Optimal controller synthesis for timed systems

Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the cumulative weight while reaching a target. Used in a reactive synthesis perspective, this quantitative extension of timed games allows one to measure the q...

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Bibliographic Details
Published in:Logical methods in computer science Vol. 19, Issue 1
Main Authors: Busatto-Gaston, Damien, Monmege, Benjamin, Reynier, Pierre-Alain
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science Association 15.03.2023
Logical Methods in Computer Science e.V
Subjects:
Computer Science
computer science - computer science and game theory
computer science - logic in computer science
Computer Science and Game Theory
d.2.4
Formal Languages and Automata Theory
Logic in Computer Science
computational game theory
timed automata
weighted timed games
quantitative constraints
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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Summary:Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the cumulative weight while reaching a target. Used in a reactive synthesis perspective, this quantitative extension of timed games allows one to measure the quality of controllers in real-time systems. Weighted timed games are notoriously difficult and quickly undecidable, even when restricted to non-negative weights. For non-negative weights, the largest class that can be analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the value problem is undecidable, the authors show how to approximate the value by considering regions with a refined granularity. In this work, we extend this class to incorporate negative weights, allowing one to model energy for instance, and prove that the value can still be approximated, with the same complexity. A small restriction also allows us to obtain a class of decidable weighted timed games with negative weights and an arbitrary number of clocks. In addition, we show that a symbolic algorithm, relying on the paradigm of value iteration, can be used as an approximation/computation schema over these classes. We also consider the special case of untimed weighted games, where the same fragments are solvable in polynomial time: this contrasts with the pseudo-polynomial complexity, known so far, for weighted games without restrictions.
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-19(1:20)2023