Normality and Nondegeneracy of the Maximum Principle in Optimal Impulsive Control Under State Constraints

Monica Motta () and Caterina Sartori ()
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Monica Motta: University of Padua
Caterina Sartori: University of Padua

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 1, No 4, 44-71

Abstract: Abstract We investigate nondegenerate and normal forms of the maximum principle for general, free end-time, impulsive optimal control problems with state and endpoint constraints. We introduce constraint qualifications sufficient to avoid degeneracy or abnormality phenomena, which do not require any convexity and impose the existence of an inward pointing velocity just on the subset of times, in which the extended optimal trajectory has an outward pointing velocity (w.r.t. the state constraint). These conditions extend to impulsive problems some conditions, recently proposed by F. Fontes and H. Frankowska, for conventional optimization problems. The nontriviality of this extension is illustrated through some examples.

Keywords: Impulsive optimal control problems; Maximum principle; State constraints; Constraint qualifications; Normality; Degeneracy; 49N25; 49J15; 34K45 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01641-w

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