Probability-Guaranteed Set-Membership Filtering For The Complex Networks With Random Delays

The progress of 5G and other communication technologies promote the development of complex networks theory.However,one of the problems brought by complex networks is how to make use of limited resources to achieve better performance in the complex network-induced environment.As an important part of complex networks problems,the set-membership filtering is to construct the set-membership filter according to the measurements of the systems so as to ensure the filtering errors in the desired region.The Probability-guaranteed set-membership filtering problem being an extension of set-membership filtering problem is a new research focus developed in recent years.When the systems have randomness for the internal or external disturbance or sudden changes of external environment,the original performance objective of set-membership filtering cannot be completely realized.At the time,the probability-guaranteed set-membership filtering problem only requires to complete the predetermined target with a certain probability,which can be widely used in signal tracking and target positioning.As a common network-induced phenomenon,time delay is also an important factor considered in filtering,including process delay and transmission delay.In this paper,we study three kinds of probability-guaranteed set-membership filtering problems for time-varying complex networks with random delay.The specific research content is as follows:1.The probability-guaranteed set-membership filtering problem is studied for a class of discrete nonlinear complex networks with attenuation measurements and random delays in the research.The Bernoulli random variable describes random delay as randomly occurring delay;Attenuation measurements are described by random variables followed a known probability distribution over the interval.In this paper,the probability-guaranteed set-membership filter is designed,and the sufficient condition expressed by RLMI is given to ensure that the filtering errors are limited to the known probability ellipsoid sets.A convex optimization problem is established in the sense of matrix trace to minimize the set of probability ellipsoids obtained at each time,and an algorithm is designed to solve the filter gain matrix.Finally,a numerical example proves the effectiveness of the proposed filtering scheme.2.We explore the probability-guaranteed set-membership filtering problem for discrete nonlinear complex networks with DoS attacks and random delay.The DoS attacks are characterized by periodic jump signals which can interrupt communication.The delay is assumed to be random occurrence delay with uncertain probability,the system noises are Gaussian noises,and the nonlinearity meets the Lipschitz condition.Introduce dynamic ETS to reduce unnecessary information transmission.The probability-guaranteed set-membership filter is designed to ensure that the probability of the filtering errors in the desired ellipsoid is not less than a given probability value.The recursive optimization algorithm is designed to obtain the optimal filter gain matrix based on the convex optimization method.In the end,the numerical example is brought to verify the effectiveness of the proposed filtering scheme.3.Under aperiodic DoS attacks,the probability-guaranteed set-membership filtering problem is investigated for discrete nonlinear complex networks subject to random delay.Consider that each networks node is in different aperiodic DoS attacks environment.It is assumed that random delay is a discrete random variable with uncertainty of probability,the nonlinearity satisfies the Lipschitz condition and the continuous differentiable condition respectively,and the systems noises are mixed noises of UBB noises and Gaussian noises.At the same time,the adaptive ETS based on the filtering errors is introduced in order to save networks resources.Then,the distributed non-fragile probability-guaranteed set-membership filter is designed in the case of delay,nonlinearity and aperiodic DoS attacks.The RLMI method and convex optimization method are utilized to obtain the sufficient condition ensuring that the filtering errors meet the constraint of probability ellipsoid,then the minimum set of probability ellipsoid is found.At last,a numerical example is given to confirm the application about the designed filtering method.