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Research and Application of Filtering for Linear Systems with Delayed Measurements

Author: ZhangZhiGang
Tutor: ZhangChengHui
School: Shandong University
Course: Control Theory and Control Engineering
Keywords: Delayed Recombinant innovation Krein space Optimal white noise estimation Riccati equation H_ ∞ filter
Type: PhD thesis
Year: 2009
Downloads: 165
Quote: 1
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Control system often in a variety of internal and external interference affect the environment, noise pollution may come from the sensor signal detection instrument, may also come from the lightning, the environment and other random factors. How to extract the signal from the contaminated real signal filtering technology to complete the task by the control industry attention. Due to the large inertial properties of the object, the transmission process and complex online analytical instruments and other factors, the inevitable introduction of observation lag. Delay systems widely exist in many engineering fields, such as signal processing, communications, network transmission and control, because such problems are very complex, many of the basic theory of the problem has not been completely solved. Existing methods, such as state augmentation, partial differential equations, linear operator theory, get the results or computationally intensive or requires the solution of complex partial differential equations, and it is difficult to get the filter performance analysis. Therefore, it is necessary around the estimated delay systems issues for further research and improvement. This article will examine and solve problems with delayed measurements H filtering, white noise optimal estimation and related technology in the control system fault diagnosis. The main work consists of the following: ● optimal white noise estimation problem optimal white noise estimators, by solving the Riccati equation based Kalman filtering theory and projective methods. The method can also make an estimate of system and measurement noise, and the two kinds of noise may be associated. ● for linear stochastic systems with delayed measurements to study the optimal input white noise estimation problem. Through the re-organization of the observation sequence, given recombinant innovation sequence. According to the orthogonal projection theorem in Hilbert space, the two-dimensional Riccati equation by solving the original system with recursive calculation. This method avoids the state augmentation, can effectively reduce the computational burden. For discrete system and continuous system of two situations were discussed. ● linear discrete systems with multiple delayed measurements, studied H filtering problem. This problem into an Indefinite Quadratic optimal estimation problem Krein space, and then use the Krein space theory and new interest-reorganization method devised by calculating a set of the same dimension of the original system, Riccati equation, H filter, and given the conditions of existence of the filter. ● fault estimation problem for linear systems with unknown inputs, studied the the disturbance energy sector H ∞. The key to solve the problem into Krein space H 2 fault. Riccati equation and solving a set of by recombinant innovation theory, fault estimator.

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