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Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models

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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.

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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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Authors and Affiliations

  1. Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, via Trieste 63, 35121, Padova, Italy

    Giovanni Colombo

  2. Department of Mathematics, Wayne State University, Detroit, MI, USA

    Boris Mordukhovich & Dao Nguyen

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  1. Giovanni Colombo
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  2. Boris Mordukhovich
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  3. Dao Nguyen
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Correspondence to Boris Mordukhovich.

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Colombo, G., Mordukhovich, B. & Nguyen, D. Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models. J Optim Theory Appl 182, 439–472 (2019). https://doi.org/10.1007/s10957-019-01521-y

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