Article

Reachability analysis of multi-affine systems

Authors:

Marius Kloetzer,

Calin BeltaAuthors Info & Claims

HSCC'06: Proceedings of the 9th international conference on Hybrid Systems: computation and control

Pages 348 - 362

https://doi.org/10.1007/11730637_27

Published: 29 March 2006 Publication History

Abstract

We present a technique for reachability analysis of continuous multi-affine systems based on rectangular partitions. The method is iterative. At each step, finer partitions and larger discrete quotients are produced. We exploit some interesting convexity properties of multi-affine functions on rectangles to show that the construction of the discrete quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. The methodology promises to be easily extendable to rectangular hybrid automata with multi-affine vector fields and is expected to find important applications in analysis of biological networks and robot control.

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M. Kloetzer and C. Belta, "Reachability analysis of multi-affine systems (ramas)," URL http://iasi.bu.edu/~software/reach-ma.htm.

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Yang IBecker-Weimann SBissell MTomlin CBelta CIvančić F(2013)One-shot computation of reachable sets for differential gamesProceedings of the 16th international conference on Hybrid systems: computation and control10.1145/2461328.2461359(183-192)Online publication date: 8-Apr-2013
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Althoff MBelta CIvančić F(2013)Reachability analysis of nonlinear systems using conservative polynomialization and non-convex setsProceedings of the 16th international conference on Hybrid systems: computation and control10.1145/2461328.2461358(173-182)Online publication date: 8-Apr-2013
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Information

Published In

cover image Guide Proceedings

HSCC'06: Proceedings of the 9th international conference on Hybrid Systems: computation and control

March 2006

582 pages

ISBN:3540331700

Editors:
João P. Hespanha
Center for Control, Dynamical Systems and Computation, University of California, Santa Barbara, CA
,
Ashish Tiwari
Center for Control, Dynamical Systems and Computation, SRI International, 333 Ravenswood Ave, Menlo Park, CA, U.S.A

Sponsors

University of California, Santa Barbara
National Science Foundation, USA
SRI Intl: SRI International

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 29 March 2006

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Cited By

Yang IBecker-Weimann SBissell MTomlin CBelta CIvančić F(2013)One-shot computation of reachable sets for differential gamesProceedings of the 16th international conference on Hybrid systems: computation and control10.1145/2461328.2461359(183-192)Online publication date: 8-Apr-2013
https://dl.acm.org/doi/10.1145/2461328.2461359
Althoff MBelta CIvančić F(2013)Reachability analysis of nonlinear systems using conservative polynomialization and non-convex setsProceedings of the 16th international conference on Hybrid systems: computation and control10.1145/2461328.2461358(173-182)Online publication date: 8-Apr-2013
https://dl.acm.org/doi/10.1145/2461328.2461358
Sassi MTestylier RDang TGirard A(2012)Reachability analysis of polynomial systems using linear programming relaxationsProceedings of the 10th international conference on Automated Technology for Verification and Analysis10.1007/978-3-642-33386-6_12(137-151)Online publication date: 3-Oct-2012
https://dl.acm.org/doi/10.1007/978-3-642-33386-6_12
Dang TTestylier RCaccamo MFrazzoli EGrosu R(2011)Hybridization domain construction using curvature estimationProceedings of the 14th international conference on Hybrid systems: computation and control10.1145/1967701.1967721(123-132)Online publication date: 12-Apr-2011
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Dang TMaler OTestylier RJohansson KYi W(2010)Accurate hybridization of nonlinear systemsProceedings of the 13th ACM international conference on Hybrid systems: computation and control10.1145/1755952.1755956(11-20)Online publication date: 12-Apr-2010
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Pace GSchneider G(2008)Relaxing Goodness Is Still GoodProceedings of the 5th international colloquium on Theoretical Aspects of Computing10.1007/978-3-540-85762-4_19(274-289)Online publication date: 1-Sep-2008
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Klaedtke FRatschan SShe Z(2007)Language-based abstraction refinement for hybrid system verificationProceedings of the 8th international conference on Verification, model checking, and abstract interpretation10.5555/1763048.1763065(151-166)Online publication date: 14-Jan-2007
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Tabuada P(2007)Approximate simulation relations and finite abstractions of quantized control systemsProceedings of the 10th international conference on Hybrid systems: computation and control10.5555/1760804.1760847(529-542)Online publication date: 3-Apr-2007
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Mitchell I(2007)Comparing forward and backward reachability as tools for safety analysisProceedings of the 10th international conference on Hybrid systems: computation and control10.5555/1760804.1760840(428-443)Online publication date: 3-Apr-2007
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Berman SHalász ÁKumar V(2007)MARCOProceedings of the 10th international conference on Hybrid systems: computation and control10.5555/1760804.1760815(76-89)Online publication date: 3-Apr-2007
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