Controller Design for TS Models Using Delayed Nonquadratic Lyapunov Functions

Lendek, Zsófia; Guerra, Thierry Marie; Lauber, Jimmy

doi:10.1109/tcyb.2014.2327657

Cited by 66 publications

(18 citation statements)

References 27 publications

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“…A shorter representation for the augmented system is given by From the literature [6], we know that, considering a control law, with delayed membership functions, of the form…”

Section: Takagi-sugeno System Identificationmentioning

confidence: 99%

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Tensor Product Model Transformation Simplification of Takagi-Sugeno Control and Estimation Laws – An Application to a Thermoelectric Controlled Chamber

2018

APH

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“…A shorter representation for the augmented system is given by From the literature [6], we know that, considering a control law, with delayed membership functions, of the form…”

Section: Takagi-sugeno System Identificationmentioning

confidence: 99%

“…In addition, given the fact that they are capable of representing nonlinear systems by a convex combination of linear models, many control, estimation and analysis problems can be recast as Linear Matrix Inequality (LMI) problems [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Tensor Product Model Transformation Simplification of Takagi-Sugeno Control and Estimation Laws – An Application to a Thermoelectric Controlled Chamber

2018

APH

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“…This allows replacing the standard one-step variation by an α-sample variationṼ (x(t + α)) −Ṽ (x(t)) < 0 and still have a sufficient condition to prove stability [61], see details in [62]; conservatism reduces as α increases. The idea was extended to general Lyapunov functions and control/observer structures in [63,64,65].…”

Section: Non-quadratic Lyapunov Functionsmentioning

confidence: 99%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

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“…Combinations including both past and future memberships appear in (Lendek et al, 2012(Lendek et al, , 2015. The conditions in the cited references are shape-independent, in the sense that they consider neither the relationship between the memberships in different times nor the one between memberships and states.…”

Section: Relation With Fuzzy Lyapunov Functionsmentioning

confidence: 99%

“…The classes of controllers are called PDC (Tanaka & Wang, 2004) if the controller is chosen as a combination of vertex actions sharing the same membership functions as the controlled plant; or non-PDC if other functions of the memberships are used (Guerra & Vermeiren, 2004). Past and future memberships may be involved in the Lyapunov function and non-PDC controllers (Guerra, Kerkeni, Lauber, & Vermeiren, 2012;Kruszewski, Wang, & Guerra, 2008;Lendek, Guerra, & Lauber, 2015).…”

Section: Introductionmentioning

confidence: 99%

Control predictivo de sistemas borrosos mediante teoria de conjuntos invariantes y programación copositiva

Ferrer¹

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This thesis studies fuzzy model predictive control, looking for novel contributions in his field. The main idea of the thesis is to adapt the classic linear model predictive control to Takagi-Sugeno fuzzy systems. Although these systems can be dealt with nonlinear model predictive control, there are many advantages when their particular structure is taken into account.The Takagi-Sugeno fuzzy systems are formed by a mixture of linear models that vary their importance weight (membership function) depending on the value of the system state. In the last 15 years, this structure has been used to develop a multitude of new applications and a whole control theory by adapting robust control through linear matrix inequalities (LMIs) to Takagi-Sugeno fuzzy systems. In these contributions the main idea is to design controllers valid for any known membership function. A priori, it seems very restrictive and too generic, but since controllers know the membership functions, the control action will depend on it, being a powerful design solution. This design philosophy has been called shape-independent design.In pre-thesis developments, it was observed that this type of design philosophy for predictive control had not been studied in depth, so a first approach to the fuzzy predictive control was addressed. Unfortunately, the complexity of the problem increased exponentially with the control horizon and it was left for the present thesis to develop the methodologies, notation and theorems necessary to treat the problem in all its complexity, reaching solutions that increase its complexity through adjustable parameters. The obtained controller solves the shape independent fuzzy predictive control problem for a finite horizon, under some complexity assumptions.Pursuing the above goal, interesting intermediate results have been iii iv also developed: the design of a controller that (with adjustable degree of complexity) stabilizes the system in the largest possible region, and a direct adaptation of some iterative nonlinear predictive control techniques to the Takagi-Sugeno fuzzy systems. Considerations about invariant set theory for the Takagi-Sugeno problem have been developed to obtain the relevant feasible/terminal sets.These developments are based, in addition on the linear model predictive control, on copositive programming. Understanding a copositivity problem, the study of whether a polynomial is positive for any positive value of its variables. In the case of fuzzy systems since the membership functions are always positive, they easily enter into this kind of problem with the proviso that there are other variables (the system state) that are not always positive. This problem has been addressed in the thesis by the application of Polya's theorem. ResumenEn esta tesis se estudia el control predictivo para modelos borrosos Takagi-Sugeno, buscando aportaciones novedosas en este campo. La idea principal de la tesis es adaptar el control predictivo lineal clásico a los modelos borrosos Takagi-Sugeno. A pesar de que estos...

show abstract

Controller Design for TS Models Using Delayed Nonquadratic Lyapunov Functions

Cited by 66 publications

References 27 publications

Tensor Product Model Transformation Simplification of Takagi-Sugeno Control and Estimation Laws – An Application to a Thermoelectric Controlled Chamber

Tensor Product Model Transformation Simplification of Takagi-Sugeno Control and Estimation Laws – An Application to a Thermoelectric Controlled Chamber

Fuzzy control turns 50: 10 years later

Control predictivo de sistemas borrosos mediante teoria de conjuntos invariantes y programación copositiva

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