Citation
Vakili, Ali (2011) Random Matrix Recursions in Estimation, Control, and Adaptive Filtering. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HCKN7W53. https://resolver.caltech.edu/CaltechTHESIS:06022011214438378
Abstract
This dissertation is devoted to the study of estimation and control over systems that can be described by linear timevarying statespace models. Examples of such systems are encountered frequently in systems theory, e.g., wireless sensor networks, adaptive filtering, distributed control, etc. Recent developments in distributed catastrophe surveillance, smart transportation, and power grid control systems further motivate such a study.
While linear timeinvariant systems are wellunderstood, there is no general theory that captures various aspects of timevarying counterparts. With little exception, tackling these problems normally boils down to studying timevarying linear or nonlinear recursive matrix equations, known as Lyapunov and Riccati recursions that are notoriously hard to analyze. We employ the theory of random matrices to elucidate different facets of these recursions and answer several important questions about the performance, stability, and convergence of estimation and control over such systems.
We make two general assumptions. First, we assume that the coefficient matrices are drawn from jointly stationary matrixvalued random processes. The stationarity assumption hardly restricts the analysis since almost all cases of practical interest fall into this category. We further assume that the state vector size, n, is relatively large. The law of large numbers however guarantees fast convergence to the asymptotic results for n being as small as 10. Under these assumptions, we develop a framework capable of characterizing steadystate and transient behavior of adaptive filters and control and estimation over communication networks. This framework proves promising by successfully tackling several problems for the first time in the literature.
We first study random Lyapunov recursions and characterize their transient and steadystate behavior. Lyapunov recursions appear in several classes of adaptive filters and also as lower bounds of random Riccati recursions in distributed Kalman filtering. We then look at random Riccati recursions whose nonlinearity makes them much more complicated to study. We investigate standard recursiveleastsquares (RLS) filtering and extend our analysis beyond the standard case to filtering with multiple measurements, as well as the case of intermittent measurements. Finally, we study Kalman filtering with intermittent observations, which is frequently used to model wireless sensor networks. In all of these cases we obtain interesting universal laws that depend on the structure of the problem, rather than specific model parameters. We verify the accuracy of our results through various simulations for systems with as few as 10 states.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Control, Estimation, Kalman Filtering, Adaptive Filtering, Lyapunov, Riccati, Random Matrix Theory, Control and Estimation over Lossy Networks 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Electrical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  13 July 2009 
Record Number:  CaltechTHESIS:06022011214438378 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:06022011214438378 
DOI:  10.7907/HCKN7W53 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6495 
Collection:  CaltechTHESIS 
Deposited By:  Ali Vakili 
Deposited On:  08 Jun 2011 18:50 
Last Modified:  09 Oct 2019 17:11 
Thesis Files

PDF
 Final Version
See Usage Policy. 743kB 
Repository Staff Only: item control page