Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00100737" target="_blank" >RIV/00216224:14310/18:00100737 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1051/cocv/2017070" target="_blank" >http://dx.doi.org/10.1051/cocv/2017070</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/cocv/2017070" target="_blank" >10.1051/cocv/2017070</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity

Popis výsledku v původním jazyce

The main focus of this paper is to develop a sufficiency criterion for optimality in nonlinear optimal control problems defined on time scales. In particular, it is shown that the coercivity of the second variation together with the controllability of the linearized dynamic system are sufficient for the weak local minimality. The method employed is based on a direct approach using the structure of this optimal control problem. The second aim pertains to the sensitivity analysis for parametric control problems defined on time scales with separately varying state endpoints. Assuming a slight strengthening of the sufficiency criterion at a base value of the parameter, the perturbed problem is shown to have a weak local minimum and the corresponding multipliers are shown to be continuously differentiable with respect to the parameter. A link is established between (i) a modification of the shooting method for solving the associated boundary value problem, and (ii) the sufficient conditions involving the coercivity of the accessory problem, as opposed to the Riccati equation, which is also used for this task. This link is new even for the continuous time setting.

Název v anglickém jazyce

Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity

Popis výsledku anglicky

The main focus of this paper is to develop a sufficiency criterion for optimality in nonlinear optimal control problems defined on time scales. In particular, it is shown that the coercivity of the second variation together with the controllability of the linearized dynamic system are sufficient for the weak local minimality. The method employed is based on a direct approach using the structure of this optimal control problem. The second aim pertains to the sensitivity analysis for parametric control problems defined on time scales with separately varying state endpoints. Assuming a slight strengthening of the sufficiency criterion at a base value of the parameter, the perturbed problem is shown to have a weak local minimum and the corresponding multipliers are shown to be continuously differentiable with respect to the parameter. A link is established between (i) a modification of the shooting method for solving the associated boundary value problem, and (ii) the sufficient conditions involving the coercivity of the accessory problem, as opposed to the Riccati equation, which is also used for this task. This link is new even for the continuous time setting.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonovské a symplektické systémy: oscilační a spektrální teorie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ESAIM: Control, Optimisation and Calculus of Variations

ISSN

1292-8119

e-ISSN

—

Svazek periodika

24

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

30

Strana od-do

1705-1734

Kód UT WoS článku

000461018200017

EID výsledku v databázi Scopus

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