Research And Application Of Filtering For Linear Systems With Delayed Measurements

Almost all control systems suffer from internal or external disturbance.The source of noise pollution may come from measuring instrument such as sensor,or come from stochastic factor such as thunder and environment,etc.The main task of filtering technique is to acquire real signals from noise pollution.Moreover,large inertia objects, transmission process and complicated on-line analyzer etc,are common in the industrial processes,which can cause measurement delays in the systems.Time-delay systems are of wide application background,and are available in many engineering fields such as signal processing,communication systems,transmission and control in networks, etc.until the present time,some problems upon fundamental theory remain unsettled as a great challenge,and the conventional approaches,covering state augmentation method,partial differential equation method and linear operator theory,etc, tend to consume enormous or complicated calculations and the results from them are hard to make further performance analysis.The filtering problems for the time-delay systems have been intriguing many researchers for decades,and remain to be perfected further.The dissertation focuses on the H∞filtering for linear time-delay systems,white noise optimal filtering,and the main results are as follows.●It considers the unified optimal white noise estimation problem in H₂ setting for linear systems.Based on the Kalman filtering method and projection theory,the optimal estimator is designed via solving Riccati equations.It can compute both system noise and measurement noise simultaneously,even when input noise and measurement noise is correlated.●It studies the optimal input white noise estimator for linear stochastic systems with delayed measurements.To improve the computational efficiency,we propose a new approach without resorting to system state augmentation.The proposed approach is based on the re-organization innovation theory.The derived white noise smoother is given in terms of a series of Riccati difference equations(RDEs) with the same order as that of the original system.We discuss this problems in two cases:discrete-time systems and continuous-time systems.●It discusses the H∞filtering problem for linear discrete system with multiple measurements time-delay,transforms the underlying problem into an indefinite quadratic optimal one in Krein space,makes use of the theory in Krein space and the reorganized innovation analysis,designs the optimal filter by solving a set of Riccati equation with the same dimension of the origin system.The sufficient condition for the present solvability of the problem is given.●It investigates the H∞fault detection estimator for linear stochastic systems with unknown input and energy-bounded disturbance.The key technique is the measurements and the innovation re-organization in Krein space.The fault estimator can be designed by applying the reorganized innovation technique in Krein space and finally giving solutions by solving Riccati equations.