Rutkowski, Michał, Ph.D. (2011) Games for optimal controller synthesis on hybrid automata. PhD thesis, University of Warwick.

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Abstract

Hybrid automata are an extension of finite automata obtained by augmenting
them with a set of real-valued variables. Hybrid automata are a natural model for
hybrid systems, i.e., systems that exhibit both discrete and continuous behaviour.
Such systems naturally arise when studying the interaction of a digital controller
with an analogue plant. In this thesis we study the problem of optimal controller
synthesis for such systems. The goal is to design a control program that will ensure
that a system behaves optimally regardless of some uncontrollable external
factors. We study this problem from the perspective of two-player games on hybrid
automata.
In this thesis two variants of hybrid automata are being considered: singleclock
timed automata and hybrid automata with strong resets. The first model
allows us to capture the passage of time between discrete events, and the other
model allows us to capture the more complex dynamics the hybrid systems.
The controller synthesis problem is modelled as follows. There are two players:
the controller and the adversarial environment. Their interaction is viewed as
a multi-stage process, in which the two players interact to create an execution of
the hybrid automaton. The problem of synthesising an optimal controller is: given
a certain optimisation objective, compute an 'optimal' strategy for the controller
player. Executions of the hybrid automaton are assigned two quantities: the price
and the reward. Two optimisation objectives are considered: price-per-reward ratio
of an infinite execution and the price of reaching a certain state of the hybrid
automaton (reachability-price).
In this thesis we prove that optimal controllers for the reachability-price objective
can be synthesised on single-clock timed automata in EXPTIME. Furthermore,
we prove that optimal controllers for reachability-price and average-price-perreward
objectives can be synthesised on hybrid automata with strong resets.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Sequential machine theory, Game theory
Official Date:	September 2011
Dates:	Date Event September 2011 Submitted
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Jurdziński, Marcin ; Lazić, Ranko
Extent:	x, 228 leaves : ill., charts
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/45832

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