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A framework for reduced order modeling with mixed moment matching and peak error objectives

Santarelli, Keith R.

We examine a new method of producing reduced order models for LTI systems which attempts to minimize a bound on the peak error between t he original and reduced order models subject to a bound on the peak value of the input. The method, which can be implemented by solving a set of linear programming problems that are parameterized v ia a single scalar quantity, is able to minimize an error bound subject to a number of moment matc hing constraints. Moreover, because all optimization is performed in the time domain, the method can also be used to perform model reduction for infinite dimensional systems, rather than being restricted to finite order state space descriptions. We begin by contrasting the method we present her e with two classes of standard model reduction algorithms, namely, moment matching algorithms and singular value-based methods. After motivating the class of reduction tools we propose, we describe the algorithm (which minimizes the Ll norm of the difference between the original and reduced order impulse responses) and formulate the corresponding linear programming problem that is solved during each iteration of the algorithm. We then prove that, for a certain class of LTI systems, the metho d we propose can be used to produce reduced order models of arbitrary accuracy even when the original system is infinite dimensional. We then show how to incorporate moment matching constraints into the basic error bound minimization algorithm, and present three examples which utilize the techni ques described herein. We conclude with some comments on extensions to multi-input, multi-output systems, as well as some general comments for future work. © 2010 Society for Industrial and Applied Mathematics.