{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1201"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1201","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"Feedback Control Theory in Stochastic Dynamical Systems","abstract":"A stochastic dynamical system is a system composed of many interacting components which includes stochastic behavior. Feedback control theory is designed to use information from the current state of the system in order to temper the final state toward the desired outcome. In this dissertation, I perform studies on two choices of classic and quantum dynamical systems to cover vast variety of statistical tools and methods. For classical model, I perform a study on finite-size effects at the phase transition in the Nagel-Schreckenberg traffic model as an example of non-equilibrium many body stochastic dynamical system. For quantum mechanical model, I introduce an optimal measurement-based feedback control protocol for cooling a single qubit as an example of complex system with one cell and many degrees of freedom. I examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. I show that the low density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, I observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed Vmax is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on Vmax The jamming transition at large Vmax can be viewed as the nucleation of jams in a background of freely flowing vehicles. Feedback control of quantum systems via continuous measurements involves complex nonlinear dynamics. As a result, even for a single qubit the optimal measurement for feedback control is known only in very special cases. I show here that for a broad class of noise processes, a series of compelling arguments can be applied to greatly simplify the problem of steady-state preparation of the ground-state, while loosing little in the way of optimality. Using numerical optimization to solve this simplified control problem, I obtain for the first time a non-trivial feedback protocol valid for all feedback strengths in the regime of good control. The protocol can be described relatively simply, and contains a discontinuity as a function of feedback strength.","abstract_html":"A stochastic dynamical system is a system composed of many interacting components which includes stochastic behavior. Feedback control theory is designed to use information from the current state of the system in order to temper the final state toward the desired outcome. In this dissertation, I perform studies on two choices of classic and quantum dynamical systems to cover vast variety of statistical tools and methods. For classical model, I perform a study on finite-size effects at the phase transition in the Nagel-Schreckenberg traffic model as an example of non-equilibrium many body stochastic dynamical system. For quantum mechanical model, I introduce an optimal measurement-based feedback control protocol for cooling a single qubit as an example of complex system with one cell and many degrees of freedom. I examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. I show that the low density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, I observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed Vmax is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on Vmax The jamming transition at large Vmax can be viewed as the nucleation of jams in a background of freely flowing vehicles. Feedback control of quantum systems via continuous measurements involves complex nonlinear dynamics. As a result, even for a single qubit the optimal measurement for feedback control is known only in very special cases. I show here that for a broad class of noise processes, a series of compelling arguments can be applied to greatly simplify the problem of steady-state preparation of the ground-state, while loosing little in the way of optimality. Using numerical optimization to solve this simplified control problem, I obtain for the first time a non-trivial feedback protocol valid for all feedback strengths in the regime of good control. The protocol can be described relatively simply, and contains a discontinuity as a function of feedback strength.","abstract_has_math":false,"creators":["Balouchi, Ashkan"],"institution":"Physics and Astronomy","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Physical Sciences and Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T02:57:12Z","subjects":["finite-size scaling","correlation","qubit","quantum control","traffic","stochastic","dynamical systems","feedback control"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-04062016-071840","https://repository.lsu.edu/gradschool_dissertations/202"],"render_values":[{"text":"etd-04062016-071840","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/202","href":"https://repository.lsu.edu/gradschool_dissertations/202","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.202","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Balouchi, Ashkan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-03-03"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:08:02Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physical Sciences and Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Physics and Astronomy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["finite-size scaling","correlation","qubit","quantum control","traffic","stochastic","dynamical systems","feedback control"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-04062016-071840","10.31390/gradschool_dissertations.202","https://repository.lsu.edu/gradschool_dissertations/202"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A stochastic dynamical system is a system composed of many interacting components which includes stochastic behavior. Feedback control theory is designed to use information from the current state of the system in order to temper the final state toward the desired outcome. In this dissertation, I perform studies on two choices of classic and quantum dynamical systems to cover vast variety of statistical tools and methods. For classical model, I perform a study on finite-size effects at the phase transition in the Nagel-Schreckenberg traffic model as an example of non-equilibrium many body stochastic dynamical system. For quantum mechanical model, I introduce an optimal measurement-based feedback control protocol for cooling a single qubit as an example of complex system with one cell and many degrees of freedom. I examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. I show that the low density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, I observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed Vmax is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on Vmax The jamming transition at large Vmax can be viewed as the nucleation of jams in a background of freely flowing vehicles. Feedback control of quantum systems via continuous measurements involves complex nonlinear dynamics. As a result, even for a single qubit the optimal measurement for feedback control is known only in very special cases. I show here that for a broad class of noise processes, a series of compelling arguments can be applied to greatly simplify the problem of steady-state preparation of the ground-state, while loosing little in the way of optimality. Using numerical optimization to solve this simplified control problem, I obtain for the first time a non-trivial feedback protocol valid for all feedback strengths in the regime of good control. The protocol can be described relatively simply, and contains a discontinuity as a function of feedback strength."]},{"key":"dc:title","label":"Title","values":["Feedback Control Theory in Stochastic Dynamical Systems"]}]}],"canonical_facts":{"dc:creator":["Balouchi, Ashkan"],"dc:date":["2016-03-03"],"dc:date.available":["2022-05-12T23:08:02Z"],"dc:description.abstract":["A stochastic dynamical system is a system composed of many interacting components which includes stochastic behavior. Feedback control theory is designed to use information from the current state of the system in order to temper the final state toward the desired outcome. In this dissertation, I perform studies on two choices of classic and quantum dynamical systems to cover vast variety of statistical tools and methods. For classical model, I perform a study on finite-size effects at the phase transition in the Nagel-Schreckenberg traffic model as an example of non-equilibrium many body stochastic dynamical system. For quantum mechanical model, I introduce an optimal measurement-based feedback control protocol for cooling a single qubit as an example of complex system with one cell and many degrees of freedom. I examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. I show that the low density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, I observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed Vmax is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on Vmax The jamming transition at large Vmax can be viewed as the nucleation of jams in a background of freely flowing vehicles. Feedback control of quantum systems via continuous measurements involves complex nonlinear dynamics. As a result, even for a single qubit the optimal measurement for feedback control is known only in very special cases. I show here that for a broad class of noise processes, a series of compelling arguments can be applied to greatly simplify the problem of steady-state preparation of the ground-state, while loosing little in the way of optimality. Using numerical optimization to solve this simplified control problem, I obtain for the first time a non-trivial feedback protocol valid for all feedback strengths in the regime of good control. The protocol can be described relatively simply, and contains a discontinuity as a function of feedback strength."],"dc:identifier":["etd-04062016-071840","10.31390/gradschool_dissertations.202","https://repository.lsu.edu/gradschool_dissertations/202"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["finite-size scaling","correlation","qubit","quantum control","traffic","stochastic","dynamical systems","feedback control"],"dc:title":["Feedback Control Theory in Stochastic Dynamical Systems"],"thesis:degree_discipline":["Physical Sciences and Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Physics and Astronomy"]},"updated_at":"2026-07-24T02:57:12Z"}