Optimal control of ODE systems involving a rate independent variational inequality

Brokate, Martin; Krejčı́, Pavel

doi:10.3934/dcdsb.2013.18.331

Cited by 69 publications

(72 citation statements)

References 8 publications

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“…In particular, [13] contains a set of necessary conditions for local minima which are derived by passing to the limit along suitable discrete approximations. Some partial results on necessary conditions for an optimal control problem acting on the perturbation f were obtained in [21], while the first complete achievement of this type appeared in [6]. The present paper owes to [6] several ideas.…”

Section: Introductionmentioning

confidence: 88%

“…Some partial results on necessary conditions for an optimal control problem acting on the perturbation f were obtained in [21], while the first complete achievement of this type appeared in [6]. The present paper owes to [6] several ideas. The problem studied in [6] involves a controlled ODE, coupled with a sweeping process with a constant moving set C, and an adjoint equation together with Pontryagin's Maximum Principle are derived by passing to the limit along suitable Moreau-Yosida approximations.…”

Section: Introductionmentioning

confidence: 88%

“…The present paper owes to [6] several ideas. The problem studied in [6] involves a controlled ODE, coupled with a sweeping process with a constant moving set C, and an adjoint equation together with Pontryagin's Maximum Principle are derived by passing to the limit along suitable Moreau-Yosida approximations. The set C is required to be both smooth and uniformly convex.…”

Section: Introductionmentioning

confidence: 99%

“…The set C is required to be both smooth and uniformly convex. The dynamics considered in [6] is different from (1.3), but the main difficulty -namely the discontinuity of ∇d C (·) at boundary points -is exactly the same. In [6], this issue is solved by imposing enough smoothness on ∂C(t) and via a smooth extension of d C up to the interior of C(t).…”

Section: Introductionmentioning

confidence: 99%

“…The results are also discussed through an example. We combine techniques from [19] and from [6], which in particular deals with a different but related control problem. Our assumptions include the smoothness of the boundary of the moving set C(t), but, differently from [6], do not require strict convexity.…”

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confidence: 99%

See 4 more Smart Citations

A Maximum Principle for the Controlled Sweeping Process

Arroud

Colombo

2017

Set-Valued Var. Anal

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Abstract. We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin's Maximum Principle type. The results are also discussed through an example. We combine techniques from [19] and from [6], which in particular deals with a different but related control problem. Our assumptions include the smoothness of the boundary of the moving set C(t), but, differently from [6], do not require strict convexity. Rather, a kind of inward/outward pointing condition is assumed on the reference optimal trajectory at the times where the boundary of C(t) is touched. The state space is finite dimensional.

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A Maximum Principle for the Controlled Sweeping Process

Arroud

Colombo

2017

Set-Valued Var. Anal

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The Space-Time Representation for Optimal Impulsive Control Problems with Hysteresis

Samsonyuk

2019

Communications in Computer and Information Science

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Global existence and Hadamard differentiability of hysteresis reaction–diffusion systems

Münch

2017

J. Evol. Equ.

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We consider a class of semilinear parabolic evolution equations subject to a hysteresis operator and a Bochner-Lebesgue integrable source term. The underlying spatial domain is allowed to have a very general boundary. In the first part of the paper, we apply semigroup theory to prove well-posedness and boundedness of the solution operator. Rate independence in reaction-diffusion systems complicates the analysis, since the reaction term acts no longer local in time. This demands careful estimates when working with semigroup methods. In the second part, we show Lipschitz continuity and Hadamard differentiability of the solution operator. We use fixed point arguments to derive a representation for the derivative in terms of the evolution system. Finally, we apply our results to an optimal control problem in which the source term acts as a control function and show existence of an optimal solution.

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Optimal control of ODE systems involving a rate independent variational inequality

Cited by 69 publications

References 8 publications

A Maximum Principle for the Controlled Sweeping Process

A Maximum Principle for the Controlled Sweeping Process

The Space-Time Representation for Optimal Impulsive Control Problems with Hysteresis

Global existence and Hadamard differentiability of hysteresis reaction–diffusion systems

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