Controller Synthesis Made Real: Reach-Avoid Specifications and Linear Dynamics

Chuchu Fan, Umang Mathur, Sayan Mitra, Mahesh Viswanathan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We address the problem of synthesizing provably correct controllers for linear systems with reach-avoid specifications. Our solution uses a combination of an open-loop controller and a tracking controller, thereby reducing the problem to smaller tractable problems. We show that, once a tracking controller is fixed, the reachable states from an initial neighborhood, subject to any disturbance, can be over-approximated by a sequence of ellipsoids, with sizes that are independent of the open-loop controller. Hence, the open-loop controller can be synthesized independently to meet the reach-avoid specification for an initial neighborhood. Exploiting several techniques for tightening the over-approximations, we reduce the open-loop controller synthesis problem to satisfiability over quantifier-free linear real arithmetic. The overall synthesis algorithm, computes a tracking controller, and then iteratively covers the entire initial set to find open-loop controllers for initial neighborhoods. The algorithm is sound and, for a class of robust systems, is also complete. We present RealSyn, a tool implementing this synthesis algorithm, and we show that it scales to several high-dimensional systems with complex reach-avoid specifications.

Original languageEnglish (US)
Title of host publicationComputer Aided Verification - 30th International Conference, CAV 2018, Held as Part of the Federated Logic Conference, FloC 2018, Proceedings
EditorsGeorg Weissenbacher, Hana Chockler
PublisherSpringer-Verlag Berlin Heidelberg
Pages347-366
Number of pages20
ISBN (Print)9783319961446
DOIs
StatePublished - 2018
Event30th International Conference on Computer Aided Verification, CAV 2018 Held as Part of the Federated Logic Conference, FloC 2018 - Oxford, United Kingdom
Duration: Jul 14 2018Jul 17 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10981 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other30th International Conference on Computer Aided Verification, CAV 2018 Held as Part of the Federated Logic Conference, FloC 2018
CountryUnited Kingdom
CityOxford
Period7/14/187/17/18

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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