Approximation Metrics for Discrete and Continuous Systems

Simple item page
dc.contributor.authorGirard, Antoine
dc.contributor.authorPappas, George J
dc.date2023-05-17T00:04:47.000
dc.date.accessioned2023-05-22T12:57:29Z
dc.date.available2023-05-22T12:57:29Z
dc.date.issued2005-01-01
dc.date.submitted2006-10-26T07:24:12-07:00
dc.description.abstractEstablished system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudo-metrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections. Our approximation framework is compositional for synchronous composition operators. Algorithms are developed for computing the proposed pseudo-metrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution a static game whose cost is the so-called branching distance between the systems. Approximations for the pseudo-metrics can be obtained by considering Lyapunov-like functions called simulation and bisimulation functions. We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems.
dc.description.commentsUniversity of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-05-10.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/7479
dc.legacy.articleid1055
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1055&context=cis_reports&unstamped=1
dc.source.issue54
dc.source.journalTechnical Reports (CIS)
dc.source.statuspublished
dc.subject.otherGRASP
dc.titleApproximation Metrics for Discrete and Continuous Systems
dc.typeReport
digcom.contributor.authorGirard, Antoine
digcom.contributor.authorisAuthorOfPublication|email:pappasg@seas.upenn.edu|institution:University of Pennsylvania|Pappas, George J
digcom.identifiercis_reports/54
digcom.identifier.contextkey219211
digcom.identifier.submissionpathcis_reports/54
digcom.typereport
dspace.entity.typePublication
relation.isAuthorOfPublication00473ef0-d415-4df9-b027-00f0cf171730
relation.isAuthorOfPublication.latestForDiscovery00473ef0-d415-4df9-b027-00f0cf171730
upenn.schoolDepartmentCenterTechnical Reports (CIS)
upenn.schoolDepartmentCenterGeneral Robotics, Automation, Sensing and Perception Laboratory
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
MS_CIS_05_10.pdf
Size:
372.38 KB
Format:
Adobe Portable Document Format
Download
Collection
Reports