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Set-Valued and Variational Analysis

, Volume 26, Issue 3, pp 607–629 | Cite as

A Maximum Principle for the Controlled Sweeping Process

  • Chems Eddine Arroud
  • Giovanni Colombo
Article

Abstract

We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin’s Maximum Principle type. The results are also discussed through an example. We combine techniques from Sene and Thibault (Journal of Nonlinear and Convex Analysis 15, 647–663, 2014) and from Brokate and Krejčí (Discrete and Continuous Dynamical Systems Series B 18, 331–348, 2013), which in particular deals with a different but related control problem. Our assumptions include the smoothness of the boundary of the moving set C(t), but, differently from Brokate and Krejčí, do not require strict convexity and time independence of C(t). Rather, a kind of inward/outward pointing condition is assumed on the reference optimal trajectory at the times where the boundary of C(t) is touched. The state space is finite dimensional.

Keywords

Mayer problem Adjoint equation Pontryagin maximum principle Moreau-Yosida approximation 

Mathematics Subject Classification (2010)

49J15 34G25 49J52 

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of MathematicsJijel UniversityJijelAlgeria
  2. 2.Mila University CenterMilaAlgeria
  3. 3.Dipartimento di Matematica “Tullio Levi-Civita”Università di PadovaPadovaItaly
  4. 4.I.N.d.A.M Research UnitPadovaItaly

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