41 research outputs found
A Unifying Framework for Strong Structural Controllability
This paper deals with strong structural controllability of linear systems. In
contrast to existing work, the structured systems studied in this paper have a
so-called zero/nonzero/arbitrary structure, which means that some of the
entries are equal to zero, some of the entries are arbitrary but nonzero, and
the remaining entries are arbitrary (zero or nonzero). We formalize this in
terms of pattern matrices whose entries are either fixed zero, arbitrary
nonzero, or arbitrary. We establish necessary and sufficient algebraic
conditions for strong structural controllability in terms of full rank tests of
certain pattern matrices. We also give a necessary and sufficient graph
theoretic condition for the full rank property of a given pattern matrix. This
graph theoretic condition makes use of a new color change rule that is
introduced in this paper. Based on these two results, we then establish a
necessary and sufficient graph theoretic condition for strong structural
controllability. Moreover, we relate our results to those that exists in the
literature, and explain how our results generalize previous work.Comment: 11 pages, 6 Figure
Necessary and Sufficient Topological Conditions for Identifiability of Dynamical Networks
This paper deals with dynamical networks for which the relations between node
signals are described by proper transfer functions and external signals can
influence each of the node signals. We are interested in graph-theoretic
conditions for identifiability of such dynamical networks, where we assume that
only a subset of nodes is measured but the underlying graph structure of the
network is known. This problem has recently been investigated from a generic
viewpoint. Roughly speaking, generic identifiability means that the transfer
functions in the network can be identified for "almost all" network matrices
associated with the graph. In this paper, we investigate the stronger notion of
identifiability for all network matrices. To this end, we introduce a new
graph-theoretic concept called the graph simplification process. Based on this
process, we provide necessary and sufficient topological conditions for
identifiability. Notably, we also show that these conditions can be verified by
polynomial time algorithms. Finally, we explain how our results generalize
existing sufficient conditions for identifiability.Comment: 13 page
Data-Driven Criteria for Detectability and Observer Design for LTI Systems
We study the problems of determining the detectability and designing a state observer for linear time-invariant systems from measured data. First, we establish algebraic criteria to verify the detectability of the system from noise-free data. Then, we formulate data-driven linear matrix inequality-based conditions for observer design. Finally, we give conditions to infer the detectability of the system from noisy data.</p
An informativity approach to the data-driven algebraic regulator problem
In this paper, the classical algebraic regulator problem is studied in a
data-driven context. The endosystem is assumed to be an unknown system that is
interconnected to a known exosystem that generates disturbances and reference
signals. The problem is to design a regulator so that the output of the
(unknown) endosystem tracks the reference signal, regardless of its initial
state and the incoming disturbances. In order to do this, we assume that we
have a set of input-state data on a finite time-interval. We introduce the
notion of data informativity for regulator design, and establish necessary and
sufficient conditions for a given set of data to be informative. Also, formulas
for suitable regulators are given in terms of the data. Our results are
illustrated by means of two extended examples