State and Time Transformations of Infinite Horizon Optimal Control Problems

Wenzke, Diana; Lykina, Valeriya; Pickenhain, Sabine

doi:10.1090/conm/619/12391

Cited by 2 publications

(3 citation statements)

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“…However, the number of immunized individuals shows a larger difference: 5 282 (constant maximum vaccination rate) versus 4 781 individuals (optimal control on finite horizont). The effect with respect to the terminal behaviour of the approximate control may be unexpected on the first glance but is typical for optimal control problems which should be modelled on an infinite horizont but are truncated by a finite horizont; see [12], [11], [19], and [26]. This can be interpreted as devil-may-care solution.…”

Section: Scenariomentioning

confidence: 99%

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Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

Thäter

Chudej

Pesch

2017

MBE

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In this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control problems with various kinds of constraints including mixed control-state and state constraints. After presenting the new model and implementing the optimal control problems by means of a first-discretize-then-optimize method, numerical results for six scenarios are discussed and compared to an analytical optimal control law based on Pontrygin's minimum principle that allows to verify these results as approximations of candidate optimal solutions.

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Section: Scenariomentioning

confidence: 99%

“…For techniques to deal with infinite horizon optimal control problems we refer to[8],[12],[11], and[26].…”

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confidence: 99%

Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

Thäter

Chudej

Pesch

2017

MBE

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“…[18,19]. It turns out that the transformed problem is not a classical optimal control problem with finite horizon, see [20], and a Pontryagin-type Maximum Principle remains hypothetical. In [19], a pseudospectral method was proposed as a direct approach.…”

Section: Introductionmentioning

confidence: 99%

An indirect pseudospectral method for the solution of linear-quadratic optimal control problems with infinite horizon

et al. 2015

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We consider a class of linear-quadratic infinite horizon optimal control problems in Lagrange form involving the Lebesgue integral in the objective. The key idea is to introduce weighted Sobolev spaces W 1 2 (IR + , μ) as state spaces and weighted Lebesgue spaces L 2 (IR + , μ) as control spaces into the problem setting. Then, the problem becomes an optimization problem in Hilbert spaces. We use the weight functions μ(t) = e ρt , ρ = 0 in our consideration. This problem setting gives us the possibility to extend the admissible set and simultaneously to be sure that the adjoint variable belongs to a Hilbert space too. For the class of problems proposed, existence results as well as a Pontryagin-type Maximum Principle, as necessary and sufficient optimality condition, can be shown. Based on this principle we develop a Galerkin method, coupled with the Gauss-Laguerre quadrature formulas as discretization scheme, to solve the problem numerically. Results are presented for the introduced model and different weight functions.

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State and Time Transformations of Infinite Horizon Optimal Control Problems

Cited by 2 publications

References 0 publications

Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

An indirect pseudospectral method for the solution of linear-quadratic optimal control problems with infinite horizon

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