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dc.contributor.authorPeng, Bowen
dc.contributor.authorStancu, Alexandru
dc.contributor.authorDang, Shuping
dc.date.accessioned2019-05-21T13:21:45Z
dc.date.available2019-05-21T13:21:45Z
dc.date.issued2019-04-29
dc.identifier.citationPeng B, Stancu A, Dang S (2019) Computation of discriminating kernel and robust capture basin with regulation map by interval methods. International Journal of Robust and Nonlinear Control. Available: http://dx.doi.org/10.1002/rnc.4577.
dc.identifier.issn1049-8923
dc.identifier.doi10.1002/rnc.4577
dc.identifier.urihttp://hdl.handle.net/10754/653088
dc.description.abstractThis paper proposes a novel algorithm that characterizes the robust capture basin and the discriminating kernel for constrained nonlinear systems with uncertainties based on viability theory. For nonlinear systems with constrained inputs and bounded uncertainties, the viability kernel is the largest set of states possessing a possibility to be viable in a set, and the capture basin is the largest set of states possessing a possibility to reach a target in a finite time, and keeping viable in a set before reaching the target. However, in the viability theory, both control and uncertainty in a parameterized system are considered as parameters: the discriminating kernel and the proposed robust capture basin link viability theory with robust control, which take both control and uncertainties into account. For the constrained uncertain nonlinear systems, the discriminating kernel is the largest set of states that is robust invariant in a set with proper control, and the robust capture basin is the largest set of states reaching their target in finite time with proper control despite of uncertainties and keeping viable in a set before reaching the target. Furthermore, we map all the states to optimal regulatory control such that the systems are regulated by a regulation map. To compute the robust capture basin and the discriminating kernel, we use interval methods to provide guaranteed solutions. The proposed algorithms in this paper approximate an outer approximation of the minimum reachable target and inner approximations of the robust capture basin and the discriminating kernel in a guaranteed way.
dc.description.sponsorshipThis work was supported by the Autonomous Systems research team and Interval Methods working group in Control Systems Centre in The University of Manchester. We wish to acknowledge the associate editor and reviewer for their precious advices.
dc.publisherWiley
dc.relation.urlhttps://onlinelibrary.wiley.com/doi/full/10.1002/rnc.4577
dc.subjectcapture basin
dc.subjectdiscriminating kernel
dc.subjectinterval methods
dc.subjectregulation map
dc.subjectrobust capture basin
dc.subjectviability kernel
dc.titleComputation of discriminating kernel and robust capture basin with regulation map by interval methods
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalInternational Journal of Robust and Nonlinear Control
dc.contributor.institutionDepartment of Electrical and Electronic Engineering; The University of Manchester; Manchester UK
dc.contributor.institutionDepartment of Engineering Science; University of Oxford; Oxford UK
kaust.personDang, Shuping
dc.date.published-online2019-04-29
dc.date.published-print2019-07-25


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