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

Boris Mordukhovich (), Dao Nguyen (), Trang Nguyen (), Norma Ortiz-Robinson () and Vinicio Ríos ()
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Boris Mordukhovich: Wayne State University
Dao Nguyen: University of Michigan
Trang Nguyen: Wayne State University
Norma Ortiz-Robinson: Grand Valley State University
Vinicio Ríos: Louisiana State University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 14, 28 pages

Abstract: 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.

Keywords: Optimal control; Sweeping processes; Time-delayed systems; Existence of solutions; Well-posedness; Discrete approximations; Stability; 49J24; 49J25; 49J53; 49M25; 93B35 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02746-w

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