Regional controllability for infinite-dimensional bilinear systems: approach and simulations

Zerrik, El Hassan; Sidi, Maawiya Ould

doi:10.1080/00207179.2011.632442

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Cited by 20 publications

(8 citation statements)

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“…Kafash and Delavarkhalafi in [7] use parameterization method for optimal control problems. Zerrik and Ould Sidi in [12][13][14]) use quadratic control problems to steer the position of infinite-dimensional bilinear systems to the desired state on specific sub-region. Zine and Ould Sidi in [15,16] treated quadratic control problems in the case of hyperbolic bi-linear systems.…”

Section: Introductionmentioning

confidence: 99%

Variational necessary conditions for optimal control problems

Sidi¹

2020

J. Math. Computer Sci.

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Section: Introductionmentioning

confidence: 99%

Variational necessary conditions for optimal control problems

Sidi¹

2020

J. Math. Computer Sci.

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“…η > 0 is a positive constant. This problem was considered by (Zerrik and al. 2011 see [14]) and solved using unbounded control set, which is difficult from numerical point of view.…”

Section: Introductionmentioning

confidence: 99%

Regional Quadratic Problem for Distributed Bilinear Systems With Bounded Controls

Sidi¹,

Beinane²

2014

Int. J. of Pure and Appl. Math.

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In this paper, we establish the approximate controllability of a class of distributed bilinear systems evolving in a spatial domain Ω. A bounded feedback control is used to drive a dynamical system from an initial state to a desired one in finite time, only on a subregion ω of the system domain. Our purpose is to prove that an regional optimal control exists, and characterized as a solution to an optimality system. Numerical approach is given and successfully illustrated by simulations.

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“…Here our problem is the following

({, \begin{array}{ll} Minimises ∥ u ∥_{L^{2} false(false[0, T false] false)}^{2} \\ u \in U_{M} \\ Under the constraint: \\ ∥ χ_{_{ω}} y_{u} false(T false) - y^{d} ∥_{L^{2} false(ω false)}^{2} is minimum \end{array})

The above problem was considered with unbounded controls, and an optimal control is obtained as solution of an optimality system (see [20]). Another approach was developed and allows an optimal control via the resolution of Riccati equation (see [21]).…”

Section: Introductionmentioning

confidence: 99%