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Optimal Control of History-Dependent Evolution Inclusions with Applications to Frictional Contact

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  • Stanisław Migórski

    (Chengdu University of Information Technology
    Jagiellonian University in Krakow)

Abstract

In this paper, we study a class of subdifferential evolution inclusions involving history-dependent operators. First, we improve an existence and uniqueness theorem and prove the continuous dependence result in the weak topologies. Next, we establish the existence of optimal solution to an optimal control problem for the evolution inclusion. Finally, we illustrate the results by an example of an optimal control of a dynamic frictional contact problem in mechanics, whose weak formulation is the evolution variational inequality.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01659-0
    DOI: 10.1007/s10957-020-01659-0
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    References listed on IDEAS

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    1. 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.
    2. 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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