chen

Chou

2009

2009 IEEE International Conference on Fuzzy Systems

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“…Furthermore, it is presumed that the estimation error between the T‐S fuzzy model and the nonlinear control system is a norm bounded uncertainty 50,51 . However, Reference 52 has demonstrated that the outcomes are more conservative than that of considering the elemental information of the parametric uncertain matrices. Moreover, the uncertainties in parameter of system have been supposed to fulfill the matching conditions, and the external disturbances should satisfy the norm conditions with defined nonnegative scalars 53,54 .…”

Section: Introductionmentioning

confidence: 99%

Observer‐based controller design for uncertain disturbed Takagi‐Sugeno fuzzy systems: A fuzzy wavelet neural network approach

Ebrahimi

Asemani

Safavi

2020

Adaptive Control & Signal

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SummaryIn this article, we develop a novel method to design a controller for nonlinear systems represented by Takagi‐Sugeno (T‐S) fuzzy model in the presence of unknown dynamics, uncertainties in parameters of nonlinear system and external disturbances. The control law is constituted two segments. The first segment derives from parallel distributed compensation (PDC) procedure, in which each control rule is drawn from the respective rule of T‐S fuzzy model. The second segment stems from fuzzy wavelet neural network (FWNN) estimator which is evoked by the hypothesis of multiresolution analysis (MRA) of wavelet transforms and fuzzy notions, so as to approximate the uncertainties and external disturbances in T‐S fuzzy model accurately. In this regard, the Lyapunov stability theorem is applied to acquire the adaptive learning laws for training and tuning online FWNN parameters such as the dilations, translations, and the weights of networks. Moreover, the asymptotic stability of the closed loop system is guaranteed based on the Lyapunov stability theorem. Furthermore, a development of the proposed method to observer‐based controller design for uncertain nonlinear systems descripted by T‐S fuzzy model is provided. The efficiency and robustness of the proposed method are illustrated by simulation outcomes. It is noteworthy that the proposed controller remarkably handles the uncertainties and external disturbances in T‐S fuzzy model without employing traditional conservative lemma and without considering bounds on uncertainties.

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Robust Stability Analysis of TS-Fuzzy-Model-Based Control Systems with Both Elemental Parametric Uncertainties and Norm-Bounded Approximation Error

Cited by 16 publications

References 20 publications

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

Robust controllability of TS fuzzy descriptor systems with structured parametric uncertainties

Observer‐based controller design for uncertain disturbed Takagi‐Sugeno fuzzy systems: A fuzzy wavelet neural network approach

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