Data-Driven Model Order Reduction of Linear Switched Systems in the Loewner Framework

Abstract

Abstract. The Loewner framework for model reduction is extended to the class of linear switched systems. One advantage of this framework is that it introduces a trade-off between accuracy and complexity. Moreover, through this procedure, one can derive state-space models directly from data which is related to the input-output behavior of the original system. Hence, another advantage of the framework is that it does not require the initial system matrices. More exactly, the data used in this framework consists in frequency domain samples of input-output mappings of the original system. The definition of generalized transfer functions for linear switched systems resembles the one for bilinear systems. A key role is played by the coupling matrices, which ensure the transition from one active mode to another. 1. Introduction. Model order reduction (MOR) seeks to transform large, complicated models of time dependent processes into smaller, simpler models that are nonetheless capable of accurately representing the behavior of the original process under a variety of operating conditions. The goal is an efficient, methodical strategy that yields a dynamical system evolving in a substantially lower dimension space (hence requiring far fewer computational resources for realization) yet retaining response characteristics close to the original system. Such reduced order models could be used as efficient surrogates for the original model, replacing it as a component in larger simulations.Hybrid systems are a class of nonlinear systems which result from the interaction of continuous time dynamical subsystems with discrete events. More precisely, a hybrid system is a collection of continuous time dynamical systems. The internal variable of each dynamical system is governed by a set of differential equations. Each of the separate continuous time systems is labeled as a discrete mode. The transitions between the discrete states may result in a jump in the continuous internal variable. Linear switched systems (LSSs) constitute a subclass of hybrid systems; the main property is that these systems switch among a finite number of linear subsystems. Also, the discrete events interacting with the subsystems are governed by a piecewise continuous function called the switching signal.Hybrid and switched systems are powerful models for distributed embedded sys-

Nonparametric System identification of Stochastic Switched Linear Systems

“…Despite substantial work on realization theory, identification and model reduction of SLS, there is little work on purely data driven approaches to model approximation. More recently, [1], [21] study data driven approaches to learning reduced order approximations of the original model. However, [21] does not assume any noise in the data generating process.…”

“…More recently, [1], [21] study data driven approaches to learning reduced order approximations of the original model. However, [21] does not assume any noise in the data generating process. This work is an extension of the work in [1] to the case of SLS.…”

Preserving the DAE structure in the Loewner model reduction and identification framework

“…For a recent survey on the Loewner framework for linear systems, see [6]. For the nonlinear case, this method requires appropriate definition of transfer functions, as described in some of its extensions, i.e., to bilinear [5], quadratic-bilinear [23], and switched systems [24].…”

New Gramians for Switched Linear Systems: Reachability, Observability, and Model Reduction

“…and observability reduction with constrained switching, [17], [18], [38] for H ∞ -type reduction, and [16], [21], [33] for balancing-based methods. For continuous-time switched linear systems, see [6], [7], [22] for a class of moment-matching methods, [23], [27], [28], [32] for balancing-based methods and [31] for model reduction of systems affected by a lowrank switching. Also, [29] presents a theoretical analysis of the techniques proposed in [32] and [33] for continuous-and discrete-time SLS.…”