Nondegenerate necessary conditions for optimal impulsive control problems with state constraints

2004 ◽  
Author(s):  
A. Arutyunov ◽  
D. Karamzin ◽  
F. Pereira
Keyword(s):  
State Constraints ◽  
Necessary Conditions ◽  
Impulsive Control ◽  
Control Problems ◽  
Optimal Impulsive Control

scholarly journals No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints

2021 ◽  
Author(s):  
Giovanni Fusco ◽  
Monica Motta
Keyword(s):  
Original Problem ◽  
State Constraints ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Continuous Data ◽  
Lipschitz Continuous ◽  
Extended Sense ◽  
Unbounded Controls ◽  
Locally Lipschitz ◽  
Optimal Impulsive Control

AbstractIn this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data.

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