Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and blocktridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistorcapacitorinductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to socalled nitedierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM statespace representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from themore »
H_\infty Optimal Estimation for Linear Coupled {PDE} Systems
In this work, we present a Linear Matrix Inequality
(LMI) based method to synthesize an optimal H1 estimator
for a large class of linear coupled partial differential equations
(PDEs) utilizing only finite dimensional measurements. Our approach
extends the newly developed framework for representing
and analyzing distributed parameter systems using operators
on the space of square integrable functions that are equipped
with multipliers and kernels of semiseparable class. We show
that by redefining the state, the PDEs can be represented using
operators that embed the boundary conditions and inputoutput
relations explicitly. The optimal estimator synthesis problem
is formulated as a convex optimization subject to LMIs that
require no approximation or discretization. A scalable algorithm
is presented to synthesize the estimator. The algorithm
is illustrated by suitable examples.
 Award ID(s):
 1935453
 Publication Date:
 NSFPAR ID:
 10113772
 Journal Name:
 Proceedings of the IEEE Conference on Decision & Control
 ISSN:
 25762370
 Sponsoring Org:
 National Science Foundation
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