No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints
| Autor: | Monica Motta, Giovanni Fusco |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
State constraints Degeneracy Gap phenomena media_common.quotation_subject 0211 other engineering and technologies 49N25 34K45 49K15 02 engineering and technology 01 natural sciences Maximum principle FOS: Mathematics Applied mathematics 0101 mathematics Mathematics - Optimization and Control Normality Mathematics media_common Numerical Analysis Impulsive optimal control problems Maximum principle State constraints Gap phenomena Normality Degeneracy 021103 operations research Applied Mathematics 010102 general mathematics Extension (predicate logic) State (functional analysis) Lipschitz continuity Optimal control Infimum and supremum Constraint (information theory) Optimization and Control (math.OC) Impulsive optimal control problems Geometry and Topology Analysis |
| Zdroj: | Set-Valued and Variational Analysis. 29:519-550 |
| ISSN: | 1877-0541 1877-0533 |
| DOI: | 10.1007/s11228-021-00576-2 |
| Popis: | In 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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