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.