Discrete Approximations of a Controlled Sweeping Process

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• 作者：G. Colombo (1)
  R. Henrion (2)
  N. D. Hoang (3)
  B. S. Mordukhovich (4)
  
• 关键词：Optimal control ; Sweeping process ; Moving controlled polyhedra ; Dissipative differential inclusions ; Discrete approximations ; Variational analysis. ; 49J52 ; 49J53 ; 49K24 ; 49M25 ; 90C30
• 刊名：Set-Valued and Variational Analysis
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：23
• 期：1
• 页码：69-86
• 全文大小：389 KB
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  6. Colombo, G., Henrion, R., Hoang, N.D., Mordukhovich, B.S.: Optimal control of the sweeping process. Dyn. Contin. Discret. Impuls. Syst. Ser. B 19, 117鈥?59 (2012)
  7. Colombo, G., Henrion, R., Hoang, N.D., Mordukhovich, B.S.: Optimal control of the sweeping process over polyhedral controlled sets. preprint (2014)
  8. Colombo, G., Thibault, L.: Prox-regular sets and applications. In: Gao, D. Y., Motreanu, D. (eds.) Handbook of Nonconvex Analysis. International Press, Boston (2010)
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  16. Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, I: Basic Theory. Springer, Berlin (2006)
  17. Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, II: Applications. Springer, Berlin (2006)
  18. Moreau, J.J.: Rafle par un convexe variable I. S茅m. Anal. Convexe Montpellier Expos茅, 15 (1971)
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• 作者单位：G. Colombo (1)
  R. Henrion (2)
  N. D. Hoang (3)
  B. S. Mordukhovich (4)
  
  1. Department of Mathematics, University of Padova, Padua, Italy
  2. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
  3. Departamento de Matem谩tica, Universidad T茅chnica Federico Santa Mar铆a, Valpara铆so, Chile
  4. Department of Mathematics, Wayne State University, Detroit, Michigan, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1877-0541

文摘

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhedral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their analysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W 1,2 topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts.