| Dynamical systems with periodic characteristics have a wide range of real-life applications,such as helicopter drive trains,rotor blade systems and wind turbine systems in engineering applications,and predator baiting systems in ecological fields.With the gradual development of control system networking,frequent network data communication brings unnecessary communication cost and computational cost for networked periodic systems.Therefore,this paper focuses on linear periodic systems in a networked environment,introduces an eventtriggered mechanism in order to save network resources,focuses on the analysis and design of linear periodic systems in this case,and proposes new methods to solve the stability analysis,controller and filter design problems of linear periodic systems under the action of the eventtriggered mechanism,respectively.The main research content of this thesis is divided as follows.(1)Firstly,the performance analysis of a class of linear periodic systems and the corresponding model reduction are investigated in Chapter 2 by considering that the higher order of periodic systems can cause difficulties in the analy sis and design of the system.In the performance analysis,the stability analysis and dissipativeness analysis of the linear periodic system are carried out by the method of Lyapunov function to obtain the sufficient conditions for the system to be asymptotically stable and the sufficient conditions for the system to be asymptotically stable and satisfy the dissipativeness.Then,the dissipative and Hankel paradigm-based reduced-order models are designed respectively.Meanwhile,the method of solving the reduced-order system matrix is designed based on convex linearization and projection theorem.The reduced-order model can approximate the higher-order periodic system to a lower-order system model,which reduces the difficulty of analysis and design of the system and lays a certain theoretical foundation for the performance analysis in the subsequent chapters.(2)Second,for networked linear periodic systems,considering that the introduction of event-triggered mechanism brings technical difficulties in analysis and design while reducing network communication costs,the state/output feedback controller design methods based on event-triggered discrete-time linear periodic systems and continuous-time linear periodic systems are given more systematically in Chapters 3,4 and 5,respectively.Chapter 3 focuses on the design of event-triggered state feedback controllers and event-triggered dynamic output feedback controllers for discrete period systems.By modeling the event-triggered discrete periodic system based on the input-to-state stabilization technique,an event-triggered mechanism with periodic time-varying parameters is designed to minimize the amount of data transmission in the network under the premise of ensuring system stability.Finally,the stability analysis and controller design of the system are solved by the method of multi-Lyapunov functions,and sufficient conditions for the system to be stable under the action of the eventtriggered controller are obtained.(3)Thirdly,the problem of designing an event-triggered state-based feedback controller is investigated in Chapter 4 for a fully state-measurable continuous-period system.The continuous-period system is approximated as a periodically piecewise system using the period piecewise approach,and the event-triggered continuous-period system is modeled by an inputto-state stabilization-based technique.When the event-triggered mechanism continuously monitors the continuous periodic system,in order to avoid the occurrence of Zeno behavior(infinite triggering in finite time),the sensor-controller event-triggered mechanism,the controller-actuator event-triggered mechanism and the sensor-controller-actuator dual eventtriggered mechanism are designed according to different network configurations,and then the stability of the closed-loop periodic system under the action of different event-triggered mechanisms is investigated separately.The stability analysis of the closed-loop periodic system with different event triggering mechanisms is carried out,and the parameters of the event triggering mechanism are designed.Finally,the sufficient conditions for the finite-time stability of the closed-loop continuous periodic system under the action of the event-triggered state feedback controller and the corresponding controller parameters are established by the method of Lyapunov function,and thus a state feedback control method for the linear periodic system based on the event-triggered mechanism is proposed.(4)Fourthly,Considering that the full states of periodic systems in practice are often difficult to obtain simultaneously,the problem of designing a dynamic output feedback controller based on event triggering is investigated in Chapter 5,based on the study in Chapter 4.The idea of period piecewise is adopted to approximate the continuous-time periodic system as a period piecewise system.In order to reduce unnecessary data transmission between the sensor(or controller)and the controller(or actuator),a dual event triggering mechanism with a period piecewise parameter is designed,and the Zeno phenomenon is avoided by introducing a special parameter,and the minimum triggering interval associated with this parameter is found.Then,the periodic piecewise system under the action of the event trigger mechanism is modeled by using the impulsive technique to obtain the periodic piecewise impulsive system,and a new method is proposed to stabilize the periodic piecewise impulsive system and satisfy the performance analysis.Finally,a method for solving the gain matrix of the dynamic output feedback controller based on event triggering is designed based on variable substitution to realize the effective control of the periodic system.(5)Finally,for periodic systems in a network environment with multiple sensors,the problem of event-triggered distributed filter design based on event triggering is investigated in Chapter 6 in order to reduce the impact of external perturbations on such systems.First,the continuous-time periodic system is approximated as a periodic piecewise system by the method of periodic piecewise.Considering the application requirements of estimation and monitoring of periodic systems by multiple sensors in practice,and in order to reduce the burden of network communication between such filter-based smart sensors,a dynamic event triggering mechanism is designed for each smart sensing unit.Under the action of the considered triggering mechanism,a distributed peak-to-peak filter design method with periodic time-varying parameters is proposed to estimate the output of a networked continuous-time periodic system with perturbations.Then,the periodic piecewise filter error system is modeled based on the impulsive technique,and the modeled system is analyzed to obtain sufficient conditions for the global asymptotic convergence of the filter error system.Then,the method for solving the distributed filter gain is designed based on convex linearization.The above research results are verified by numerical simulation. |
