Alexander B. Vladimirsky, Cornell University
"Stochastic switching systems: abrupt context changes and structured uncertainty"
Abstract: Piecewise-deterministic Markov processes (PDMPs) provide an excellent framework for modeling non-diffusive random perturbations. They are particularly useful for modeling abrupt changes in global environment (e.g., an onset of El Niño or an outcome of elections), changes in capabilities of the controlled systems (e.g., a partial breakdown of a robot on Mars), or uncertainty due to time-structured data acquisition (e.g., a just discovered location of an emergency). Both the optimality and robustness of system performance require advance planning, using statistical information about possible and likely context switches to prepare before those switches actually happen. (E.g., should a fully functional rover take a shorter risky path on Mars if it might lead to a breakdown? Should it ever stop and run diagnostics along that path to reassess the likelihood of such breakdowns? Should a foraging animal plan to visit the most food-rich part of the forest if an encounter with predators is likely along the way? How much of a detour might be justified? Should an idle ambulance be repositioned in between the emergency calls to improve the response time to the next call? ) In this talk, I will provide an introduction to the challenges of controlling PDMPs, illustrating them with simple examples motivated by robotics, sailboat racing, behavioral ecology, and surveillance-evasion applications.
Bio: Alex Vladimirsky is an applied mathematician working at Cornell University. His research interests include nonlinear PDEs, dynamical systems, optimal control & differential games, numerical analysis, mathematical biology, and algorithms on graphs. His past and current projects include efficient numerics for (& homogenization of) Hamilton-Jacobi PDEs, multiobjective & randomly-terminated optimal control, uncertainty quantification in randomly-switching systems, multi-population mean-field games, surveillance-evasion games under uncertainty, seismic imaging, 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.
This seminar will be offered in a hybrid format. Please contact [email protected] ahead of time for the Zoom link.
