Title page for ETD etd-04212010-100919

Type of Document

Dissertation

Author

Rautenberg, Carlos Nicolas

URN

etd-04212010-100919

Title

A Distributed Parameter Approach to Optimal Filtering and Estimation with Mobile Sensor Networks

Degree

PhD

Department

Mathematics

Advisory Committee

Advisor Name	Title
Burns, John A.	Committee Chair
Borggaard, Jeffrey T.	Committee Member
Cliff, Eugene M.	Committee Member
Herdman, Terry L.	Committee Member
Zietsman, Lizette	Committee Member

Keywords

Riccati Equation
Kalman Filter
Mobile Sensor Networks
Optimal Filtering

Date of Defense

2010-03-31

Availability

unrestricted

Abstract

In this thesis we develop a rigorous mathematical framework for
analyzing and approximating optimal sensor placement problems for
distributed parameter systems and apply these results to PDE
problems defined by the convection-diffusion equations. The
mathematical problem is formulated as a distributed parameter
optimal control problem with integral Riccati equations as
constraints. In order to prove existence of the optimal sensor
network and to construct a framework in which to develop rigorous
numerical integration of the Riccati equations, we develop a theory
based on Bochner integrable solutions of the Riccati equations. In
particular, we focus on $\I_p$-valued continuous solutions of the
Bochner integral Riccati equation. We give new results concerning
the smoothing effect achieved by multiplying a general strongly
continuous mapping by operators in $\I_p$. These smoothing results
are essential to the proofs of the existence of Bochner integrable
solutions of the Riccati integral equations. We also establish that
multiplication of continuous $\I_p$-valued functions improves
convergence properties of strongly continuous approximating mappings
and specifically approximating $C_0$-semigroups. We develop a
Galerkin type numerical scheme for approximating the solutions of
the integral Riccati equation and prove convergence of the
approximating solutions in the $\I_p$-norm. Numerical examples are
given to illustrate the theory.

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