Sparse and switching infinite horizon optimal controls with mixed-norm penalizations

Dante Kalise; Karl Kunisch; Zhiping Rao

doi:10.1051/cocv/2019038

Sparse and switching infinite horizon optimal controls with mixed-norm penalizations

Dante Kalise^*, Karl Kunisch, Zhiping Rao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.

Original language	English
Article number	2019038
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	26
DOIs	https://doi.org/10.1051/cocv/2019038
Publication status	Published - 2020
Externally published	Yes

Keywords

Dynamic programming
Infinite horizon control
Optimal control
Optimality conditions
Sparse controls
Switching controls

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10.1051/cocv/2019038

Cite this

@article{cd60dfef18594b3b9f107da7c93340dd,

title = "Sparse and switching infinite horizon optimal controls with mixed-norm penalizations",

abstract = "A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.",

keywords = "Dynamic programming, Infinite horizon control, Optimal control, Optimality conditions, Sparse controls, Switching controls",

author = "Dante Kalise and Karl Kunisch and Zhiping Rao",

note = "Funding Information: IResearch supported by the Imperial College London Research Fellowship program. IIResearch in part supported by the ERC advanced grant 668998 (OCLOC) under the EU{\textquoteright}s H2020 research program. IIIResearch in part supported by NSFC 11801422. Funding Information: Research in part supported by the ERC advanced grant 668998 (OCLOC) under the EU's H2020 research program. Research in part supported by NSFC 11801422. Publisher Copyright: {\textcopyright} 2020 EDP Sciences, SMAI.",

year = "2020",

doi = "10.1051/cocv/2019038",

language = "English",

volume = "26",

journal = "ESAIM - Control, Optimisation and Calculus of Variations",

issn = "1292-8119",

}

TY - JOUR

T1 - Sparse and switching infinite horizon optimal controls with mixed-norm penalizations

AU - Kalise, Dante

AU - Kunisch, Karl

AU - Rao, Zhiping

N1 - Funding Information: IResearch supported by the Imperial College London Research Fellowship program. IIResearch in part supported by the ERC advanced grant 668998 (OCLOC) under the EU’s H2020 research program. IIIResearch in part supported by NSFC 11801422. Funding Information: Research in part supported by the ERC advanced grant 668998 (OCLOC) under the EU's H2020 research program. Research in part supported by NSFC 11801422. Publisher Copyright: © 2020 EDP Sciences, SMAI.

PY - 2020

Y1 - 2020

N2 - A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.

AB - A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.

KW - Dynamic programming

KW - Infinite horizon control

KW - Optimal control

KW - Optimality conditions

KW - Sparse controls

KW - Switching controls

UR - http://www.scopus.com/inward/record.url?scp=85092045835&partnerID=8YFLogxK

U2 - 10.1051/cocv/2019038

DO - 10.1051/cocv/2019038

M3 - Article

AN - SCOPUS:85092045835

SN - 1292-8119

VL - 26

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

M1 - 2019038

ER -

Sparse and switching infinite horizon optimal controls with mixed-norm penalizations

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Keywords

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NSFC Young Scientists Fund 11801422

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Sparse and switching infinite horizon optimal controls with mixed-norm penalizations

Abstract

Keywords

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Fingerprint

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NSFC Young Scientists Fund 11801422

Cite this