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Extended Euler–Lagrange and Hamiltonian Conditions in Optimal Control of Sweeping Processes with Controlled Moving Sets

Author

Listed:
  • Nguyen D. Hoang

    (Universidad de Concepción)

  • Boris S. Mordukhovich

    (Wayne State University)

Abstract

This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by applications to hysteresis, we consider a general setting where moving sets are given as inverse images of closed subsets of finite-dimensional spaces under nonlinear differentiable mappings dependent on both state and control variables. Developing the method of discrete approximations and employing generalized differential tools of first-order and second-order variational analysis allow us to derive nondegenerate necessary optimality conditions for such problems in extended Euler–Lagrange and Hamiltonian forms involving the Hamiltonian maximization. The latter conditions of the Pontryagin Maximum Principle type are the first in the literature for optimal control of sweeping processes with control-dependent moving sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:1:d:10.1007_s10957-018-1384-4
    DOI: 10.1007/s10957-018-1384-4
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    Cited by:

    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. Fernando Lobo Pereira & Nathalie T. Khalil, 2022. "A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 1022-1051, March.
    3. 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.
    4. 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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