442 research outputs found
Balanced Truncation of Networked Linear Passive Systems
This paper studies model order reduction of multi-agent systems consisting of
identical linear passive subsystems, where the interconnection topology is
characterized by an undirected weighted graph. Balanced truncation based on a
pair of specifically selected generalized Gramians is implemented on the
asymptotically stable part of the full-order network model, which leads to a
reduced-order system preserving the passivity of each subsystem. Moreover, it
is proven that there exists a coordinate transformation to convert the
resulting reduced-order model to a state-space model of Laplacian dynamics.
Thus, the proposed method simultaneously reduces the complexity of the network
structure and individual agent dynamics, and it preserves the passivity of the
subsystems and the synchronization of the network. Moreover, it allows for the
a priori computation of a bound on the approximation error. Finally, the
feasibility of the method is demonstrated by an example
Model reduction of networked passive systems through clustering
In this paper, a model reduction procedure for a network of interconnected
identical passive subsystems is presented. Here, rather than performing model
reduction on the subsystems, adjacent subsystems are clustered, leading to a
reduced-order networked system that allows for a convenient physical
interpretation. The identification of the subsystems to be clustered is
performed through controllability and observability analysis of an associated
edge system and it is shown that the property of synchronization (i.e., the
convergence of trajectories of the subsystems to each other) is preserved
during reduction. The results are illustrated by means of an example.Comment: 7 pages, 2 figures; minor changes in the final version, as accepted
for publication at the 13th European Control Conference, Strasbourg, Franc
Reduced-order modeling of large-scale network systems
Large-scale network systems describe a wide class of complex dynamical
systems composed of many interacting subsystems. A large number of subsystems
and their high-dimensional dynamics often result in highly complex topology and
dynamics, which pose challenges to network management and operation. This
chapter provides an overview of reduced-order modeling techniques that are
developed recently for simplifying complex dynamical networks. In the first
part, clustering-based approaches are reviewed, which aim to reduce the network
scale, i.e., find a simplified network with a fewer number of nodes. The second
part presents structure-preserving methods based on generalized balanced
truncation, which can reduce the dynamics of each subsystem.Comment: Chapter 11 in the book Model Order Reduction: Volume 3 Application
Applied Koopman Operator Theory for Power Systems Technology
Koopman operator is a composition operator defined for a dynamical system
described by nonlinear differential or difference equation. Although the
original system is nonlinear and evolves on a finite-dimensional state space,
the Koopman operator itself is linear but infinite-dimensional (evolves on a
function space). This linear operator captures the full information of the
dynamics described by the original nonlinear system. In particular, spectral
properties of the Koopman operator play a crucial role in analyzing the
original system. In the first part of this paper, we review the so-called
Koopman operator theory for nonlinear dynamical systems, with emphasis on modal
decomposition and computation that are direct to wide applications. Then, in
the second part, we present a series of applications of the Koopman operator
theory to power systems technology. The applications are established as
data-centric methods, namely, how to use massive quantities of data obtained
numerically and experimentally, through spectral analysis of the Koopman
operator: coherency identification of swings in coupled synchronous generators,
precursor diagnostic of instabilities in the coupled swing dynamics, and
stability assessment of power systems without any use of mathematical models.
Future problems of this research direction are identified in the last
concluding part of this paper.Comment: 31 pages, 11 figure
Model Reduction Methods for Complex Network Systems
Network systems consist of subsystems and their interconnections, and provide
a powerful framework for analysis, modeling and control of complex systems.
However, subsystems may have high-dimensional dynamics, and the amount and
nature of interconnections may also be of high complexity. Therefore, it is
relevant to study reduction methods for network systems. An overview on
reduction methods for both the topological (interconnection) structure of the
network and the dynamics of the nodes, while preserving structural properties
of the network, and taking a control systems perspective, is provided. First
topological complexity reduction methods based on graph clustering and
aggregation are reviewed, producing a reduced-order network model. Second,
reduction of the nodal dynamics is considered by using extensions of classical
methods, while preserving the stability and synchronization properties.
Finally, a structure-preserving generalized balancing method for simplifying
simultaneously the topological structure and the order of the nodal dynamics is
treated.Comment: To be published in Annual Review of Control, Robotics, and Autonomous
System
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