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Well-Posedness and Stability of Discrete Approximations for Controlled Sweeping Processes with Time Delay

Author

Listed:
  • Boris Mordukhovich

    (Wayne State University)

  • Dao Nguyen

    (University of Michigan
    San Diego State University)

  • Trang Nguyen

    (Wayne State University)

  • Norma Ortiz-Robinson

    (Grand Valley State University)

  • Vinicio Ríos

    (Louisiana State University)

Abstract

This paper addresses optimal control problems for dynamical systems governed by a novel class of sweeping processes with time delay. We establish the well-posedness of such processes in the sense of the existence and uniqueness of feasible trajectories corresponding to feasible controls under fairly unrestrictive assumptions. We then construct a well-posed family of discrete approximations and find efficient conditions ensuring the stability of the discretized time-delayed sweeping process with respect to strong convergence of feasible and optimal solutions. This creates a bridge between the optimization of continuous-time and discrete-time sweeping control systems and justifies the effective use of discrete approximations in deriving optimality conditions and numerical techniques to solve the original time-delayed sweeping control problems via discrete approximations.

Suggested Citation

  • Boris Mordukhovich & Dao Nguyen & Trang Nguyen & Norma Ortiz-Robinson & Vinicio Ríos, 2025. "Well-Posedness and Stability of Discrete Approximations for Controlled Sweeping Processes with Time Delay," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-28, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02746-w
    DOI: 10.1007/s10957-025-02746-w
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