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postgraduate thesis: Estimation and synthesis of reachable set for discrete systems with switching characteristics
Title  Estimation and synthesis of reachable set for discrete systems with switching characteristics 

Authors  
Issue Date  2016 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Chen, Y. [陈勇]. (2016). Estimation and synthesis of reachable set for discrete systems with switching characteristics. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. 
Abstract  This thesis is concerned with the problems of reachable set estimation and synthesis for a class of dynamic systems with switching characteristics.
In terms of estimation of the reachable set, some ellipsoids and hyperpyramids are utilized to bounded the reachable set of systems with switching characteristics. Specifically, the following four types of systems are exploited: (1) For generally switched systems under arbitrarily switching signal, the reachable set bounding conditions which determine the bounding ellipsoids are derived by using a Lypunovbased inequality and the quadratic Sprocedure. Usually, the bounding ellipsoids are expected to be as small as possible, three optimization approaches are developed to minimize the bounded ellipsoids. In addition, Genetic Algorithm (GA) is used to search for the optimal value of the decision variables in the obtained reachable set estimation conditions. (2) For general switched systems under periodically switching signal (also termed as periodic systems in the thesis), the lifting approach and the pseudoperiodic Lyapunov function approach are utilized to determine the bounding ellipsoids for the reachable set. GA is adopted in the pseudoperiodic Lyapunov function approach to search for the optimal value of the decision variables. (3) For switched positive systems under arbitrarily switching signal, the reachable set bounding conditions which determine the bounding hyperpyramids are derived by utilizing two Lyapunovbased inequalities and the Sprocedure technique. The bounding hyperpyramids are minimized through two optimization methods. (4) For switched positive systems under periodically switching signal (also termed as periodic positive systems in the thesis), the lifting approach and the pseudoperiodic copositive Lyapunov function approach are used to determine the bounding hyperpyramids for the reachable set.
In terms of synthesis of the reachable set, the control objective is to manipulate the reachable set of closedloop system to lie within a given region or to make the reachable set as small as possible. Based on the reachable set estimation results, sufficient conditions are established for the existence of the desired statefeedback controllers. GA is used to search for the optimal statefeedback controller that makes the reachable set of closedloop system as small as possible. 
Degree  Doctor of Philosophy 
Subject  Control theory Dynamic programming 
Dept/Program  Mechanical Engineering 
Persistent Identifier  http://hdl.handle.net/10722/227943 
HKU Library Item ID  b5774081 
DC Field  Value  Language 

dc.contributor.author  Chen, Yong   
dc.contributor.author  陈勇   
dc.date.accessioned  20160726T23:17:43Z   
dc.date.available  20160726T23:17:43Z   
dc.date.issued  2016   
dc.identifier.citation  Chen, Y. [陈勇]. (2016). Estimation and synthesis of reachable set for discrete systems with switching characteristics. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.   
dc.identifier.uri  http://hdl.handle.net/10722/227943   
dc.description.abstract  This thesis is concerned with the problems of reachable set estimation and synthesis for a class of dynamic systems with switching characteristics. In terms of estimation of the reachable set, some ellipsoids and hyperpyramids are utilized to bounded the reachable set of systems with switching characteristics. Specifically, the following four types of systems are exploited: (1) For generally switched systems under arbitrarily switching signal, the reachable set bounding conditions which determine the bounding ellipsoids are derived by using a Lypunovbased inequality and the quadratic Sprocedure. Usually, the bounding ellipsoids are expected to be as small as possible, three optimization approaches are developed to minimize the bounded ellipsoids. In addition, Genetic Algorithm (GA) is used to search for the optimal value of the decision variables in the obtained reachable set estimation conditions. (2) For general switched systems under periodically switching signal (also termed as periodic systems in the thesis), the lifting approach and the pseudoperiodic Lyapunov function approach are utilized to determine the bounding ellipsoids for the reachable set. GA is adopted in the pseudoperiodic Lyapunov function approach to search for the optimal value of the decision variables. (3) For switched positive systems under arbitrarily switching signal, the reachable set bounding conditions which determine the bounding hyperpyramids are derived by utilizing two Lyapunovbased inequalities and the Sprocedure technique. The bounding hyperpyramids are minimized through two optimization methods. (4) For switched positive systems under periodically switching signal (also termed as periodic positive systems in the thesis), the lifting approach and the pseudoperiodic copositive Lyapunov function approach are used to determine the bounding hyperpyramids for the reachable set. In terms of synthesis of the reachable set, the control objective is to manipulate the reachable set of closedloop system to lie within a given region or to make the reachable set as small as possible. Based on the reachable set estimation results, sufficient conditions are established for the existence of the desired statefeedback controllers. GA is used to search for the optimal statefeedback controller that makes the reachable set of closedloop system as small as possible.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject.lcsh  Control theory   
dc.subject.lcsh  Dynamic programming   
dc.title  Estimation and synthesis of reachable set for discrete systems with switching characteristics   
dc.type  PG_Thesis   
dc.identifier.hkul  b5774081   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Mechanical Engineering   
dc.description.nature  published_or_final_version   