General input balancing and model reduction for linear and nonlinear systems

IEEE Trans. Automat. Contr.

2016

Abstract-Model reduction by moment matching for "interpolation signals" which do not have an implicit model, i.e. they do not satisfy a differential equation, is considered. Particular attention is devoted to discontinuous, possibly periodic, signals. The notion of moment is reformulated using an integral matrix equation. It is shown that, under specific conditions, the new definition and the one based on the Sylvester equation are equivalent. New parameterized families of models achieving moment matching are given. The results are illustrated by means of a numerical example.

“…Assumption 1 is a standard condition for the existence of a well-defined steady-state response of the state of system (1) driven by (6) [24], [25], [26].…”

Section: B Problem Formulationmentioning

confidence: 99%

“…The model reduction problem has been addressed from several perspectives: exploiting Hankel operators [1], [2], [3]; the theory of balanced realizations [4], [5], [6]; the notion of moment matching [7], [8], [9], [10]. For an extensive list of references see the monograph [11].…”

Section: Introductionmentioning

confidence: 99%

Model Reduction by Matching the Steady-State Response of Explicit Signal Generators

IEEE Trans. Automat. Contr.

2016

“…It has been extensively studied exploiting the singular value decomposition (SVD), e.g. [2], [3], [4], [5], [6], [7], [8], and the Krylov projection method (also known as moment matching), e.g. [9], [10], [11], [12], [13], [14] and [15].…”

Section: Introductionmentioning

confidence: 99%

Model Reduction of Neutral Linear and Nonlinear Time-Invariant Time-Delay Systems With Discrete and Distributed Delays

IEEE Trans. Automat. Contr.

2016

Abstract-The problem of model reduction by moment matching for linear and nonlinear differential time-delay systems is studied. The class of models considered includes neutral differential time-delay systems with discrete-delays and distributeddelays. The description of moment is revisited by means of a Sylvester-like equation for linear time-delay systems and by means of the center manifold theory for nonlinear time-delay systems. In addition the moments at infinity are characterized for both linear and nonlinear time-delay systems. Parameterized families of models achieving moment matching are given. The parameters can be exploited to derive delay-free reduced order models or time-delay reduced order models with additional properties, e.g. interpolation at an arbitrary large number of points. Finally, the problem of obtaining a reduced order model of an unstable system is discussed and solved.

“…Some of these techniques are based on the singular value decomposition, see e.g. [2], [3], [4] which make use of Hankel operators and [5], [6], [7], [8] which make use of balanced realizations. Another family of techniques belongs to the Krylov projection theory, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Model reduction for nonlinear systems and nonlinear time-delay systems from input/output data

2015 54th IEEE Conference on Decision and Control (CDC)

2015

Abstract-An algorithm for the estimation of the moments of nonlinear systems and nonlinear time-delay systems from input/output data is proposed. The estimate is exploited to construct a family of reduced order models. Conditions to enforce additional properties, e.g. matching with asymptotic stability, matching with prescribed relative degree, matching with prescribed zero dynamics, upon the reduced order model are provided. The use of the technique is illustrated by a few examples based on the averaged model of the DC-to-DCĆuk converter.