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

We examine a new method of producing reduced order models for LTI systems which attempts to minimize a bound on the peak error between the 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 via a single scalar quantity, is able to minimize an error bound subject to a number of moment matching 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 here to 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 L₁ 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 show how to incorporate moment matching constraints into the basic error bound minimization algorithm, and present an example which utilizes the techniques described herein. We conclude with some general comments for future work, including a nonlinear programming formulation with potential implementation benefits.