{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/86729"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/86729","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Optimal Control of Differentially Flat Systems","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Ogunbodede, Oladapo; 0000-0003-3838-1964"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Singh, Tarunraj","Mechanical and Aerospace Engineering"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-02-21T21:36:55Z","date_published":"2025-02-21T21:36:55Z","updated_at":"2026-07-27T19:05:34Z","subjects":["aerospace engineering","mechanical engineering"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/86729","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Singh, Tarunraj","Mechanical and Aerospace Engineering"]},{"key":"dc:creator","label":"Author","values":["Ogunbodede, Oladapo; 0000-0003-3838-1964"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-02-21T21:36:55Z","2020"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["aerospace engineering","mechanical engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/86729"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","The aim of this dissertation is to examine optimal control of a class of system known as differentially flat systems. These are systems in which the states and inputs can be expressed as functions of an output vector and its derivatives. The flat outputs can be described as components of the mapping from the system space to a smaller dimensional space. This property allows one to systematically generate feasible trajectories in a relatively simple way. Using this property, optimal control formulations can be transformed into a Linear Programming problem (LP) or a Nonlinear Programming problem (NLP) hence making it more tractable. In this dissertation an overview of differentially flat systems is given, stating the conditions needed for a system to be differentially flat. Examples to illustrate how the optimal control problem is transformed to a nonlinear or linear programming problem is discussed before highlighting the shortcomings of differential flatness. Polynomial chaos, a tool used in uncertainty quantification is discussed to serve as a surrogate model for uncertainty propagation for differentially flat system. Also, the Bonferroni Approximation used in rewriting probabilistic constraints in deterministic form is also discussed in this work. A case study of finding an efficient way of flying fixed wing Unmanned Aerial Vehicles motivated by locomotion observed in birds and sea mammals is presented with emphasis on how differential flatness makes solving the problem easier. This new approach to optimal flight of Unmanned Aerial Vehicle is known as periodic flight. A test to determine if optimal periodic flight results in a better cost compared to optimal steady state flight known as the Π test is also discussed. The concept of differential flatness is explored to solve the optimal control path planning towards finding the desired periodic trajectories which will optimize either the range, power or endurance of UAVs for both translation and loiter trajectories. Another case study which seeks to find an optimal trajectory that minimizes the vibration in the load of UAV with suspended load using the concept of differential flatness is also examined. The optimal solution obtained from the differential flatness formulation is compared to the solution from other standard vibration mitigation methods. The resulting solutions are validated with experiments for both point-to-point trajectory and a waypoint based trajectory. Also, a method of dealing with time invariant parametric uncertainties in this class of systems using polynomial chaos is also presented. The method seeks to find a robust feedforward controller for differentially flat system without the need for feedback. It is also shown that for flat linear systems, the polynomial chaos surrogate model is also flat. The surrogate model is then used in a chance constraint optimization. A single mass spring damper and two mass spring damper systems are used to illustrate the proposed method.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Optimal Control of Differentially Flat Systems"]}]}],"canonical_facts":{"dc:contributor":["Singh, Tarunraj","Mechanical and Aerospace Engineering"],"dc:creator":["Ogunbodede, Oladapo; 0000-0003-3838-1964"],"dc:date":["2025-02-21T21:36:55Z","2020"],"dc:description":["Ph.D.","The aim of this dissertation is to examine optimal control of a class of system known as differentially flat systems. These are systems in which the states and inputs can be expressed as functions of an output vector and its derivatives. The flat outputs can be described as components of the mapping from the system space to a smaller dimensional space. This property allows one to systematically generate feasible trajectories in a relatively simple way. Using this property, optimal control formulations can be transformed into a Linear Programming problem (LP) or a Nonlinear Programming problem (NLP) hence making it more tractable. In this dissertation an overview of differentially flat systems is given, stating the conditions needed for a system to be differentially flat. Examples to illustrate how the optimal control problem is transformed to a nonlinear or linear programming problem is discussed before highlighting the shortcomings of differential flatness. Polynomial chaos, a tool used in uncertainty quantification is discussed to serve as a surrogate model for uncertainty propagation for differentially flat system. Also, the Bonferroni Approximation used in rewriting probabilistic constraints in deterministic form is also discussed in this work. A case study of finding an efficient way of flying fixed wing Unmanned Aerial Vehicles motivated by locomotion observed in birds and sea mammals is presented with emphasis on how differential flatness makes solving the problem easier. This new approach to optimal flight of Unmanned Aerial Vehicle is known as periodic flight. A test to determine if optimal periodic flight results in a better cost compared to optimal steady state flight known as the Π test is also discussed. The concept of differential flatness is explored to solve the optimal control path planning towards finding the desired periodic trajectories which will optimize either the range, power or endurance of UAVs for both translation and loiter trajectories. Another case study which seeks to find an optimal trajectory that minimizes the vibration in the load of UAV with suspended load using the concept of differential flatness is also examined. The optimal solution obtained from the differential flatness formulation is compared to the solution from other standard vibration mitigation methods. The resulting solutions are validated with experiments for both point-to-point trajectory and a waypoint based trajectory. Also, a method of dealing with time invariant parametric uncertainties in this class of systems using polynomial chaos is also presented. The method seeks to find a robust feedforward controller for differentially flat system without the need for feedback. It is also shown that for flat linear systems, the polynomial chaos surrogate model is also flat. The surrogate model is then used in a chance constraint optimization. A single mass spring damper and two mass spring damper systems are used to illustrate the proposed method.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/86729"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["aerospace engineering","mechanical engineering"],"dc:title":["Optimal Control of Differentially Flat Systems"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:34Z"}