A new method to estimate a guaranteed subset of the domain of attraction for non-polynomial systems

Saleme, Ahmed; Tibken, Bernd

doi:10.1109/acc.2012.6315052

Cited by 7 publications

(13 citation statements)

References 14 publications

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“…It is easy to prove that the inner optimization problem for a given gain k and a constant value of the coefficient vector h can be solved using our proposed method in [1]. In the second step we find the controller parameters, so that the estimated DOA is as large as possible.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the second step we find the controller parameters, so that the estimated DOA is as large as possible. To solve the inner optimization problem for non-polynomial systems we use our method presented in [1]. On the basis of this method, we present a technique for computing state feedback controllers to enlarge the DOA for non-polynomial systems.…”

Section: Problem Formulationmentioning

confidence: 99%

“…An interval arithmetic approach was presented in [11]. Two different multidimensional gridding approaches for non-polynomial systems were presented in [1] and [2], in which a theorem of Ehlich and Zeller [12] for polynomial systems was modified and adjusted to deal with non-polynomial systems using the interpolation error of the non-polynomial terms. According to this, polynomial lower and upper bounds for non-polynomial functions were established.…”

Section: Introductionmentioning

confidence: 99%

“…The designed state feedback controller is supposed to be polynomial, whose coefficients are unknown and belong to an a priori selectable range. The problem designing state feedback controllers enlarging the DOA is formulated as a minimum-maximum optimization problem, for which our very efficient algorithm presented in [1] is used. Moreover, a branch-and-bound algorithm is developed to calculate an inner and outer approximation of the enlarged DOA over the range of the coefficients of the chosen parameterized state feedback controllers.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…With regard to nonpolynomial systems, researchers are interested in polynomial approximation methods, like replacing the nonlinear terms with new variables and recasting the state space to an expanded one [17], covering the non-polynomial functions into a convex hull of a group of polynomials [20]. In [21], an approach is provided by using Chebychev points with a chosen quadratic Lyapunov function for the uncertainty-free case. Related to this work is the method of [22], where a rational Lyapunov function is used to estimate the RDA of uncertain polynomial systems.…”

Section: Introductionmentioning

confidence: 99%

On estimating the Robust Domain of Attraction for uncertain non-polynomial systems: An LMI approach

Han

Althoff

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-An increasingly important issue in the area of uncertain systems is the estimation of the Robust Domain of Attraction (RDA). Though this topic is of great interest, most of attention has been paid to the RDA for uncertain polynomial systems. This paper considers the RDA for rational polynomial systems and non-polynomial systems, both with parametric uncertainties, which are constrained in a semialgebraic set. The main underlying idea is to reformulate the original system to an uncertain rational polynomial system by using the truncated Taylor expansion and the parameterizable remainder of nonpolynomial functions. A novel way to compute the largest estimate of the RDA is proposed by using a given rational Lyapunov function and the squared matrix representation technique (SMR). Lastly, the benefits of this approach are presented by a numerical example.

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Domain-of-attraction estimation for uncertain non-polynomial systems

Yang

Wang

2014

Communications in Nonlinear Science and Numerical Simulation

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In this paper, we consider the problem of computing estimates of the domain-ofattraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining functions, is applied to compute an uncertain polynomial system, whose set of trajectories contains that of the original non-polynomial system. Experiments on the benchmark nonpolynomial systems show that our approach gives better estimates of the domain-ofattraction.

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A new method to estimate a guaranteed subset of the domain of attraction for non-polynomial systems

Cited by 7 publications

References 14 publications

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

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

On estimating the Robust Domain of Attraction for uncertain non-polynomial systems: An LMI approach

Domain-of-attraction estimation for uncertain non-polynomial systems

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