Distributed State Estimation For Periodic Stochasitc Systems

Periodic phenomena,such as the rotation of crops in agriculture,the seasonal variation of natural climate,the rotation of man-made satellites,and so on,are common in nature.Periodic systems with periodic coefficients of differential or difference equations have aroused a lot of attention.Due to the prolonged exponential growth in semiconductor technology and wireless communications,the low-cost,low-power and multi-functional small size sensor nodes became widely available,followed by the development of sensor networks.The wide application of the sensor networks also brings about many challenges,among which the distributed state estimation problem is the most representative one.It becomes a vital matter of how to estimate the periodic system state more efficiently through the collaborative way.This article focuses on the periodic character of multiplicative noise and parameter uncertainties in periodic stochastic systems,as well as the problem of packet dropout,communication constraints,and sensor nonlinearity in wireless sensor networks.Based on the distributed strategy and robust performance analysis method,the main results are obtained as follows.1.Considering the situation that each element of system parameter occurring uncertainty randomly,a new model,representing the parameter uncertainty occurs randomly and independently by a diagonal matrix consisted of n mutually independent Bernoulli processes,is proposed for periodic stochastic system.According to the periodically changed topology of wireless sensor networks,topology-dependent quantizers with multi quantization densities are designed to optimize the using of communication channels.Sufficient conditions are established to ensure that the estimation error system is globally asymptotically stable in the mean square sense and achieves H_?performance and the gains of estimators are derived.Finally,a numerical example is given to explain the theoretical results.2.Considering the fact that large quantity of sensors work in harsh and changeable environment,periodical changed sensor nonlinearities are studied for periodic stochastic systems.In consideration of randomly occurred packet dropout during transmission in wireless sensor networks,a new model with randomly occurred successive packet dropout of neighbor information is proposed.Sufficient conditions are established to ensure that the augmented estimation error system is globally asymptotically stable in the mean square sense with the prescribed l₂-l_?performance index ? and the gains of estimators are derived.Simulation results are given to demonstrate the usefulness of the method.3.Based on periodic Lyapunov stabilization theorem,considering the fact that multiplicative noises exist in state and measurement in practical application,sufficient conditions are obtained to guarantee the stability and the average-sense l₂-l_?performance for periodic stochastic system with multiplicative noises.The l₂-l_?performance in average sense is firstly introduced in this paper to reduce the effect that the increased sensor number impact on performance index.Finally,a simulation result is given to demonstrate the availability of the method.