Title
Surveillance-evasion games under uncertainty
Abstract
Adversarial path planning problems are important in robotics applications and in modeling the behavior of humans in dangerous environments. Surveillance-Evasion (SE) games form an important subset of such problems and require a blend of numerical techniques from multiobjective dynamic programming, game theory, numerics for Hamilton-Jacobi PDEs, and convex optimization. We model the basic SE problem as a semi-infinite zero-sum game between two players: an Observer (O) and an Evader (E) traveling through a domain with occluding obstacles. O chooses a pdf over a finite set of predefined surveillance plans, while E chooses a pdf over an infinite set of trajectories that bring it to a target location. The focus of this game is on “E’s expected cumulative exposure to O”, and we have recently developed an algorithm for finding the Nash Equilibrium open-loop policies for both players. I will use numerical experiments to illustrate algorithmic extensions to handle multiple Evaders, moving Observes, and anisotropic observation sensors. Joint work with M.Gilles, E.Cartee, and REU participants.
Bio
Alex Vladimirsky is an applied mathematician at Cornell University, whose research interests include numerical analysis, nonlinear PDEs, dynamical systems, optimal control & differential games, mathematical biology, and algorithms on graphs. His past and current projects include numerical methods for (& homogenization of) Hamilton-Jacobi PDEs, multiobjective & randomly-terminated optimal control, uncertainty quantification in randomly-switching systems, multipopulation mean-field games, surveillance-evasion games under uncertainty, inverse problems in geophysical explorations, dimensional reduction in turbulent combustion, approximation of invariant manifolds, macro-scale models of pedestrian interactions, optimization of drug therapies for cancer patients, models of microbial competition, sailboat navigation under wind-pattern uncertainty, behavioral ecology, immunology, and traffic engineering. Vladimirsky joined Cornell University in 2001 after receiving his Ph.D in Applied Mathematics at UC Berkeley under supervision of James Sethian . Vladimirsky’s research has been partially funded by the US National Science Foundation, the Air Force Office of Scientific Research, the Simons Foundation, and the Royal Society (through a Wolfson Visiting Fellowship to support his sabbatical year at Imperial College London in 2025-26).