Set-Valued and Variational Analysis

, Volume 19, Issue 2, pp 203–235 | Cite as

Optimal Control of Non-convex Measure-driven Differential Inclusions



Necessary conditions for optimality in control problems with differential-inclusion dynamics have recently been developed in the non-convex case by Clarke, Vinter, and others. Using appropriate reparametrizations of the time variable, we extend these results to systems whose dynamics involve a differential inclusion where a vector-valued measure appears. An auxiliary result central to our proof is an extension of existing free end-time necessary conditions to Clarke’s stratified framework.


Optimal control Necessary conditions Impulsive systems Measure-driven dynamics 

Mathematics Subject Classifications (2010)

49N25 49K21 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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