Optimal Control of Sweeping Processes

Discrete approximations, optimality conditions, and applications of Moreau's sweeping process and its controlled variants.

Moreau’s sweeping process is a class of evolution differential inclusions in which the state is “swept” by the normal cone to a moving convex set — a powerful model for systems with unilateral constraints, friction, and contact dynamics. My research program develops the optimization and optimal-control theory for these processes, including their nonconvex and discontinuous variants.

Main lines of work

  • Existence and necessary optimality conditions for nonconvex perturbed sweeping processes, using generalized differentiation (Mordukhovich coderivatives) and discrete approximations.
  • Fully controlled sweeping processes where both the moving set and the perturbation field are control variables.
  • Variable-time / free-time problems where the terminal time is a decision variable, with finite-difference approximations.
  • Applications: nonlinear crowd motion models with obstacles; marine surface vehicle navigation; robotics; hysteresis in ODE systems.

Selected publications

This program has produced several papers in the Journal of Differential Equations, DCDS-B, IEEE Control Systems Letters, JOTA, and most recently Nonlinear Analysis: Hybrid Systems (accepted, 2026).

Collaborators

Boris S. Mordukhovich (Wayne State), Giovanni Colombo (Padova), Dao Nguyen (SDSU), Trang Nguyen (SDSU), Nguyen Nang Thieu (Institute of Mathematics, VAST), Nathalie T. Khalil, Fernando Lobo Pereira (Porto).

References