Set-Valued and Variational Analysis

, Volume 19, Issue 2, pp 203-235

First online:

Optimal Control of Non-convex Measure-driven Differential Inclusions

  • Warren Joseph CodeAffiliated withDepartment of Mathematics, University of British Columbia Email author 
  • , Philip D. LoewenAffiliated withDepartment of Mathematics, University of British Columbia

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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