49 research outputs found
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
A Robust Consensus Algorithm for Current Sharing and Voltage Regulation in DC Microgrids
In this paper a novel distributed control algorithm for current sharing and
voltage regulation in Direct Current (DC) microgrids is proposed. The DC
microgrid is composed of several Distributed Generation units (DGUs), including
Buck converters and current loads. The considered model permits an arbitrary
network topology and is affected by unknown load demand and modelling
uncertainties. The proposed control strategy exploits a communication network
to achieve proportional current sharing using a consensus-like algorithm.
Voltage regulation is achieved by constraining the system to a suitable
manifold. Two robust control strategies of Sliding Mode (SM) type are developed
to reach the desired manifold in a finite time. The proposed control scheme is
formally analyzed, proving the achievement of proportional current sharing,
while guaranteeing that the weighted average voltage of the microgrid is
identical to the weighted average of the voltage references.Comment: 12 page
Block-Diagonal Solutions to Lyapunov Inequalities and Generalisations of Diagonal Dominance
Diagonally dominant matrices have many applications in systems and control
theory. Linear dynamical systems with scaled diagonally dominant drift
matrices, which include stable positive systems, allow for scalable stability
analysis. For example, it is known that Lyapunov inequalities for this class of
systems admit diagonal solutions. In this paper, we present an extension of
scaled diagonally dominance to block partitioned matrices. We show that our
definition describes matrices admitting block-diagonal solutions to Lyapunov
inequalities and that these solutions can be computed using linear algebraic
tools. We also show how in some cases the Lyapunov inequalities can be
decoupled into a set of lower dimensional linear matrix inequalities, thus
leading to improved scalability. We conclude by illustrating some advantages
and limitations of our results with numerical examples.Comment: 6 pages, to appear in Proceedings of the Conference on Decision and
Control 201
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