Enlarging region of attraction via LMI-based approach and Genetic Algorithm

Hamidi, Faiçal; Jerbi, Houssem; Aggoune, Woihida; Djemaï, Mohamed; Abdkrim, M. Naceur

doi:10.1109/ccca.2011.6031233

Cited by 24 publications

(10 citation statements)

References 11 publications

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“…In this figure, the DA ( blue line) illustrates the results obtained through the optimization of parameters p 1 , p 2 , p 3 , u 1 , u 2 , u 3 , u 4 and u 5 by combining GA and LMI. DA with red line : obtained results while optimizing parameters p 1 , p 2 , p 3 , u 1 by combining the GA and LMI [2]. DA with the black line : obtained results by optimizing parameters p 1 , p 2 , p 3 , u 1 , with LMI [3].This result demonstrates the consistency of the proposed method.…”

Section: Illustrative Examplesupporting

confidence: 66%

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Enlarging the Domain of Attraction in Nonlinear Polynomial Systems

Hamidi

Jerbi

Aggoune

et al. 2013

INT J COMPUT COMMUN

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This paper addresses the problem of enlarging the Domain of Attraction (DA) based on a Generalized Eigenvalue Problem (GEVP) approach. The main contribution is the maximization of the (DA) while characterizing the asymptotic stability region by a Lyapunov Function. Such result is obtained using a Genetic Algorithm (GA). A theoretical proof of the validity of the obtained domain is developed. An illustrative example ends the paper.

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Section: Illustrative Examplesupporting

confidence: 66%

“…The problem of enlarging the Domain of Attractions (DA) has been the topic of an important number of research works (see for example [2] [4], [5], [6] [11], [13] and the references cited therein). The DA is defined as the set of initial conditions from which the states converge to the asymptotically stable equilibrium point [7].…”

Section: Introductionmentioning

confidence: 99%

Enlarging the Domain of Attraction in Nonlinear Polynomial Systems

Hamidi

Jerbi

Aggoune

et al. 2013

INT J COMPUT COMMUN

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“…In [15] Chesi presented a technique to compute output feedback controllers of a given class, which maximize the DOA induced by a given polynomial LF. An improved approach to enlarge the DOA using a parameterized LF is proposed in [16]. Both methods exploit known relaxations based on sums of squares of polynomials.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear static state feedback controller design to enlarge the domain of attraction for a class of nonlinear systems

Saleme

Tibken

2013

2013 American Control Conference

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In this paper, the problem of computing state feedback controllers to enlarge the domain of attraction (DOA) in non-polynomial systems is considered. An optimization strategy based on a multidimensional gridding approach to estimate and to enlarge the guaranteed DOA of equilibrium points of nonpolynomial systems is developed. Our intention is to extend our approach for the estimation of the DOA for non-polynomial systems presented in [1] to controller design, which maximizes the estimated DOA induced by a given quadratic Lyapunov function (QLF). An inner and an outer approximation of the enlarged DOA and the corresponding state feedback controller can be calculated. Two illustrative examples with different state feedback controllers demonstrate the effectiveness of the presented method.

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“…In [12] a technique to compute output feedback controllers of a given class, which maximizes the DOA included by a given polynomial LF, is proposed. An improved approach to enlarge the DOA using a parametrized LF is proposed in [13]. In order to enlarge the DOA of an equilibrium point of interest, which is defined by a given QLF, we propose in this paper an optimization technique to compute nonlinear state feedback controllers for polynomial systems.…”

Section: Introductionmentioning

confidence: 99%

State feedback controller design to enlarge the domain of attraction in polynomial systems

Saleme

Tibken

2012

2012 IEEE International Conference on Control Applications

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In this paper, a technique of enlarging the domain of attraction (DOA) for polynomial systems using state feedback controllers is considered. In order to deal with such a problem, we present a technique for computing state feedback controllers, which maximize the guaranteed DOA induced by a quadratic Lyapunov function (QLF). The state feedback controller design is formulated as a minimum-maximum optimization problem. The main theme of this contribution is to show that lower and upper bounds of the maximized DOA and a corresponding controller can be calculated. Moreover, two conditions for the tightness of the lower and upper bounds are established. An illustrative example with two different controllers is presented to verify this method.

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Enlarging region of attraction via LMI-based approach and Genetic Algorithm

Cited by 24 publications

References 11 publications

Enlarging the Domain of Attraction in Nonlinear Polynomial Systems

Enlarging the Domain of Attraction in Nonlinear Polynomial Systems

Nonlinear static state feedback controller design to enlarge the domain of attraction for a class of nonlinear systems

State feedback controller design to enlarge the domain of attraction in polynomial systems

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