State Estimation For Descriptor Linear Systems

Descriptor systems occur naturally in robotics, economic, electronic and chemical systems, which are more common than conventional systems to describe the actual systems. The estimation problems for descriptor systems are fundamental to control and synthesis problems for them. With the advent of multi-sensor systems, fused estimation problems for multi-sensor descriptor systems have been received more and more attentions, but they are still in the preliminary stage.Based on Kalman filtering theory and white noise estimators, this dissertation mainly considers the problem of state estimation for single-channel descriptor linear systems and multi-sensor descriptor linear systems, respectively. The main research results in this dissertation can be given as the following.Firstly, reduced-order fixed-interval Kalman smoother for Y-observable single-chanel descriptor linear systems is proposed. By constrained equivalent transformation, the descriptor systems are changed into two conventional subsystems. Based on Kalman filtering theory and white noise estimators, state estimators for subsystems are obtained and therefore fixed-interval Kalman smoother for descriptor systems is proposed. The new smoother avoids the evaluation of the inverse of prediction error variance matrix P (t |t?1) and achieves positive direction calculation.Secondly,reduced-order fixed-lag Kalman smoother for completely observable single-chanel descriptor linear systems is proposed. By singular value decomposition, the descriptor systems are changed into two conventional subsystems. Hence, an asymptotically stable steady-state Kalman fixed-lag smoother is gained by pole assignments. The new algorithm can reduce the computational burden and quickly eliminate the influence of initial values by assigning poles. Thirdly,the reduced-order Wiener state estimation problem is considered for single-chanel descriptor linear systems. Based on steady-state Kalman filters, reduced-order Wiener state estimators are proposed under completely observable assumption. Reduced-order Wiener state estimators are expressed in transfer functions with measurements as inputs, which can handle the prediction, filtering and smoothing problems in an unified form and have asymptotical stability without considering the selection of initial values. A numerical example is given to demonstrate the effectiveness of the proposed algorithm.Fourthly, under the assumption that descriptor systems are regular and casual, the state information fusion optimal estimation problem is considered for multi-sensor descriptor linear systems. One method is that by constrained equivalent transformations a descriptor linear system is changed into a conventional system with color system noises. And the one-step forward Kalman predictor, N-step forward Kalman predictor and Kalman filter are derived based on Kalman filtering theory. Under linear least variance fusion rules, decentralized optimal Kalman fused predictors and fused filters weighted by matrices, diagonal matrices and scalars are proposed by calculating the cross-variance matrices between the th subsystem and the jth subsystem.Another method is to change the descriptor systems into conventional systems with correlated measurement noises by constrained equivalent transformations. A recursive steady-state Kalman filter is derived and therefore filter error cross-variance matrices are obtained. According to the linear least variance fusion rules, three kinds of steady-state Kalman fused filters weighted by matrices, diagonal matrices and scalars are proposed.Fifthly, two kinds of fused Kalman filters weighted by measurements are proposed for descriptor systems with same and different measurements matrices. When the descriptor systems have same dimensionality matrices and uncorrelated system noise and measurement noises , functional equivalence between fused measurement Kalman filters is verified. All results are illustrated by numerical examples and utilizing the forms of graphs and tables shows the comparison between true values and estimated values. w( t)vi(t)Finally, the information fusion state Wiener prediction problem is considered for multi-sensor descriptor linear systems. Based on steady-state Kalman predictors, asymptotically stable Wiener state predictors for subsystems and cross-variance matrices between them are derived. According to the linear least variance fusion rules, fused Wiener predictors weighted by matrices, diagonal matrices and scalars are proposed. The effectiveness of the proposed algorithms is demonstrated by a numerical example.