Abstract
This thesis is about parameter estimation and control of timevarying stochastic systems. It can be divided into two parts.
The first part deals with an estimation algorithm commonly used when estimating parameters in timevarying stochastic systems, the Recursive Least Squares (RLS) algorithm with forgetting factor. The exact statistical properties for the RLSestimator with forgetting factor are in most cases difficult to find, due to the complex dependency of the timevarying characteristics and on the forgetting factor. In the first part of this thesis, the RLSestimator with forgetting factor is applied to different timevarying as well as stationary FIR, AR and ARXstructures and some distribution properties for the parameter estimates are derived.
A method to compute the exact distribution and moments of the RLSestimator in timevarying Gaussian AR(1)processes is presented. For stationary vector autoregressions and stationary ARXmodels the asymptotic bias and covariance function of the RLS estimates are derived. The estimated covariance matrix of the parameter estimates is important when analyzing RLS with forgetting factor. The first moment of this estimate is calculated showing that the asymptotic bias is nonzero. Furthermore, the MSE for the parameter estimate is derived for timevarying FIRmodels, giving a possibility to find an optimal forgetting factor in the RLS algorithm.
The second part concerns the problem on controlling timevarying stochastic systems. Optimal control of such systems is generally a very difficult task, which simultaneously must take the character of the unknown timevarying parameters and the fulfilment of the control action into account. The optimal controller action thus must have dual features. However, the optimal dual controller is in most cases impossible to derive, so suboptimal dual controllers must be used.
In the thesis a new optimal adaptive predictive controller (APC) for timevarying stochastic systems is presented that can be explicitely computed for arbitrary prediction horizons. Also a large simulation study of different suboptimal dual controllers is made. The study shows that the APC can successfully be used as a suboptimal dual controller.
The first part deals with an estimation algorithm commonly used when estimating parameters in timevarying stochastic systems, the Recursive Least Squares (RLS) algorithm with forgetting factor. The exact statistical properties for the RLSestimator with forgetting factor are in most cases difficult to find, due to the complex dependency of the timevarying characteristics and on the forgetting factor. In the first part of this thesis, the RLSestimator with forgetting factor is applied to different timevarying as well as stationary FIR, AR and ARXstructures and some distribution properties for the parameter estimates are derived.
A method to compute the exact distribution and moments of the RLSestimator in timevarying Gaussian AR(1)processes is presented. For stationary vector autoregressions and stationary ARXmodels the asymptotic bias and covariance function of the RLS estimates are derived. The estimated covariance matrix of the parameter estimates is important when analyzing RLS with forgetting factor. The first moment of this estimate is calculated showing that the asymptotic bias is nonzero. Furthermore, the MSE for the parameter estimate is derived for timevarying FIRmodels, giving a possibility to find an optimal forgetting factor in the RLS algorithm.
The second part concerns the problem on controlling timevarying stochastic systems. Optimal control of such systems is generally a very difficult task, which simultaneously must take the character of the unknown timevarying parameters and the fulfilment of the control action into account. The optimal controller action thus must have dual features. However, the optimal dual controller is in most cases impossible to derive, so suboptimal dual controllers must be used.
In the thesis a new optimal adaptive predictive controller (APC) for timevarying stochastic systems is presented that can be explicitely computed for arbitrary prediction horizons. Also a large simulation study of different suboptimal dual controllers is made. The study shows that the APC can successfully be used as a suboptimal dual controller.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  1997 Sep 26 
Publisher  
ISBN (Print)  9162826190 
Publication status  Published  1997 
Bibliographical note
Defence detailsDate: 19970926
Time: 10:15
Place: Sal A, Matematikhuset, Lund
External reviewer(s)
Name: Brockwell, Peter
Title: Prof
Affiliation: Dept. of Statistics, Colorado State University, USA

Subject classification (UKÄ)
 Probability Theory and Statistics
Keywords
 Statistics
 Adaptive Predictive Control
 Adaptive Stochastic Control
 Dual Control
 Convergence Analysis
 Quadratic Forms
 Forgetting Factor
 Recursive Least Squares
 Recursive Estimation
 Linear Systems
 TimeVarying Stochastic Systems
 operations research
 programming
 actuarial mathematics
 Statistik
 operationsanalys
 programmering
 aktuariematematik