{"id":{"repo_id":"must-thes","oai_identifier":"oai:scholarsmine.mst.edu:doctoral_dissertations-4123"},"canonical_url":"https://search.dev.ndltd.org/etd/must-thes/oai:scholarsmine.mst.edu:doctoral_dissertations-4123","repository":{"repo_id":"must-thes","name":"Missouri University of Science and Technology","base_url":"https://scholarsmine.mst.edu/do/oai/"},"display":{"title":"Finite time suboptimal control design of nonlinear systems with θ-D technique and implementation to aerospace applications","abstract":"“A finite time suboptimal control strategy (named θ - D approximated algorithm) was proposed in this study, which can provide the control engineers with a novel effective and efficient design tool from the finite time optimal perspective. Based on the framework of this proposed method, the original nonlinear dynamics were formulated in pseudo-linear form, and the performance index was denoted by a linear quadratic regulator prototype in this research. After that, the approximated solutions to intractable Hamilton-Jacobi-Bellman (HJB) equation were acquired by putting vanishing perturbation terms into the performance index. By tuning the parameters in perturbation terms, semi-global stability and sub-optimalilty was guaranteed. By taking the advantages of the perturbation terms, the large control was not required to cope with the large deviation at the initial time, which alleviates the severe tests of the actuators. The detailed procedure to develop this technique and corresponding stability proof were provided. The effectiveness of the proposed technique was verified by solving the two-dimensional benchmark problem, and the other three aerospace applications, including Reusable Launch Vehicle (RLV) landing problem, multiple satellites docking problem, and satellite maneuvering considering J<sub>2</sub> perturbation problem. In this research, contrary to the finite-time state dependent Riccati equation (FSDRE) technique , the proposed technique did not need excessive online computation, which makes the real-time implementation in various engineering scenarios possible since the computational resources are always limited for any specific engineering application; thus, leading to the major contribution of this research for avoiding the online computation of nonlinear Riccati equation and matrix inverse operation at each sample time”--Abstract, page iii.","abstract_html":"“A finite time suboptimal control strategy (named θ - D approximated algorithm) was proposed in this study, which can provide the control engineers with a novel effective and efficient design tool from the finite time optimal perspective. Based on the framework of this proposed method, the original nonlinear dynamics were formulated in pseudo-linear form, and the performance index was denoted by a linear quadratic regulator prototype in this research. After that, the approximated solutions to intractable Hamilton-Jacobi-Bellman (HJB) equation were acquired by putting vanishing perturbation terms into the performance index. By tuning the parameters in perturbation terms, semi-global stability and sub-optimalilty was guaranteed. By taking the advantages of the perturbation terms, the large control was not required to cope with the large deviation at the initial time, which alleviates the severe tests of the actuators. The detailed procedure to develop this technique and corresponding stability proof were provided. The effectiveness of the proposed technique was verified by solving the two-dimensional benchmark problem, and the other three aerospace applications, including Reusable Launch Vehicle (RLV) landing problem, multiple satellites docking problem, and satellite maneuvering considering J&lt;sub&gt;2&lt;/sub&gt; perturbation problem. In this research, contrary to the finite-time state dependent Riccati equation (FSDRE) technique , the proposed technique did not need excessive online computation, which makes the real-time implementation in various engineering scenarios possible since the computational resources are always limited for any specific engineering application; thus, leading to the major contribution of this research for avoiding the online computation of nonlinear Riccati equation and matrix inverse operation at each sample time”--Abstract, page iii.","abstract_has_math":false,"creators":["Yao, Jie"],"institution":"Missouri University of Science and Technology","degree_name":"Ph. D. in Mechanical Engineering","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T03:18:09Z","subjects":["Aerospace Engineering","Mechanical Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/3118","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Yao, Jie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Mechanical Engineering"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Missouri University of Science and Technology"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Aerospace Engineering","Mechanical Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/3118"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["“A finite time suboptimal control strategy (named θ - D approximated algorithm) was proposed in this study, which can provide the control engineers with a novel effective and efficient design tool from the finite time optimal perspective. Based on the framework of this proposed method, the original nonlinear dynamics were formulated in pseudo-linear form, and the performance index was denoted by a linear quadratic regulator prototype in this research. After that, the approximated solutions to intractable Hamilton-Jacobi-Bellman (HJB) equation were acquired by putting vanishing perturbation terms into the performance index. By tuning the parameters in perturbation terms, semi-global stability and sub-optimalilty was guaranteed. By taking the advantages of the perturbation terms, the large control was not required to cope with the large deviation at the initial time, which alleviates the severe tests of the actuators. The detailed procedure to develop this technique and corresponding stability proof were provided. The effectiveness of the proposed technique was verified by solving the two-dimensional benchmark problem, and the other three aerospace applications, including Reusable Launch Vehicle (RLV) landing problem, multiple satellites docking problem, and satellite maneuvering considering J<sub>2</sub> perturbation problem. In this research, contrary to the finite-time state dependent Riccati equation (FSDRE) technique , the proposed technique did not need excessive online computation, which makes the real-time implementation in various engineering scenarios possible since the computational resources are always limited for any specific engineering application; thus, leading to the major contribution of this research for avoiding the online computation of nonlinear Riccati equation and matrix inverse operation at each sample time”--Abstract, page iii."]},{"key":"dc:title","label":"Title","values":["Finite time suboptimal control design of nonlinear systems with θ-D technique and implementation to aerospace applications"]}]}],"canonical_facts":{"dc:creator":["Yao, Jie"],"dc:description.abstract":["“A finite time suboptimal control strategy (named θ - D approximated algorithm) was proposed in this study, which can provide the control engineers with a novel effective and efficient design tool from the finite time optimal perspective. Based on the framework of this proposed method, the original nonlinear dynamics were formulated in pseudo-linear form, and the performance index was denoted by a linear quadratic regulator prototype in this research. After that, the approximated solutions to intractable Hamilton-Jacobi-Bellman (HJB) equation were acquired by putting vanishing perturbation terms into the performance index. By tuning the parameters in perturbation terms, semi-global stability and sub-optimalilty was guaranteed. By taking the advantages of the perturbation terms, the large control was not required to cope with the large deviation at the initial time, which alleviates the severe tests of the actuators. The detailed procedure to develop this technique and corresponding stability proof were provided. The effectiveness of the proposed technique was verified by solving the two-dimensional benchmark problem, and the other three aerospace applications, including Reusable Launch Vehicle (RLV) landing problem, multiple satellites docking problem, and satellite maneuvering considering J<sub>2</sub> perturbation problem. In this research, contrary to the finite-time state dependent Riccati equation (FSDRE) technique , the proposed technique did not need excessive online computation, which makes the real-time implementation in various engineering scenarios possible since the computational resources are always limited for any specific engineering application; thus, leading to the major contribution of this research for avoiding the online computation of nonlinear Riccati equation and matrix inverse operation at each sample time”--Abstract, page iii."],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/3118"],"dc:subject":["Aerospace Engineering","Mechanical Engineering"],"dc:title":["Finite time suboptimal control design of nonlinear systems with θ-D technique and implementation to aerospace applications"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Mechanical Engineering"],"thesis:institution_name":["Missouri University of Science and Technology"]},"updated_at":"2026-07-24T03:18:09Z"}