Continuous Takagi–Sugeno's Models: Reduction of the Number of LMI Conditions in Various Fuzzy Control Design Technics

Delmotte, François; Guerra, Thierry Marie; Ksantini, Mohamed

doi:10.1109/tfuzz.2006.889829

Cited by 118 publications

(54 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Before providing the PDC control design procedure, let us remind the following lemma [23][24][25]: Lemma 1. The following statements are equivalent 1.…”

Section: Fault Estimation and Robust Controlmentioning

confidence: 99%

“…Note that (32) requires further relaxation procedure in order to be tractable within the effective LMI framework. A basic sufficient solution to this problem were described in [28] and further improved by many researchers (see, e.g., [25,29] and the references therein). As indicated in [29], the conditions provided by [30] lead to a good compromise between complexity and conservatism, which in the case (32) leads to the following lemma: Lemma 2.…”

Section: Fault Estimation and Robust Controlmentioning

confidence: 99%

See 1 more Smart Citation

A robust predictive actuator fault-tolerant control scheme for Takagi-Sugeno fuzzy systems

Witczak¹,

Witczak²,

Korbicz³

et al. 2015

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. The paper deals with the problem of robust predictive fault-tolerant control for nonlinear discrete-time systems described by the Takagi-Sugeno models. The proposed approach is based on a triple stage procedure, i.e. it starts from fault estimation while the fault is compensated with a robust controller. The robust controller is designed without taking into account the input constraints related with the actuator saturation that may change due to its faulty behaviour. Thus, to check the compensation feasibility, the robust invariant set is developed, which takes into account the input constraints. If the current state does not belong to the robust invariant set, then suitable predictive control actions are performed in order to enhance the invariant set. This appealing phenomenon makes it possible to enlarge the domain of attraction, which makes the proposed approach an efficient solution for the fault-tolerant control. The final part of the paper shows an illustrative example regarding the application of the proposed approach to the twin-rotor system.

show abstract

“…Before providing the PDC control design procedure, let us remind the following lemma [23][24][25]: Lemma 1. The following statements are equivalent 1.…”

Section: Fault Estimation and Robust Controlmentioning

confidence: 99%

Section: Fault Estimation and Robust Controlmentioning

confidence: 99%

A robust predictive actuator fault-tolerant control scheme for Takagi-Sugeno fuzzy systems

Witczak¹,

Witczak²,

Korbicz³

et al. 2015

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

show abstract

“…Lemma 3: [9] For any matrices T 1 , T 2 , T 3 and A of appropriate dimensions, finding P = P T > 0 satisfying (12) is equivalent to finding P = P T > 0 and G satisfying (13)…”

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

Ichalal

Marx

Mammar

et al. 2012

2012 IEEE International Symposium on Intelligent Control

View full text Add to dashboard Cite

To cite this version:Abstract-The problem of observer design for nonlinear Lipschitz systems is dealt with in this work. An emphasis is put on the maximization of the admissible Lipschitz constant for which the observer design is possible. This problem is tackled using a Takagi-Sugeno modeling approach. The idea is to rewrite the state estimation error dynamics as an autonomous Takagi-Sugeno system, using the Mean Value Theorem and the sector nonlinearity transformation. State estimation error dynamics stability is studied with the Lyapunov theory by choosing a non-quadratic Lyapunov function and by computing its variation between m consecutive samples. The interest of these manipulations is to obtain LMI conditions admitting solutions for large values of the Lipschitz constant. Finally, illustrative examples are provided in order to highlight the performances of the proposed approach.

show abstract

“…For this case there also exists a simple stability analysis method [39], while for the affine models, stability analysis is more complex and is usually solved using linear matrix inequalities [10,16]. Unfortunately, when global approximation of Takagi-Sugeno model is improved, local interpretability of the rules is lost [1,15,16,25] as we can see in Figure 3: the linear consequent for R (2) , −2x, is not a linearization of the empirical model at x (2) = 2.…”

Section: Takagi-sugeno Model As An Universal Approximatormentioning

confidence: 99%

An affine fuzzy model with local and global interpretations

Matı́a

Al‐Hadithi

Jiménez

et al. 2011

Applied Soft Computing

View full text Add to dashboard Cite

Continuous Takagi–Sugeno's Models: Reduction of the Number of LMI Conditions in Various Fuzzy Control Design Technics

Cited by 118 publications

References 23 publications

A robust predictive actuator fault-tolerant control scheme for Takagi-Sugeno fuzzy systems

A robust predictive actuator fault-tolerant control scheme for Takagi-Sugeno fuzzy systems

Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

An affine fuzzy model with local and global interpretations

Contact Info

Product

Resources

About