A Maximum Principle for One Infinite Horizon Impulsive Control Problem

Khlopin, Dmitry

doi:10.1016/j.ifacol.2018.11.383

Cited by 2 publications

(1 citation statement)

References 14 publications

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“…Under a strong assumption on asymptotics of x and J , for infinite-horizon control problem with state constraints, a similar condition was also shown in [32,Theorem 6.1]. Under assumption of boundedness of gradients ∂ Ĵ ∂x (b; θ) , the necessity of (11a) is deduced for overtaking optimality in [7] and [34].…”

Section: Additional Transversality Conditions For the Pontryagin Maxi...mentioning

confidence: 67%

Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions

Khlopin¹

2019

Preprint

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We consider a Bolza-type infinite-horizon control problem with free right end. We propose a modification of Halkin's general construction of necessary conditions of optimality in which the transversality condition is obtained through the theorems on stability of subdifferentials. For the weakly overtaking criterion, a necessary boundary condition on co-state arc is deduced, regardless of any assumptions on the asymptotic behavior of trajectories, adjoint variables, or their derivatives. Regardless of any assumptions, the Pontryagin Maximum Principle with this boundary condition allows to educe some convex hull of co-state arcs, corresponding to the convex subdifferential of payoff function (fixing the optimal control) at infinity. In the case of smooth payoff function at infinity, this condition educes the unique co-state arc, and the corresponding co-state arc coincides with the solution of the Cauchy-type formula proposed by S. M. Aseev and A. V. Kryazhimskii. These results are illustrated with a pair of examples.

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Section: Additional Transversality Conditions For the Pontryagin Maxi...mentioning

confidence: 67%

Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions

Khlopin¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

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Necessary Conditions in Infinite-Horizon Control Problems that Need no Asymptotic Assumptions

Khlopin

2023

Set-Valued Var. Anal

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A Maximum Principle for One Infinite Horizon Impulsive Control Problem

Cited by 2 publications

References 14 publications

Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions

Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions

Necessary Conditions in Infinite-Horizon Control Problems that Need no Asymptotic Assumptions

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