Modeling and Optimal Identification of Pseudodifferential Electrical Dynamics by Means of Diffusive Representation—Part I: Modeling

Laudebat, Lionel; Bidan, Pierre; Montseny, G.

doi:10.1109/tcsi.2004.834501

Cited by 32 publications

(55 citation statements)

References 14 publications

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“…A complete theoretical statement will be found in Montseny [2005] and various applications to non trivial problems will be found in , Carmona and Coutin [1998a,b], Carmona et al [2003], Casenave andMontseny [2009, 2008], Degerli et al [Ap. 1999], Garcia and Bernussou [1998], Lenczner and Montseny [2005], Lenczner et al [2010], Levadoux and Montseny [2003], Montseny [2007], Mouyon and Imbert [2002], Rumeau et al [2006], Bidan et al [2001], , , Devy-Vareta and , Helie and Matignon [2006], Laudebat et al [2004], Lavernhe et al [2001], Lavernhe and Solhusvik [1998], Leger and Pontier [1999], Lubich and Schädler [2002], Matignon [July 2001], Matignon and Prieur [2005], Mbodge et al [1994], Mbodge and Montseny [1995], Montseny [2002bMontseny [ ,a, 1998], Montseny et al [2000], Nihtila and Tervo [2002], Rouzaud [1998].…”

Section: H(t S)u(s)dsmentioning

confidence: 99%

Introduction to Diffusive Representation

Casenave

Montseny

2010

IFAC Proceedings Volumes

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Diffusive representation is an operator theory elaborated during the last years. It is devoted to time-nonlocal problems, allowing significant simplifications for analysis and numerical realization of integral time operators encountered in many physical situations. Namely, most of the shortcomings induced by time-nonlocal formulations are by-passed by use of suitable time-local state realizations deduced from diffusive representation and whose numerical approximations are straightforward, thanks to good properties of diffusion equations. In this paper, we introduce the notion of diffusive representation and its dual one: the diffusive symbol, and we briefly describe the associated mathematical framework and numerical techniques. The interest of this approach is highlighted by numerical examples.

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Section: H(t S)u(s)dsmentioning

confidence: 99%

Introduction to Diffusive Representation

Casenave

Montseny

2010

IFAC Proceedings Volumes

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“…Laudebat et al [3], and Hélie et al [2], on various pseudodifferential operators. Those of C. Lubich and collaborators, e.g.…”

Section: Introductionmentioning

confidence: 99%

Diffusive Realization of a Lyapunov Equation Solution, and Parallel Algorithms Implementation

Huu¹,

Lenczner²,

Couturier³

et al. 2015

2015 Proceedings of the Conference on Control and Its Applications

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In Yakoubi [11] and Lenczner et al. [5] the authors developed a theoretical framework of diffusive realization for state-realizations of some linear operators. Those are solutions to certain linear operator differential equations posed in one-dimensional bounded domains. They illustrate the theory on a Lyapunov equation arising from the optimal control theory of the heat equation. In principle their method might be very efficient for real-time computations, however it suffers from strong limitations. Here, we present significant improvements and report numerical results. A method of contour optimization is provided. It is based on a theoretical error estimate of the solution. Finally, we discuss expected gains if the method is implemented on different parallel computer topologies. The envisioned applications are for real-time distributed control on distributed computing architectures.

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“…Its formulation relates to an interesting technique applicable to causal operator realizations which is well developed in the context of time operators. One of the main advantages of this approach is its low computational cost; see the papers by G. Montseny et al [16], [24], [13], [2], [3] and by D. Matignon et al [10], [11], [22] for representations of various pseudodifferential operators and their approximation. C. Lubich et al [21], [20], [17], [5], [26], [18] apply a similar idea to convolution operators and develop optimized numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Diffusive realizations for solutions of some operator equations: The one-dimensional case

Lenczner¹,

Montseny²,

Yakoubi³

2012

Math. Comp.

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Abstract. In this paper we deal with the derivation of state-realizations of linear operators that are solutions to certain operator linear differential equations in one-dimensional bounded domains. We develop two approaches in the framework of diffusive representations: one with complex diffusive symbols; the other with real diffusive symbols. Then, we illustrate the theories and develop numerical methods for a Lyapunov equation arising from optimal control theory of the heat equation. A practical purpose of this approach is real-time computation on a semi-decentralized architecture with low granularity.

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Modeling and Optimal Identification of Pseudodifferential Electrical Dynamics by Means of Diffusive Representation—Part I: Modeling

Cited by 32 publications

References 14 publications

Introduction to Diffusive Representation

Introduction to Diffusive Representation

Diffusive Realization of a Lyapunov Equation Solution, and Parallel Algorithms Implementation

Diffusive realizations for solutions of some operator equations: The one-dimensional case

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