dc.contributor.author | Dankowicz, H | |
dc.contributor.author | Sieber, J | |
dc.date.accessioned | 2022-03-09T08:57:17Z | |
dc.date.issued | 2022-04-22 | |
dc.date.updated | 2022-03-08T15:13:17Z | |
dc.description.abstract | This paper presents a rigorous framework for the continuation of solutions to nonlinear constraints and the simultaneous analysis of the sensitivities of test functions to constraint violations at each solution point using an adjoint-based approach. By the linearity of a problem Lagrangian in the associated Lagrange multipliers, the formalism is shown to be directly amenable to analysis using the COCO software package, specifically its paradigm for staged problem construction. The general theory is illustrated in the context of algebraic equations and boundary-value problems, with emphasis on periodic orbits in smooth and hybrid dynamical systems, and quasiperiodic invariant tori of flows. In the latter case, normal hyperbolicity is used to prove the existence of continuous solutions to the adjoint conditions associated with the sensitivities of the orbital periods to parameter perturbations and constraint violations, even though the linearization of the governing boundary-value problem lacks a bounded inverse, as required by the general theory. An assumption of transversal stability then implies that these solutions predict the asymptotic phases of trajectories based at initial conditions perturbed away from the torus. Example COCO code is used to illustrate the minimal additional investment in setup costs required to append sensitivity analysis to regular parameter continuation. | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
dc.identifier.citation | Published online 22 April 2022 | en_GB |
dc.identifier.doi | 10.3934/jcd.2022006 | |
dc.identifier.grantnumber | EP/N023544/1 | en_GB |
dc.identifier.grantnumber | EP/V04687X/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/128975 | |
dc.identifier | ORCID: 0000-0002-9558-1324 (Sieber, Jan) | |
dc.language.iso | en | en_GB |
dc.publisher | American Institute of Mathematical Sciences | en_GB |
dc.relation.url | https://github.com/jansieber/adjoint-sensitivity2022-supp | en_GB |
dc.rights | © 2022 American Institute of Mathematical Sciences | |
dc.subject | hybrid systems | en_GB |
dc.subject | numerical continuation | en_GB |
dc.subject | constraint Lagrangian | en_GB |
dc.subject | persistence | en_GB |
dc.subject | software implementation | en_GB |
dc.title | Sensitivity analysis for periodic orbits and quasiperiodic invariant tori using the adjoint method | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2022-03-09T08:57:17Z | |
dc.identifier.issn | 2158-2491 | |
dc.description | This is the author accepted manuscript. The final version is available from the American Institute of Mathematical Sciences via the DOI in this record | en_GB |
dc.description | Code availability: The code included in this paper constitutes fully executable
scripts. Complete code, including that used to generate the results in Fig. 1, is
available at https://github.com/jansieber/adjoint-sensitivity2022-supp. | en_GB |
dc.identifier.journal | Journal of Computational Dynamics | en_GB |
dc.rights.uri | http://www.rioxx.net/licenses/all-rights-reserved | en_GB |
dcterms.dateAccepted | 2022-03-03 | |
rioxxterms.version | AM | en_GB |
rioxxterms.licenseref.startdate | 2022-03-03 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2022-03-08T15:13:21Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2022-05-04T15:08:42Z | |
refterms.panel | B | en_GB |