The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are unknown. We present numerical simulations to demonstrate the stability, transient and steady state responses, and the performance of the state feedback controller.
","abstract_html":"<p>The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are unknown. We present numerical simulations to demonstrate the stability, transient and steady state responses, and the performance of the state feedback controller.</p>","abstract_has_math":false,"creators":["Tran, Anh V"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Yan Wu","Alex Stokolos","Frank Goforth"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:52Z","subjects":["ETD","adaptive control","Lyapunov stability","feedback control","multi-equilibrium","natural convection loops","Lorenz system","Control Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1109","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Yan Wu","Alex Stokolos","Frank Goforth"]},{"key":"dc:creator","label":"Author","values":["Tran, Anh V"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-04-23T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","adaptive control","Lyapunov stability","feedback control","multi-equilibrium","natural convection loops","Lorenz system","Control Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1109"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are unknown. We present numerical simulations to demonstrate the stability, transient and steady state responses, and the performance of the state feedback controller.
"]},{"key":"dc:title","label":"Title","values":["Adaptive State Feedback Control of Lorenz Systems to Its Non-Trivial Equilibrium"]}]}],"canonical_facts":{"dc:contributor":["Yan Wu","Alex Stokolos","Frank Goforth"],"dc:creator":["Tran, Anh V"],"dc:date.available":["2015-04-23T07:00:00Z"],"dc:description.abstract":["The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are unknown. We present numerical simulations to demonstrate the stability, transient and steady state responses, and the performance of the state feedback controller.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1109"],"dc:subject":["ETD","adaptive control","Lyapunov stability","feedback control","multi-equilibrium","natural convection loops","Lorenz system","Control Theory"],"dc:title":["Adaptive State Feedback Control of Lorenz Systems to Its Non-Trivial Equilibrium"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:52Z"}