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Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models

Author

Listed:
  • Giovanni Colombo

    (Università di Padova)

  • Boris Mordukhovich

    (Wayne State University)

  • Dao Nguyen

    (Wayne State University)

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.

Suggested Citation

  • Giovanni Colombo & Boris Mordukhovich & Dao Nguyen, 2019. "Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 439-472, August.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-019-01521-y
    DOI: 10.1007/s10957-019-01521-y
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    References listed on IDEAS

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    1. Abderrahim Jourani & Emilio Vilches, 2017. "Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 91-116, April.
    2. Samir Adly, 2019. "A Coderivative Approach to the Robust Stability of Composite Parametric Variational Systems: Applications in Nonsmooth Mechanics," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 62-90, January.
    3. Nguyen D. Hoang & Boris S. Mordukhovich, 2019. "Extended Euler–Lagrange and Hamiltonian Conditions in Optimal Control of Sweeping Processes with Controlled Moving Sets," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 256-289, January.
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    Citations

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    Cited by:

    1. Aram Arutyunov & Dmitry Karamzin, 2020. "A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 697-723, March.
    2. Stanisław Migórski, 2020. "Optimal Control of History-Dependent Evolution Inclusions with Applications to Frictional Contact," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 574-596, May.

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