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postgraduate thesis: Riccati equation and eventtriggered control for constrained systems
Title  Riccati equation and eventtriggered control for constrained systems 

Authors  
Issue Date  2015 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Zhang, L. [张良银]. (2015). Riccati equation and eventtriggered control for constrained systems. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5570784 
Abstract  This thesis is concerned with the control of networked systems subject to such constraints as channel noise and actuator saturation. In the increasingly popular networked control systems (NCSs), the sensors, controllers, and actuators are usually geographically dispersed, and the entire system is subject to various constraints such as channel noise, limited channel capacity, measurement quantization, time delay, packet loss, limited control energy, and actuator saturation, which has motivated enormous research interest in the control of constrained systems.
The eventtriggered control (ETC) is a new technology that reduces unnecessary control updates in NCSs comparing with the periodic sampled control. In periodic control, the feedback updating action is performed according to periodic time. In ETC, feedback control is updated based on the state variation. This eventtrigger strategy has attracted a great deal of research interest in the last two decades.
The Riccati equation plays an important role in mathematics and engineering. A scalar Riccati equation is an ordinary differential equation (ODE) containing a quadratic term of the dependent variable and can be regarded as a quadratic polynomial system. The matrix Riccati equation is a matrix generalization of Riccati ODE. Its algebraic version, called the algebraic Riccati equation (ARE), can be utilized to resolve problems including the semiglobal stabilization of systems subject to actuator saturation and the ETC for noisy systems.
In this thesis, a modified algebraic Riccati equation (MARE) is studied in the case of a zero parameter matrix. The MARE can be applied to the eventbased synchronization of linear dynamical networks and the semiglobal synchronization subject to actuator saturation. For the controllable singleinput systems, a novel solution of the MARE is obtained in terms of the eigenvalues of the system matrix. It is an explicit analytic solution in the sense that no eigenvector of such associated parameter matrices as the Hamiltonian matrix is required, which distinguishes this new result from other results for ARE.
The thesis also addresses the problem of ETC over noisy channels. In the presence of channel noise, the error between estimated control and desirable control is nonzero at the updating instant. Nevertheless, the stabilization is achieved via an appropriate ETC law. Based on the robust control theory, a sufficient condition for closedloop stability is established. A highlight is that the tuning rule for parameters can be identified in a straightforward manner.
The problems of eventbased global and semiglobal stabilization of systems subject to actuator saturation are investigated as well. When global stabilization is considered, an inherent lower bound of the interevent time does not exist for continuoustime inputsaturated systems. A minimum interevent time is properly selected such that the event trigger is active only after the prescribed time interval. For any marginally stable systems, the semiglobal stabilization is achieved via ETC law based on ARE and Riccati ODE. 
Degree  Doctor of Philosophy 
Subject  Realtime control Riccati equation 
Dept/Program  Mechanical Engineering 
Persistent Identifier  http://hdl.handle.net/10722/230615 
DC Field  Value  Language 

dc.contributor.author  Zhang, Liangyin   
dc.contributor.author  张良银   
dc.date.accessioned  20160826T23:36:19Z   
dc.date.available  20160826T23:36:19Z   
dc.date.issued  2015   
dc.identifier.citation  Zhang, L. [张良银]. (2015). Riccati equation and eventtriggered control for constrained systems. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5570784   
dc.identifier.uri  http://hdl.handle.net/10722/230615   
dc.description.abstract  This thesis is concerned with the control of networked systems subject to such constraints as channel noise and actuator saturation. In the increasingly popular networked control systems (NCSs), the sensors, controllers, and actuators are usually geographically dispersed, and the entire system is subject to various constraints such as channel noise, limited channel capacity, measurement quantization, time delay, packet loss, limited control energy, and actuator saturation, which has motivated enormous research interest in the control of constrained systems. The eventtriggered control (ETC) is a new technology that reduces unnecessary control updates in NCSs comparing with the periodic sampled control. In periodic control, the feedback updating action is performed according to periodic time. In ETC, feedback control is updated based on the state variation. This eventtrigger strategy has attracted a great deal of research interest in the last two decades. The Riccati equation plays an important role in mathematics and engineering. A scalar Riccati equation is an ordinary differential equation (ODE) containing a quadratic term of the dependent variable and can be regarded as a quadratic polynomial system. The matrix Riccati equation is a matrix generalization of Riccati ODE. Its algebraic version, called the algebraic Riccati equation (ARE), can be utilized to resolve problems including the semiglobal stabilization of systems subject to actuator saturation and the ETC for noisy systems. In this thesis, a modified algebraic Riccati equation (MARE) is studied in the case of a zero parameter matrix. The MARE can be applied to the eventbased synchronization of linear dynamical networks and the semiglobal synchronization subject to actuator saturation. For the controllable singleinput systems, a novel solution of the MARE is obtained in terms of the eigenvalues of the system matrix. It is an explicit analytic solution in the sense that no eigenvector of such associated parameter matrices as the Hamiltonian matrix is required, which distinguishes this new result from other results for ARE. The thesis also addresses the problem of ETC over noisy channels. In the presence of channel noise, the error between estimated control and desirable control is nonzero at the updating instant. Nevertheless, the stabilization is achieved via an appropriate ETC law. Based on the robust control theory, a sufficient condition for closedloop stability is established. A highlight is that the tuning rule for parameters can be identified in a straightforward manner. The problems of eventbased global and semiglobal stabilization of systems subject to actuator saturation are investigated as well. When global stabilization is considered, an inherent lower bound of the interevent time does not exist for continuoustime inputsaturated systems. A minimum interevent time is properly selected such that the event trigger is active only after the prescribed time interval. For any marginally stable systems, the semiglobal stabilization is achieved via ETC law based on ARE and Riccati ODE.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.subject.lcsh  Realtime control   
dc.subject.lcsh  Riccati equation   
dc.title  Riccati equation and eventtriggered control for constrained systems   
dc.type  PG_Thesis   
dc.identifier.hkul  b5570784   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Mechanical Engineering   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b5570784   