Crowd Motion & Marine Vehicle Control

Optimal control of nonconvex sweeping processes applied to pedestrian dynamics, evacuation, and autonomous marine surface vehicles.

Sweeping-process control theory has powerful real-world applications when the state constraints encode physical non-overlap or boundary conditions. Two application threads I have pursued:

Crowd motion models

The planar crowd motion model treats each pedestrian as a disk constrained not to overlap with others or with fixed obstacles. The resulting nonconvex sweeping process governs the velocity field, and the optimal-control problem seeks evacuation strategies, optimal egress paths, or congestion-minimizing flows.

  • Joint work with B.S. Mordukhovich (Wayne State) and Giovanni Colombo (Padova).
  • Bilevel sweeping control formulations (with N.T. Khalil and F.L. Pereira) allow leader–follower dynamics.
  • Models with obstacles handled in IEEE Control Systems Letters (2021).

Marine surface vehicles

Free-time / variable-time sweeping process control models the navigation of an autonomous marine surface vehicle that must reach a destination while avoiding obstacles (other vessels, shorelines, exclusion zones). Optimization is over both the steering control and the (free) terminal time.

  • Joint work with N.T. Khalil, B.S. Mordukhovich, D. Nguyen, T. Nguyen, F.L. Pereira.
  • Published in IEEE Control Systems Letters (2021).

Ongoing extensions

  • Reinforcement learning in nonsmooth dynamical systems, including policy-gradient methods for mean-variance portfolio optimization under regime-switching (with L. Vu, in preparation).
  • Optimal control of ODE systems with hysteresis via discrete approximations.
  • Robotics applications of controlled sweeping processes.

References