Coding Scheme Design And Stability Analysis Of Quantized Control Systems

Under communication constraints, it is important to take into account the interplaybetween control and communication performance for the analysis and synthesis of thesystems. Since the system information is needed to be qiantized, encoded and decodedfor transmission through finite data rate channels, coding scheme, as the other compo-nents in feedback loop, has significant efect on the system stability. This paper considersthe coding scheme design and stability analysis of quantized control systems. The pa-per is composed of two parts: in the first part (including Chapter2to5), coding schemebased on spherical polar coordinate is proposed for quantized control system with sin-gle channel, and then applied to several kinds of quantized control systems with singlechannel to guarantee them stable; in the second part (including Chapter6and7), codingscheme based on boundary function is proposed for quantized control system with multi-ple channels, and then applied to several kinds of quantized control systems with multiplechannels to guarantee them convergent.In Chapter2, coding scheme based on spherical polar coordinate is proposed forquantized control system with single channel. In the existing literature, the system in-formation is encoded based on Descartes coordinate. Diferently, the proposed codingscheme is based on spherical polar coordinate. Thus, one merit of the coding scheme isthat the definite relation between the quantized data and the quantized error is developed,which does not exist in coding scheme using uniform quantization. Utilizing this rela-tion, we simplify the stability analysis of the system. Another merit is that the proposedcoding scheme uses only finite and constant channel data rate. But coding scheme usinglogarithmic quantization has not this merit. In addition, when coding, the coding schemeneeds only the present state of the systems and does not use the control input and the paststate of the systems, which is convenient for application.In Chapter3, linear discrete time invariant system with noiseless channel in feed-back loop is considered. Coding scheme based on spherical polar coordinate is adopted toasymptotically stabilize the system. Sufcient condition for asymptotical stability of thesystem is presented, which shows the tradeof between control and communication per-formance. By this condition, the design procedures for encoder, decoder and controllerare given respectively. Furthermore, in Chapters4and5, linear discrete time invariant system with erasure channel and linear continuous time invariant system with networkeddelay channel are considered respectively. By coding scheme based on spherical polarcoordinate, sufcient conditions for asymptotical stability of these systems are present-ed respectively, which is used for considering control performance and communicationperformance together.In Chapter6, coding scheme based on boundary function is proposed for quantizedcontrol system with multiple channels. When coding, the coding scheme only needs thepresent state or output of the systems and uses finite and constant channel data rates. Thedefinite relation between the boundary function and the quantized error is developed forconvergence analysis of the system. Then the coding scheme is applied to linear discretetime invariant system with multiple sensors and one controller to guarantee the systemconvergent. Sufcient condition for the convergence of the system with multiple reliablechannels is presented and the procedure for the design of the encoders and decoders andcontroller is given. Further, the same thing for the system with multiple erasure channelsis done. These sufcient conditions show the tradeof between control and communicationperformance.In Chapter7, consensus control of multi-agent system is considered. Coding schemebased on boundary function is used to guarantee the state of each agent to converge to acommon value under the following four cases of channels:1) uplink channels with fixedtopology,2) uplink channels with time-varying topology,3) downlink channels with fixedtopology,4) downlink channels with time-varying topology. Sufcient conditions for theconvergence of the systems for four cases are presented respectively. These conditionscontain the parameters of encoders and decoders and the parameter of controller, whichare used for considering control performance and communication performance together.