On Control And Filtering Of Networked Systems With Communication Protocols

Control and filtering problems for networked systems have been one of the main stream of research topics in control community. The past decades have witnessed a surge of research interest on the networked systems due primarily to their extensive applications in various fields including environmental monitoring, industrial automation, smart grids and distributed/mobile communications. The communication of networked systems is implemented via a shared network in which the signal transmissions would be scheduled by certain communication protocols for the purpose of preventing the data from collisions. Under such protocols, only one(or a limited number of) node is permitted to get access to the communication network. These communication protocols include, but are not limited to, the Round-Robin(RR) protocol, the Weighted Try-Once-Discard(WTOD)protocol and the stochastic communication protocol(SCP). Up to now, the analysis and synthesis issues for linear deterministic systems with communication protocols have been well developed. However, the study on the control and filtering problems for nonlinear stochastic systems, time-varying systems, delayed systems and complex systems needs to be further investigated, and there still exists certain important yet difficult problems to be dealt with.This thesis is concerned with the control and filtering problems for several kinds of networked systems subject communication protocols. More specifically, with the given communication protocols, we have focused our attention on the control and filtering problems for time-varying systems, the state estimation and ultimate boundedness control problems for nonlinear systems, as well as the consensus control and state estimation problems for complex systems. Furthermore, some new approaches are introduced including the mapping technology, backward Riccati difference equations based analysis and Lyapunov-like functional based approach. The content of this thesis could be divided into six parts. Chapters 1 first introduce the background and the existing results on the topics. Based on this, we present some open problems for improvement and summarize the main results of this thesis.In the second part, we study the filtering/state estimation issues for networked systems with communication protocols which is introduced in Chapter 2. First, the movinghorizon estimation(MHE) problem is investigated for nonlinear systems subject to the SCP scheduling. A Markov chain is utilized to characterize the selection of sensor nodes obtaining access to the network under the protocol scheduling. By extending the robust MHE method, a novel nonlinear moving-horizon estimator and an approximate moving-horizon estimator are presented to generate the estimates. Sufficient conditions are proposed under which the estimation error is exponentially ultimately bounded in mean square. Based on that, the main results are further specialized to linear systems with the SCP scheduling. Then, the set-membership filtering problem is dealt with for time-varying systems with mixed time-delays and communication protocols. Two kinds of protocol(the RR protocol and the WTOD protocol) are considered. The main purpose of the set-membership filtering under consideration is to design the filter parameters capable of confining the state estimation of the system to certain ellipsoidal region subject to the bounded non-Gaussian noises. Sufficient condition is first derived for the desired filter at each time step in terms of a recursive algorithm. Two optimization problems are solved by optimizing the constraint ellipsoid of the estimation error subject to the underlying protocol.In the third part, the state estimation problem is investigated for delayed complex networks with stochastic disturbances under the RR scheduling in Chapter 3. For the purpose of preventing data from collisions, the RR protocol is utilized to orchestrate the transmission order of nodes. The purposed of the problem addressed is to design an estimator such that the estimation error is ultimately bounded with a certain asymptotic upper bound in mean square subject to the stochastic noise and exogenous disturbance.A novel Lyapunov-like functional is employed to deal with the dynamics analysis issue of the estimation error. Then, such a bound is subsequently minimized by the designed estimator parameters. Moreover, the main results are further specialized to nonlinear complex networks without delays and linear complex networks with delays.The forth part is concerned with the control problems for networked systems subject to communication protocols which is proposed in Chapter 4. First, we study the ultimate boundedness control problem for nonlinear stochastic systems subject to the WTOD protocol. Both the uniform quantization effects and protocol scheduling are considered in the communication between sensors and the controller. A nonlinear observer based controller is constructed in which an extra controller parameter is employed compared with the Luenberger observer based controller. By constructing a Lyapunov-like function, sufficient conditions are derived under which the closed-loop system is ultimately bounded in mean square. Furthermore, the controller parameters are derived by minimizing the asymptotic upper bound of the controller output in mean square. Then, the finite-horizon H∞control problem is considered for time-varying systems subject to the SCP scheduling. Two communication networks(i.e. the sensor-to-controller network and the controller-to-actuator network) have been considered where only one sensor and one actuator are allowed to get access to networks at each transmission instant. The aim of the problem addressed is to design an observer-based controller such that the H∞performance of the closed-loop system is guaranteed over a given finite horizon. The mapping technology is utilized to generate a new Markov chain associating with the SCP scheduling of networks. Both the methods of stochastic analysis and completing squares are employed to establish the sufficient conditions for the existence of the desired controller. The controller parameters are characterized by solving two coupled backward recursive Riccati difference equations.In the fifth part, the distributed H∞consensus control problem is considered in Chapter 5 for a discrete time-varying multi-agent system with the SCP scheduling. A directed graph is used to characterize the communication topology of the multi-agent network.The data transmission between each agent and the neighboring ones is implemented via a constrained communication channel where only one neighboring agent is allowed to transmit data at each time instant. The SCP is applied to schedule the signal transmission of the multi-agent system, and a sequence of random variables is utilized to capture the scheduling behavior of the SCP. By using the mapping technology combined with the Hadamard product, the closed-loop multi-agent system is modeled as a time-varying system with a stochastic parameter matrix. The purpose of this chapter is to design a cooperative controller for each agent such that, for all probabilistic scheduling behaviors,the H∞consensus performance is achieved over a given finite horizon for the closed-loop multi-agent system. A necessary and sufficient condition is derived to ensure the H∞consensus performance based on the completing squares approach and the stochastic analysis technique. Then, the controller parameters are obtained by solving two coupled backward recursive Riccati difference equations.In the six part, we consider the state estimation problem for communication-based train control(CBTC) systems with the p-persistent CSMA protocol scheduling which is introduced in Chapter 6. First, the dynamics of a train with n cars linked by couplers is described based on the Newton’s motion equations. Then, the transmission model reflecting the behavior of p-persistent CSMA protocol is presented by using a Bernoulli distributed sequence whose probability distribution is dependent on the number of trains sharing with one communication channel(i.e. N(k)). Furthermore, the value of N(k) is assumed to be unknown but bounded by two known positive integers. The purpose of the problem addressed is to design an estimator such that the estimation error is exponentially ultimately bounded(with a certain asymptotic upper bound) in mean square subject to the external resistive force. By utilizing the approach introduced in Chapters 4-6, sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square. Two optimization problems are solved in terms of linear matrix inequalities to design the desired estimator gains under different requirements(e.g. the smallest ultimate bound and the fastest decay rate). This part represents the first attempt of applying the stochastic state estimation approach to practical engineering problems subject communication protocols.