Networked Control For Continuous-time Systems With Multi-rate Sampling

In recent two decades,with the rapid development of computer science and network technology,networked control systems(NCSs)have received more and more attention.Different from the point-to-point traditional control systems,some system nodes(sensors,controllers and/or actuators)in NCSs transmit information via networks instead of physical media,which have many advantages,such as saving wire,lower cost,and easy installation and maintenance.So far,the networked control of single-rate sampled-data systems(SRSDSs)has attracted considerable attention in both control theory and engineering applications,where all the measured variables are synchronously sampled by sensors.However,in practical applications,the single-rate sampling(SRS)may sometimes be high cost and even unrealistic.Therefore,it is a natural way that different types of measured variables are divided into multiple groups and these different groups are individually sampled at different sampling rates,such a system is called the multi-rate sampled-data system(MR-SDS).From some different perspectives,this thesis presents several new control methods to study the networked control problem of continuous-time MR-SDSs.The main contents in this thesis consist of the following four parts:(1)The second chapter investigates the time-delay control problem for a class of linear dual-rate sampled-data systems(DR-SDSs)under a perfect network environment.Different from the traditional idea that delays are regarded as a negative factor of system stability,this chapter considers the positive effect of delays.To this end,we firstly propose a novel separation theorem to determine the schur property of a matrix product,and the theorem can be used to obtain a less conservative stability criterion for impulsive switched systems.Then SR-SDSs and DR-SDSs are respectively modeled as different impulsive switched systems with fixed switching laws.By using the separation theorem and a loop-functional approach,some new stability criteria for the two systems are given in terms of linear matrix inequalities.Finally,some classical numerical examples are used to test the efficiency of the stability results and to illustrate the advantage of the proposed method.(2)The third chapter studies the observer-based networked control for a class of nonlinear MR-SDSs.Considering that output variables are sampled by multi-rate sampling(MRS)and transmitted to the controller node via imperfect networks.A matching mechanism is proposed to compute the synchronous estimation errors of the multirate sampled-data between the plant and an observer.Then the multi-rate observer isdeveloped to estimate the state of the plant in real time.Based on the estimated state,a state feedback controller is utilized to control the plant.Unlike the discrete-time modeling methods,the resulting closed-loop system is modeled as a continuous-time system with multiple input-delays.Inspired from Wirtinger's inequality,a new storage function is constructed to analyze efficiently the stability of the closed-loop system with multiple input-delays.The sufficient conditions for H?performance analysis and corresponding controller design are given in terms of linear matrix inequalities.Finally,two illustrative examples are used to show the effectiveness of the proposed method.(3)The fourth chapter investigates the fuzzy dynamic output feedback(FDOF)control problem for networked nonlinear MR-SDSs.Due to the MRS and transmissions over imperfect networks,the traditional parallel distributed compensation technique can not be used for controller design.This chapter considers an FDOF controller with nonparallel distributed compensation technique,where the deviations of the mismatched membership functions between the plant and the controller are bounded by their error bounds.The resulting closed-loop system is modeled as a perturbed system with two perturbed terms,where the two terms respectively result from the MRS and the deviations of the mismatched membership functions.To analyze the stability of the perturbed system,a novel integral inequality is constructed to characterize and distinguish the two types of delays caused by sample-and-hold devices and transmission processes.By using the inequality and constructing a new energy storage function,the stability criterion and the controller design method for the perturbed system are given.Finally,three illustrative examples are used to verify the effectiveness and advantages of the proposed results.(4)The fifth chapter studies the state feedback control of a class of networked nonlinear MR-SDSs.Different from the third and fourth chapters wherein the distribution characteristics of packet dropouts are not considered,this chapter assumes that the packet dropout obeys a Bernoulli process.The resulting closed-loop system is modeled as a perturbed system with a perturbed term which is used to describe the effect of the MRS on its nominal system.Then,we respectively consider the two cases without a retransmission protocol and with a retransmission protocol,and provide multiple new integral inequalities.These inequalities include the information of packet dropout rates,sampling periods and networked-induced delays.Subsequently,based on the in-equalities,the stability criterion for the resulting closed-loop system is given in terms of linear matrix inequalities,and the controller design method is solved by introducing a new iteration algorithm.Finally,an example is used to verify the effectiveness of the proposed method.