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Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models

  • Giovanni Colombo
  • Boris MordukhovichEmail author
  • Dao Nguyen
Article
  • 27 Downloads

Abstract

The paper is mostly devoted to applications of a novel optimal control theory for perturbed sweeping/Moreau processes to two practical dynamical models. The first model addresses mobile robot dynamics with obstacles, and the second one concerns control and optimization of traffic flows. Describing these models as controlled sweeping processes with pointwise/hard control and state constraints and applying new necessary optimality conditions for such systems allow us to develop efficient procedures to solve naturally formulated optimal control problems for the models under consideration and completely calculate optimal solutions in particular situations.

Keywords

Optimal control Sweeping process Variational analysis Discrete approximations Necessary optimality conditions Robotics Traffic flows 

Mathematics Subject Classification

49K24 49J53 49M25 70B15 90B10 

Notes

Acknowledgements

Research of the second and third authors was partly supported by the USA National Science Foundation under grants DMS-1512846 and DMS-1808978, and by the USA Air Force Office of Scientific Research under grant #15RT0462. The research of the second author was also supported by the Australian Research Council under Discovery Project DP-190100555. The authors are thankful to Tan Cao for many useful discussions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Giovanni Colombo
    • 1
  • Boris Mordukhovich
    • 2
    Email author
  • Dao Nguyen
    • 2
  1. 1.Dipartimento di Matematica “Tullio Levi-Civita”Università di PadovaPadovaItaly
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

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