research-article

Specification-guided controller synthesis for linear systems and safe linear-time temporal logic

Authors:

Matthias Rungger,

Manuel Mazo, Jr.,

Paulo TabuadaAuthors Info & Claims

HSCC '13: Proceedings of the 16th international conference on Hybrid systems: computation and control

Pages 333 - 342

https://doi.org/10.1145/2461328.2461378

Published: 08 April 2013 Publication History

Abstract

In this paper we present and analyze a novel algorithm to synthesize controllers enforcing linear temporal logic specifications on discrete-time linear systems. The central step within this approach is the computation of the maximal controlled invariant set contained in a possibly non-convex safe set. Although it is known how to compute approximations of maximal controlled invariant sets, its exact computation remains an open problem. We provide an algorithm which computes a controlled invariant set that is guaranteed to be an under-approximation of the maximal controlled invariant set. Moreover, we guarantee that our approximation is at least as good as any invariant set whose distance to the boundary of the safe set is lower bounded. The proposed algorithm is founded on the notion of sets adapted to the dynamics and binary decision diagrams. Contrary to most controller synthesis schemes enforcing temporal logic specifications, we do not compute a discrete abstraction of the continuous dynamics. Instead, we abstract only the part of the continuous dynamics that is relevant for the computation of the maximal controlled invariant set. For this reason we call our approach specification guided. We describe the theoretical foundations and technical underpinnings of a preliminary implementation and report on several experiments including the synthesis of an automatic cruise controller. Our preliminary implementation handles up to five continuous dimensions and specifications containing up to 160 predicates defined as polytopes in about 30 minutes with less than 1 GB memory.

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cover image ACM Conferences

HSCC '13: Proceedings of the 16th international conference on Hybrid systems: computation and control

April 2013

378 pages

ISBN:9781450315678

DOI:10.1145/2461328

Program Chairs:
Calin Belta
Boston University, USA
,
Franjo Ivančić
NEC Laboratories America, USA

Copyright © 2013 ACM.

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Published: 08 April 2013

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HSCC '13: Computation and Control

April 8 - 11, 2013

Pennsylvania, Philadelphia, USA

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HSCC '13 Paper Acceptance Rate 40 of 86 submissions, 47%;

Overall Acceptance Rate 153 of 373 submissions, 41%

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Zhong BZamani MCaccamo M(2024)Formal Synthesis of Controllers for Uncertain Linear Systems Against -Regular Properties: A Set-Based ApproachIEEE Transactions on Automatic Control10.1109/TAC.2023.326739769:1(214-229)Online publication date: Jan-2024
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Macoveiciuc EReissig G(2023)On-the-Fly Symbolic Synthesis With Memory Reduction GuaranteesIEEE Transactions on Automatic Control10.1109/TAC.2022.318848368:4(2576-2583)Online publication date: Apr-2023
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