80 citations · 173 across the 18 of their papers we have counts for
25 papers
Optimality of delayed reward attainment under uncertainty
Chuwei Wang, Alexander Vladimirsky, Anastasia Bizyaeva
Decision making under uncertainty requires balancing the value of additional information against the cost of delaying the decision until that information becomes available. This ch…
Behavioral patterns and mean-field games in epidemiological models
Finnegan Buckley, Alexander Vladimirsky
We introduce a new type of Mean Field Game epidemiological models, in which subpopulations have different behavioral patterns: some are viewed as "highly rational" (choosing Nash-e…
Risk-aware stochastic control of a sailboat
MingYi Wang, Natasha Patnaik, Anne Somalwar +2
Sailboat path-planning is a natural hybrid control problem (due to continuous steering and occasional "tack-switching" maneuvers), with the actual path-to-target greatly affected b…
Optimal Driving Under Traffic Signal Uncertainty
Mallory E. Gaspard, Alexander Vladimirsky
We study driver's optimal trajectory planning under uncertainty in the duration of a traffic light's green phase. We interpret this as an optimal control problem with an objective…
Surveillance Evasion Through Bayesian Reinforcement Learning
Dongping Qi, David Bindel, Alexander Vladimirsky
We consider a task of surveillance-evading path-planning in a continuous setting. An Evader strives to escape from a 2D domain while minimizing the risk of detection (and immediate…
Stochastic Optimal Control of a Sailboat
Cole Miles, Alexander Vladimirsky
In match race sailing, competitors must steer their boats upwind in the presence of unpredictably evolving weather. Combined with the tacking motion necessary to make upwind progre…
Optimal Path-Planning with Random Breakdowns
Marissa Gee, Alexander Vladimirsky
We propose a model for path-planning based on a single performance metric that accurately accounts for the the potential (spatially inhomogeneous) cost of breakdowns and repairs. T…
Optimality and robustness in path-planning under initial uncertainty
Dongping Qi, Adam Dhillon, Alexander Vladimirsky
Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful,…
Quantifying and managing uncertainty in piecewise-deterministic Markov processes
Elliot Cartee, Antonio Farah, April Nellis +2
In piecewise-deterministic Markov processes (PDMPs) the state of a finite-dimensional system evolves continuously, but the evolutive equation may change randomly as a result of dis…
Control-Theoretic Models of Environmental Crime
Elliot Cartee, Alexander Vladimirsky
We present two models of perpetrators' decision-making in extracting resources from a protected area. It is assumed that the authorities conduct surveillance to counter the extract…
Time-Dependent Surveillance-Evasion Games
Elliot Cartee, Lexiao Lai, Qianli Song +1
Surveillance-Evasion (SE) games form an important class of adversarial trajectory-planning problems. We consider time-dependent SE games, in which an Evader is trying to reach its…
Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory
Mark Gluzman, Jacob G. Scott, Alexander Vladimirsky
Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradi…
Evasive path planning under surveillance uncertainty
Marc Aurèle Gilles, Alexander Vladimirsky
The classical setting of optimal control theory assumes full knowledge of the process dynamics and the costs associated with every control strategy. The problem becomes much harder…
Corner cases, singularities, and dynamic factoring
Dongping Qi, Alexander Vladimirsky
In Eikonal equations, rarefaction is a common phenomenon known to degrade the rate of convergence of numerical methods. The `factoring' approach alleviates this difficulty by deriv…
Anisotropic Challenges in Pedestrian Flow Modeling
Elliot Cartee, Alexander Vladimirsky
Macroscopic models of crowd flow incorporating individual pedestrian choices present many analytic and computational challenges. Anisotropic interactions are particularly subtle, b…
Piecewise-Deterministic Optimal Path Planning
Zhengdi Shen, Alexander Vladimirsky
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected…
A bi-criteria path planning algorithm for robotics applications
Zachary Clawson, Xuchu Ding, Brendan Englot +3
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path plannin…
Deterministic control of randomly-terminated processes
June Andrews, Alexander Vladimirsky
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programmin…
Causal Domain Restriction for Eikonal Equations
Zachary Clawson, Adam Chacon, Alexander Vladimirsky
Many applications require efficient methods for solving continuous shortest path problems. Such paths can be viewed as characteristics of static Hamilton-Jacobi equations. Several…
A fast implicit method for time-dependent Hamilton-Jacobi PDEs
Alexander Vladimirsky, Changxi Zheng
We present a new efficient computational approach for time-dependent first-order Hamilton-Jacobi-Bellman PDEs. Since our method is based on a time-implicit Eulerian discretization,…
A parallel Heap-Cell Method for Eikonal equations
Adam Chacon, Alexander Vladimirsky
Numerous applications of Eikonal equations prompted the development of many efficient numerical algorithms. The Heap-Cell Method (HCM) is a recent serial two-scale technique that h…
Fast two-scale methods for Eikonal equations
Adam Chacon, Alexander Vladimirsky
Fast Marching and Fast Sweeping are the two most commonly used methods for solving the Eikonal equation. Each of these methods performs best on a different set of problems. Fast Sw…
Optimal control with reset-renewable resources
Ryo Takei, Weiyan Chen, Zachary Clawson +2
We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space.…
An efficient method for multiobjective optimal control and optimal control subject to integral constraints
Ajeet Kumar, Alexander Vladimirsky
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on exten…