Ing. Jiří Fejlek (graduate student)

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advisor:doc. Dr. techn. Stefan Ratschan, Dipl.-Ing.
study start date:01.03.2018
study form:prezenční
state exam:10.09.2020
title of dissertation thesis:Optimal Control with Adversarial Events
POPIS_DISERTACNI_PRACE:Assume an ordinary differential equation with inputs. Classical optimal control is the problem of finding inputs such that resulting solution of the differential equation optimizes a given objective function. The thesis will study an extension of this problem where some random events beyond our control can influence the differential equation, and the goal is to optimize the expected value of the objective function. This amounts to optimal control for a certain class of stochastic hybrid dynamical systems [1].
The goal of this thesis topic will be the design of an algorithm for solving this problem that can efficiently solve benchmark problems of a size that goes beyond the capabilities of current methods.
Suggested basic ingredients will be: - Multiple shooting: a method that can solve highly non-trivial classical optimal control problems [2], but creates inputs that are not able to react to external events. - Approximate dynamic programming [3]: a method that efficiently solves the optimal control problem for Markov decision processes, which corresponds to the given problem, but without the presence of differential equations.
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Czech Technical Univeristy in Prague | Faculty of Nuclear Sciences and Physical Engineering | Department of Mathematics