An Existence Theorem for Control Problems with Unbounded Control Domain

1993 ◽  
Vol 12 (1) ◽  
pp. 171-178
Author(s):  
H. Kraut
Keyword(s):  
Existence Theorem ◽  
Control Problems ◽  
Unbounded Control

Existence of optimal controls for viscous flow problems

1992 ◽  
Vol 439 (1905) ◽  
pp. 81-102 ◽  
Keyword(s):  
Optimal Control ◽  
Flow Control ◽  
Viscous Flow ◽  
Existence Theorem ◽  
General Class ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Optimal Controls ◽  
Flow Problems ◽  
Existence Of Optimal Controls

A class of optimal control problems in viscous flow is studied. Main result is the existence theorem for optimal control. Three typical flow control problems are formulated within this general class.

scholarly journals Normality and gap phenomena in optimal unbounded control

2018 ◽  
Vol 24 (4) ◽  
pp. 1645-1673 ◽  
Author(s):  
Monica Motta ◽  
Franco Rampazzo ◽  
Richard Vinter
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Absolutely Continuous ◽  
Unbounded Control ◽  
Existence Of Minimizers ◽  
Continuous State ◽  
Control Dependence ◽  
Absolutely Continuous State

Optimal unbounded control problems with affine control dependence may fail to have minimizers in the class of absolutely continuous state trajectories. For this reason, extended impulsive versions – which cannot be of measure-theoretic type – have been investigated, in which the domain is enlarged to include discontinuous state trajectories of bounded variation, and for which existence of minimizers is guaranteed. It is of interest to know whether the passage from the original optimal control problem to its extension introduces an infimum gap. This paper provides sufficient conditions for the absence of an infimum gap based on normality of extremals. In certain cases, the normality conditions reduce to simple verifiable criteria, which improve on earlier, directly-derived sufficient conditions for no infimum gap.

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