Towards the theory of strong minimum in calculus of variations and optimal control: a view from variational analysis

The paper offers a self-contained account of the theory of first and second order necessary conditions for optimal control problems (with state constraints) based on new principles coming from variational analysis. The key element of the theory is reduction of the problem to unconstrained minimizati...

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Veröffentlicht in:Calculus of variations and partial differential equations Jg. 59; H. 2
1. Verfasser: Ioffe, A. D.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020
Springer Nature B.V
Schlagworte:
Analysis
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Control
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimal control
Optimization
Systems Theory
Theoretical
49J53
49K05
49K15
ISSN:0944-2669, 1432-0835
Online-Zugang:Volltext
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Zusammenfassung:The paper offers a self-contained account of the theory of first and second order necessary conditions for optimal control problems (with state constraints) based on new principles coming from variational analysis. The key element of the theory is reduction of the problem to unconstrained minimization of a Bolza-type functional with necessarily non-differentiable integrand and off-integral term. This allows to substantially shorten and simplify the proofs and to get new results not detected earlier by traditional variational techniques. This includes a totally new and easily verifiable second order necessary condition for a strong minimum in the classical problem of calculus of variations. The condition is a consequence of a new and more general second order necessary condition for optimal control problems with state constraints. Simple examples show that the new conditions may work when all known necessary conditions fail.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-020-01736-2