Time optimal boundary controls for the heat equation

Micu, Sorin; Rovenţa, Ionel; Tucsnak, Marius

doi:10.1016/j.jfa.2012.04.009

Cited by 52 publications

(57 citation statements)

References 26 publications

(33 reference statements)

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“…Let us also note that since, as mentioned in Remark 5.1, the property R ∞ τ = X, no longer follows from the exact controllability in time τ of (A, B), the above mentioned duality results cannot be applied to characterize by duality the property R ∞ τ = X. However, we have the following result, which goes back to [30] (see also [22 …”

Section: Remark 51 We Have Seen In Proposition 21 That For Boundedmentioning

confidence: 79%

Maximum Principle and Bang-Bang Property of Time Optimal Controls for Schrödinger-Type Systems

Lohéac¹,

Tucsnak²

2013

SIAM J. Control Optim.

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We consider the time optimal control problem, with a point target, for a class of infinite dimensional systems with a dynamics governed by an abstract Schrödinger type equation. The main results establish a Pontryagyn type maximum principle and give sufficient conditions for the bangbang property of optimal controls. The results are then applied to some systems governed by partial differential equations. The paper ends by a discussion of possible extensions and by stating some open problems.

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Section: Remark 51 We Have Seen In Proposition 21 That For Boundedmentioning

confidence: 79%

Maximum Principle and Bang-Bang Property of Time Optimal Controls for Schrödinger-Type Systems

Lohéac¹,

Tucsnak²

2013

SIAM J. Control Optim.

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“…Recently, a general class of optimal control problems described by delay differential inclusions in infinite dimensions with finitely has been studied in Mordukhovich et al [6,7], and Micu et al [8] developed the time optimal boundary controls for the heat equation. In [9], Krakowiak studied the time optimal control problem for retarded parabolic systems with the Neumann boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Time Optimal Control of Semilinear Control Systems Involving Time Delays

Jeong

Son

2014

J Optim Theory Appl

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This paper investigates the time optimal control problem to a target set for semilinear control systems involving time delays or memories when a principal operator is unbounded by the construction of a fundamental solution and an easy consequence of the definition of real interpolation spaces. A convergence theorem of time optimal controls for the given semilinear retarded system to a point target set is also given.

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“…In the recent paper [13], the existence, uniqueness and bang-bang property for the boundary time-optimal controls of the heat equation are shown in the case of rectangular domains. It is proved that an observation inequality for the solutions of the heat equation with a finite number of modes and a careful estimate of the corresponding control cost enable us to apply the Lebeau-Robbiano method mentioned above and to solve the problem.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A time-optimal boundary controllability problem for the heat equation in a ball

Micu¹,

Temereancă²

2014

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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The aim of this paper is to study a boundary time-optimal control problem for the heat equation in a two-dimensional ball. The main ingredient is the extension of a result concerning Müntz polynomials due to Borwein and Erdélyi that allows us to prove an observability inequality for the dynamical system's truncation to a finite number of modes. This result, combined with a well-known Lebeau-Robbiano argument used to show the null-controllability of parabolic type equations, enables us to deduce the existence, uniqueness and bang-bang properties for the boundary time-optimal control.

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Time optimal boundary controls for the heat equation

Cited by 52 publications

References 26 publications

Maximum Principle and Bang-Bang Property of Time Optimal Controls for Schrödinger-Type Systems

Maximum Principle and Bang-Bang Property of Time Optimal Controls for Schrödinger-Type Systems

Time Optimal Control of Semilinear Control Systems Involving Time Delays

A time-optimal boundary controllability problem for the heat equation in a ball

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