Damien Busatto-Gaston ; Benjamin Monmege ; Pierre-Alain Reynier - Optimal controller synthesis for timed systems

lmcs:7419 - Logical Methods in Computer Science, March 15, 2023, Volume 19, Issue 1 - https://doi.org/10.46298/lmcs-19(1:20)2023
Optimal controller synthesis for timed systemsArticle

Authors: Damien Busatto-Gaston ; Benjamin Monmege ; Pierre-Alain Reynier

    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.

    Volume: Volume 19, Issue 1
    Published on: March 15, 2023
    Accepted on: January 2, 2023
    Submitted on: April 29, 2021
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Computer Science and Game Theory,D.2.4

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