Recursive Filtering For Networked Systems With Incomplete Information

Filtering problems for networked systems have been one of the hot issues in control field.With the wide applications of networked systems in various fields such as military,transportation,medical treatment and power grid,the filtering problems of networked systems have received a lot of research attention.Due to the nature of the networks(constrained bandwidth,constrained communication capacity and etc.)and the sudden environmental disturbances,some unpredictable phenomena(missing measurements,measurements quantization and transmission delays)inevitably occur when the measurement signals are transmitted through the communication network,which are the so-called incomplete information.The influence of incomplete information on system performance makes the traditional filtering methods need to be extended and innovated,which brings new challenges to the research of filtering theories.Therefore,it is an urgent and challenging research topic to develop some new methods for the filtering problems of networked systems subject to incomplete information.In this thesis,the recursive filtering problems are discussed for several net-worked systems with incomplete information.The content of this thesis is mainly divided into two parts.In the first part,we focus on the recursive filtering prob-lems for both of nonlinear stochastic systems and stochastic parameter systems in the presence of random transmission delays(RTDs),RTD-induced packet disorders,measurements quantization as well as stochastic nonlinearities.Based on the solu-tions to Riccati-like difference equations,the filter gains are presented by utilizing the matrix derivative method,and then the desired filters are designed accordingly to obtain more accurate state estimation.In the second part,the recursive filter-ing problems are investigated for complex networks based on Round-Robin protocol and the measurements from partial nodes.We design appropriate recursive filters to estimate the system states,and further analyze the boundedness of the estimation error by using the stochastic analysis techniques and Lyapunov stability theories.The detailed results of this thesis are given as follows:(1)The recursive filtering problem is studied for a class of nonlinear discrete-time stochastic systems with packet disorders.The influence of the RTDs and RTD-induced packet disorders on the measurement outputs is considered,and the relationship between the RTDs and the resulting packet disorders is also discussed.The bounded RTDs,which take place in the sensor-to-filter channel,are modeled as independent and identically distributed random variables obeying a certain proba-bility distribution.A novel filter structure is proposed that utilizes an integer-valued function of the mathematical expectation of the RTDs so as to compensate the RTD-induced effects.Under the proposed extended Kalman filter,an upper bound for the filtering error covariance is derived in terms of the solutions to two Riccati-like difference equations,and subsequently minimized by appropriately designing the filter gains.(2)The resilient filtering problem is considered for a class of nonlinear stochas-tic systems with packet disorders.The underlying system is quite comprehensive that involves both deterministic and stochastic nonlinearities.The phenomenon of packet disorders takes place in the sensor-to-filter channel as a result of the limited capability of the communication network.The RTD,which is the main cause for the packet disorders,is modeled as a bounded random variable obeying a known probability distribution and its influence on the filter performance is examined.Furthermore,the resilient issue of the proposed recursive filter against random fluc-tuations of the filter gain is thoroughly studied.Based on the above discussion,a resilient filter is proposed for the addressed nonlinear stochastic systems such that,in the presence of both stochastic nonlinearities and packet disorders,an up-per bound of the filtering error covariance is ensured and then locally minimized through adequate design of the filter gains.(3)The recursive filtering problem is investigated for a class of discrete-time stochastic parameter systems with measurements quantization and packet disorders.It is assumed that the measurements are quantized via a logarithmic quantizer be-fore transmitted to the filter from nodes.Additionally,the data packets during the transmission are assumed to be not time-stamped,which means the filter has no knowledge of the sending time instant of the received packet,and the transmis-sion delay of the received packet is also accordingly unknown.Consequently,the transmission delays are assumed to occur randomly in the communication network obeying a known probability distribution.In the simultaneous existence of random parameter matrices,measurements quantization as well as packet disorders,a novel recursive filter is designed to guarantee an upper bound matrix for the filtering error covariance.Furthermore,the boundedness of the estimation error is analyzed by means of the stochastic analysis techniques and some sufficient conditions ensuring the mean-square boundedness of the estimation error are derived.(4)The recursive filtering problem is discussed for a class of stochastic discrete-time systems subject to packet disorders and Round-Robin communication protocol over complex networks.The phenomenon of packet disorders resulted from the time delays is considered in the sampling process of signals,and a sequence of random variables obeying a known probability distribution are utilized to characterize the time delays.For the sake of mitigating the communication burden of the network,the Round-Robin protocol is introduced to schedule the transmission order of the sensor nodes.Based on the Round-Robin protocol,only one sensor node is per-mitted to send its data at each time instant.Under such a situation,a recursive filter is developed such that an upper bound is guaranteed for the filtering error co-variance,and then the obtained upper bound is minimized by choosing appropriate filter gains.Moreover,some sufficient conditions are derived by using the Lyapunov stability theories to ensure the mean-square boundedness of estimation error.(5)The recursive filtering problem is addressed for a class of discrete-time stochastic complex networks with switched topology.In the network under con-sideration,we estimate the system states via the measurement outputs from only partial nodes instead of the whole nodes,which is the so-called partial-nodes-based state estimation problem.Besides,the switching rule of this network is charac-terized by a sequence of Bernoulli random variables.To deal with the difficulties resulted from nonlinearization process of the nonlinear functions,the Taylor series expansion is utilized and the high-order terms of linearization errors are expressed in an exact way.Based on the framework of extended Kalman filter,a recursive filter is designed to ensure an upper bound for the filtering error covariance.Furthermore,the gain matrices can be acquired at each time instant via the matrix derivative method.Finally,we also prove that the estimation error is bounded in mean-square sense under some conditions with the aid of stochastic analysis techniques.