Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models
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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.
KeywordsOptimal control Sweeping process Variational analysis Discrete approximations Necessary optimality conditions Robotics Traffic flows
Mathematics Subject Classification49K24 49J53 49M25 70B15 90B10
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.
- 1.Moreau, J.J.: On unilateral constraints, friction and plasticity. In: Capriz, G., Stampacchia, G. (eds.): Proceedings of C.I.M.E. Summer Schools on new variational techniques in mathematical physics, pp. 173–322. Cremonese, Rome (1974)Google Scholar
- 2.Colombo, G., Thibault, L.: Prox-Regular Sets and Applications. In: Gao, D.Y., Motreanu, D. (eds.) Handbook of Nonconvex Analysis, pp. 99–182. International Press, Boston (2010)Google Scholar
- 13.Cao, T.H., Mordukhovich, B.S.: Applications of optimal control of a nonconvex sweeping process to optimization of the planar crowd motion model. Discrete Contin. Dyn. Syst. Ser. B. arXiv:1802.08083 (2018, to appear)
- 18.de Pinho, M.R., Ferreira, M.M., Smirnov, G.V.: Optimal control involving sweeping processes. Set-Valued Var. Anal. (2018, to appear)Google Scholar
- 19.Colombo, G., Mordukhovich, B.S., Nguyen, D.: Optimization of a perturbed sweeping process by constrained discontinuous controls. arXiv:1808.04041 (2018)
- 20.Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, II: Applications. Springer, Berlin (2006)Google Scholar
- 22.Venel, J.: Modelisation Mathematiques et Numerique de Mouvements de Foule. Ph.D. Thesis. Universite Paris XI (2008)Google Scholar