{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/121972"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/121972","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Tackling performativity in discrete-time dynamical systems: An iterative refinement approach","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms","abstract_has_math":false,"creators":["Zhang, Heling"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Dong, Roy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-12","date_published":"2023-12","updated_at":"2026-07-22T22:25:00Z","subjects":["Control","Robust Optimal Control","Iterative Methods","Discrete-time Dynamical Systems","Conformal Prediction"],"languages":["en","eng"],"rights":["Copyright 2023 Heling Zhang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/121972","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dong, Roy"]},{"key":"dc:creator","label":"Author","values":["Zhang, Heling"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-12","2023-11-10"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Control","Robust Optimal Control","Iterative Methods","Discrete-time Dynamical Systems","Conformal Prediction"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2023 Heling Zhang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/121972"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms","The student, Heling Zhang, accepted the attached license on 2023-11-08 at 14:36.","The student, Heling Zhang, submitted this Thesis for approval on 2023-11-08 at 14:36.","This Thesis was approved for publication on 2023-11-10 at 08:51.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19887 on 2024-03-01 at 13:14:11","In many real-world dynamical systems, obtaining precise prior knowledge about system noise remains a challenge. This uncertainty complicates traditional control strategies, such as stochastic and robust control, especially when the noise exhibits \"performativity''--- an explicit dependence on control inputs. Addressing this challenge, this paper presents a novel iterative method tailored for such systems. Our approach finds the open-loop control law that minimizes the worst-case loss, given that the noise induced by this control lies in its $(1 - p)$-confidence set for a predetermined $p$. At each iteration, we harness conformal prediction techniques to empirically estimate the confidence set shaped by the preceding control law. These derived confidence sets offer empirical constraints on the system's noise, guiding a robust control design that targets worst-case loss minimization. Under specific regularity conditions, our method is shown to converge to a near-optimal open-loop control. While our focus is on open-loop controls, the adaptive, data-driven nature of our approach suggests its potential applicability across diverse scenarios and extensions."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Tackling performativity in discrete-time dynamical systems: An iterative refinement approach"]}]}],"canonical_facts":{"dc:contributor":["Dong, Roy"],"dc:creator":["Zhang, Heling"],"dc:date":["2023-12","2023-11-10"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms","The student, Heling Zhang, accepted the attached license on 2023-11-08 at 14:36.","The student, Heling Zhang, submitted this Thesis for approval on 2023-11-08 at 14:36.","This Thesis was approved for publication on 2023-11-10 at 08:51.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19887 on 2024-03-01 at 13:14:11","In many real-world dynamical systems, obtaining precise prior knowledge about system noise remains a challenge. This uncertainty complicates traditional control strategies, such as stochastic and robust control, especially when the noise exhibits \"performativity''--- an explicit dependence on control inputs. Addressing this challenge, this paper presents a novel iterative method tailored for such systems. Our approach finds the open-loop control law that minimizes the worst-case loss, given that the noise induced by this control lies in its $(1 - p)$-confidence set for a predetermined $p$. At each iteration, we harness conformal prediction techniques to empirically estimate the confidence set shaped by the preceding control law. These derived confidence sets offer empirical constraints on the system's noise, guiding a robust control design that targets worst-case loss minimization. Under specific regularity conditions, our method is shown to converge to a near-optimal open-loop control. While our focus is on open-loop controls, the adaptive, data-driven nature of our approach suggests its potential applicability across diverse scenarios and extensions."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/121972"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Heling Zhang"],"dc:subject":["Control","Robust Optimal Control","Iterative Methods","Discrete-time Dynamical Systems","Conformal Prediction"],"dc:title":["Tackling performativity in discrete-time dynamical systems: An iterative refinement approach"],"dc:type":["text"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:00Z"}