13 papers
Drone Swarm Energy Management
Michael Z. Zgurovsky, Pavlo O. Kasyanov, Liliia S. Paliichuk
This note presents an analytical framework for decision-making in drone swarm systems operating under uncertainty, based on the integration of Partially Observable Markov Decision…
Markov Decision Processes with Incomplete Information and Semi-Uniform Feller Transition Probabilities
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with sem…
Semi-Uniform Feller Stochastic Kernels
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduce…
Average Cost Markov Decision Processes with Semi-Uniform Feller Transition Probabilities
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper studies average-cost Markov decision processes with semi-uniform Feller transition probabilities. This class of MDPs was recently introduced by the authors to study MDPs…
A Class of Solvable Markov Decision Models with Incomplete Information
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper investigates natural conditions for the existence of optimal policies for a Markov decision process with incomplete information (MDPII) and with expected total costs. Th…
An example showing that A-lower semi-continuity is essential for minimax continuity theorems
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
Recently Feinberg et al. [arXiv:1609.03990] established results on continuity properties of minimax values and solution sets for a function of two variables depending on a paramete…
Solutions for Zero-Sum Two-Player Games with Noncompact Decision Sets and Unbounded Payoffs
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision s…
Uniform Global Attractors for Non-Autonomous Dissipative Dynamical Systems
Michael Zgurovsky, Mark Gluzman, Nataliia Gorban +3
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensiona…
Continuity of Equilibria for Two-Person Zero-Sum Games with Noncompact Action Sets and Unbounded Payoffs
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper extends Berge's maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-…
Uniform Fatou's Lemma
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
Fatou's lemma is a classic fact in real analysis that states that the limit inferior of integrals of functions is greater than or equal to the integral of the inferior limit. This…
Convergence of Probability Measures and Markov Decision Models with Incomplete Information
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First,…
Partially Observable Total-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities
Eugene A. Feinberg, Pavlo O. Kasyanov, Michael Z. Zgurovsky
This paper describes sufficient conditions for the existence of optimal policies for Partially Observable Markov Decision Processes (POMDPs) with Borel state, observation, and acti…
Existence of Strong Solutions for the 3D Navier-Stokes System
Michael Z. Zgurovsky, Pavlo O. Kasyanov
Regularity properties of strong solutions are considered.