Link to the University of Pittsburgh Homepage
Link to the University Library System Homepage Link to the Contact Us Form

Parameter identification and estimation of dynamical systems from a single trajectory

Duan, Xiaoyu (2022) Parameter identification and estimation of dynamical systems from a single trajectory. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

PDF (XiaoyuDuan_PhDdissertationDraft, uploaded so that potential format mistakes can be found. Thank you!)
Draft Version

Download (18MB) | Preview


Parameter identification and estimation from experimental data is an important problem in mathematical model development. Motivated from disease and immunological study, where repeated collection of data from a single subject is impossible and data could be limited, we focus on the parameter identification/estimation of ODE dynamical systems from a single trajectory, on which there are small amount of exactly measured discrete data, particularly considered uniformly spaced in time. This is an inverse problem where we treat the solution map of initial value problem of the ODE system given the parameter as the corresponding forward problem. We put concentration on mathematical establishment of theories on the existence, uniqueness, robustness, uncertainty quantification about the inverse problem, and provide theoretical proofs on some results. Previous study has been completed for such inverse problems of linear systems. We generalize the results to affine dynamical systems, find sufficient and necessary conditions of existence and uniqueness from either full trajectory or discrete data, and then give bounds on maximal allowable uncertainty. There are also results on affine systems that require new proof techniques or never appear in linear systems. We apply the analysis of affine systems into parameter estimation of linear-in-parameters(LIP) systems, which can yield more accurate estimates than those based on finite differences. We then focus on a two-dimensional Lotka-Volterra system as the first example of LIP systems. We sketch diagrams that partially show the continuous dependence of qualitative behavior of inverse problem solution on data. Novel situations also appear for LV systems where data points are compatible with distinct parameter sets corresponding to same or different qualitative types. Finally, we design a numerical algorithm that estimate parameters faster and with less computation time than direct methods, apply to stiff and higher-dimensional linear-in-parameters systems as well as certain nonlinear systems.


Social Networking:
Share |


Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Duan, Xiaoyuxid33@pitt.eduxid330000-0002-0958-6189
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairRubin, Jonathanjonrubin@pitt.edujonrubin
Committee CoChairSwigon, Davidswigon@pitt.eduswigon
Committee MemberTrenchea, Catalintrenchea@gmail.comtrenchea
Committee MemberParker, Robertrparker@pitt.edurparker
Date: 30 September 2022
Date Type: Publication
Defense Date: 20 May 2022
Approval Date: 30 September 2022
Submission Date: 10 May 2022
Access Restriction: 1 year -- Restrict access to University of Pittsburgh for a period of 1 year.
Number of Pages: 172
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: parameter estimation, inverse problem, affine system, Lotka-Volterra system, linear-in-parameters system
Date Deposited: 30 Sep 2022 18:11
Last Modified: 30 Sep 2023 05:15


Monthly Views for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item