{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/102525"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/102525","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control","abstract":"This study aims to address the problem of attitude control of spacecraft in presence of thrust uncertainty, which leads to stochastic accelerations. Spacecraft equipped with electric propulsion and other low thrust mechanisms, often experience random fluctuations in thrust. These stochastic processes arise from sources such as uncertain power supply output, varying propellant flow rate, faulty thrusters, etc. Mission requirements and mass/fuel limitations demand an optimal and proactive method of control to mitigate the thrust uncertainty and parasitic torque. Stabilizing stochastic optimal control of the satellite attitude dynamics is derived through formulation of the Hamilton-Jacobi-Bellman equation associated with a stochastic differential equation. The solution to the Hamilton-Jacobi-Bellman partial differential equation is approximated through the method of Al’brekht [1]. Extension of Albrekht method for a stochastic system was first presented in [2]; detailed derivations of linear and nonlinear stochastic control laws along with their analytical and numerical analyses are presented in this thesis. A planning method is then discussed to lower the error due to local nature of the control.","abstract_html":"This study aims to address the problem of attitude control of spacecraft in presence of thrust uncertainty, which leads to stochastic accelerations. Spacecraft equipped with electric propulsion and other low thrust mechanisms, often experience random fluctuations in thrust. These stochastic processes arise from sources such as uncertain power supply output, varying propellant flow rate, faulty thrusters, etc. Mission requirements and mass/fuel limitations demand an optimal and proactive method of control to mitigate the thrust uncertainty and parasitic torque. Stabilizing stochastic optimal control of the satellite attitude dynamics is derived through formulation of the Hamilton-Jacobi-Bellman equation associated with a stochastic differential equation. The solution to the Hamilton-Jacobi-Bellman partial differential equation is approximated through the method of Al’brekht [1]. Extension of Albrekht method for a stochastic system was first presented in [2]; detailed derivations of linear and nonlinear stochastic control laws along with their analytical and numerical analyses are presented in this thesis. A planning method is then discussed to lower the error due to local nature of the control.","abstract_has_math":false,"creators":["Golpashin, Alen Envieh"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":["Namachchivaya, Navaratnam S.","Ho, Koki"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-02-06T19:36:45Z","date_published":"2019-02-06T19:36:45Z","updated_at":"2026-07-22T22:24:42Z","subjects":["Stochastic Optimal Control","Attitude Control","Thrust Uncertainty","Hamilton-Jacobi-Bellman","HJB","Al'brekht Method"],"languages":["en"],"rights":["Copyright 2018 Alen Golpashin"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/102525","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Namachchivaya, Navaratnam S.","Ho, Koki"]},{"key":"dc:creator","label":"Author","values":["Golpashin, Alen Envieh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-02-06T19:36:45Z","2018-12-14","2018-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"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":["Stochastic Optimal Control","Attitude Control","Thrust Uncertainty","Hamilton-Jacobi-Bellman","HJB","Al'brekht Method"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Alen Golpashin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/102525"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This study aims to address the problem of attitude control of spacecraft in presence of thrust uncertainty, which leads to stochastic accelerations. Spacecraft equipped with electric propulsion and other low thrust mechanisms, often experience random fluctuations in thrust. These stochastic processes arise from sources such as uncertain power supply output, varying propellant flow rate, faulty thrusters, etc. Mission requirements and mass/fuel limitations demand an optimal and proactive method of control to mitigate the thrust uncertainty and parasitic torque. Stabilizing stochastic optimal control of the satellite attitude dynamics is derived through formulation of the Hamilton-Jacobi-Bellman equation associated with a stochastic differential equation. The solution to the Hamilton-Jacobi-Bellman partial differential equation is approximated through the method of Al’brekht [1]. Extension of Albrekht method for a stochastic system was first presented in [2]; detailed derivations of linear and nonlinear stochastic control laws along with their analytical and numerical analyses are presented in this thesis. A planning method is then discussed to lower the error due to local nature of the control.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-02-05 without embargo terms","The student, Alen Golpashin, accepted the attached license on 2018-12-13 at 16:20.","The student, Alen Golpashin, submitted this Thesis for approval on 2018-12-13 at 16:40.","This Thesis was approved for publication on 2018-12-14 at 11:48.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13321 on 2019-02-05 at 11:16:18","Made available in DSpace on 2019-02-06T19:36:45Z (GMT). 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These stochastic processes arise from sources such as uncertain power supply output, varying propellant flow rate, faulty thrusters, etc. Mission requirements and mass/fuel limitations demand an optimal and proactive method of control to mitigate the thrust uncertainty and parasitic torque. Stabilizing stochastic optimal control of the satellite attitude dynamics is derived through formulation of the Hamilton-Jacobi-Bellman equation associated with a stochastic differential equation. The solution to the Hamilton-Jacobi-Bellman partial differential equation is approximated through the method of Al’brekht [1]. Extension of Albrekht method for a stochastic system was first presented in [2]; detailed derivations of linear and nonlinear stochastic control laws along with their analytical and numerical analyses are presented in this thesis. A planning method is then discussed to lower the error due to local nature of the control.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-02-05 without embargo terms","The student, Alen Golpashin, accepted the attached license on 2018-12-13 at 16:20.","The student, Alen Golpashin, submitted this Thesis for approval on 2018-12-13 at 16:40.","This Thesis was approved for publication on 2018-12-14 at 11:48.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13321 on 2019-02-05 at 11:16:18","Made available in DSpace on 2019-02-06T19:36:45Z (GMT). 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