Semi-decentralized approximation of optimal control for partial differential equations in bounded domains

Lenczner, Michel; Yakoubi, Youssef

doi:10.1016/j.crme.2009.03.013

Cited by 7 publications

(14 citation statements)

References 5 publications

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“…at the previous node x n for all k. Now, we comment on the advantage of our approach compared to other works [1], [12], [15] on the problem of realizations, on semi-decentralized architectures, of operators issued from optimal control for partial differential equations. Such operators are solutions to Riccati equations, which are nonlinear, and therefore do not fall within the scope of our paper.…”

Section: −θmentioning

confidence: 97%

“…The paper [6] covers a very restricted class of boundary value problems with observations and controls distributed over the entire space also. The method used in [15] is applicable to a much broader class of boundary value problems posed in bounded or unbounded domains, but with the same restriction on control and observation operators. In the present paper, the domain is bounded and the operators are not assumed to be distributed over the whole domain.…”

Section: −θmentioning

confidence: 99%

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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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Section: −θmentioning

confidence: 97%

Section: −θmentioning

confidence: 99%

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

Lenczner¹,

Montseny²,

Yakoubi³

2012

Math. Comp.

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“…In Section 7.3, there is an example of observation operator C that is not a function of Λ, while in the paper , it is the case for B the control operator. For boundary control or observation problems, it is impossible to find such isomorphisms. Nevertheless, in Section 7.4, we show how to proceed to address some boundary control problems. Multiscale models with controls at the microscale, as in and , are also possible applications.…”

Section: Bounded Control Operatorsmentioning

confidence: 99%

Semi-decentralized approximation of optimal control of distributed systems based on a functional calculus

Yakoubi

Lenczner

Ratier

2014

Optim. Control Appl. Meth.

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SummaryThis paper discusses a new approximation method for operators that are solution to an operational Riccati equation. The latter is derived from the theory of optimal control of linear problems posed in Hilbert spaces. The approximation is based on the functional calculus of self‐adjoint operators and the Cauchy formula. Under a number of assumptions, the approximation is suitable for implementation on a semi‐decentralized computing architecture in view of real‐time control. Our method is particularly applicable to problems in optimal control of systems governed by partial differential equations with distributed observation and control. Some relatively academic applications are presented for illustration. More realistic examples relating to microsystem arrays have already been published. Copyright © 2014 John Wiley & Sons, Ltd.

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“…This subsection is devoted to apply the approximation method introduced in [7] and [8]. We denote by Λ, the mapping :…”

Section: Functional Calculus Based Approximationmentioning

confidence: 99%

Modeling, Filtering and Optimization for AFM Arrays

Huang

Yakoubi

Lenczner

et al. 2012

2012 Second Workshop on Design, Control and Software Implementation for Distributed MEMS

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In this paper, we present new tools and results developed for Arrays of Microsystems and especially for Atomic Force Microscope (AFM) array design. For modeling, we developed a two-scale model of cantilever arrays in elastodynamics. A robust optimization toolbox is interfaced to aid for design before the microfabrication process. A model based algorithm of static state estimation using measurement of mechanical displacements by interferometry is stated. Quantization of interferometry data processing is analyzed for FPGA implementation. A robust H ∞ filtering problem of the coupled cantilevers is solved for time-invariant system with random noise effects. Our solution allows semi-decentralized computing based on functional calculus that can be implemented by networks of distributed electronic circuits as shown in a previous paper.

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Semi-decentralized approximation of optimal control for partial differential equations in bounded domains

Cited by 7 publications

References 5 publications

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

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

Semi-decentralized approximation of optimal control of distributed systems based on a functional calculus

Modeling, Filtering and Optimization for AFM Arrays

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