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Topics on switched systems
Get PDFThis thesis presents several results pertaining two rather distinct research topics within the broader area of the so-called "Switched Systems".
The first part of the work features a deep investigation of the structural properties, namely reachability and zero-controllability, of "Positive Switched Systems", both for the discrete-time and the continuous-time case.
All the notation relative to this contribution is defined in Chapter 1. Together with considerations on the motivational aspect, in Chapter 2, the familiar concepts of reachability and zero-controllability are properly defined within the context of positive switched systems. Then, several results are presented, first dealing with the discrete-time case, and subsequently addressing the continuous-time one. More specifically, in Chapter 3, the zero-controllability of a discrete-time positive switched system is proved to be equivalent to the mortality property of the set of system matrices; some sufficient conditions for this property to hold are then provided, together with an algorithm designed to find the correct switching sequence, if any, which is needed to drive any positive state
vector to the zero vector.
In Chapter 4 the reachability issue for discrete-time positive switched systems is addressed. First, the problem is restated into a geometric form, then the property of monomial reachability, known to be equivalent to the reachability for standard (meaning non-switched) positive systems, but only necessary in our setting, is fully explored and characterized.
All the chapters from 5 to 8 tackle with the continuous-time case.
In particular, in Chapter 5 the possibility for a continuous-time positive switched system to be zero-controllable is ruled out.
The reachability issue is first addressed in Chapter 6 where, similarly to the discrete-time case, we investigate the monomial as well as the pattern reachability property, which represent two necessary conditions for the general reachability of the system. Then, in Chapter 7, a useful sufficient condition for the reachability is provided; a geometric equivalent description of a reachable system is also introduced. Finally, further contributions to the problem of finding conditions ensuring the reachability of a continuous-time positive switched system are presented in Chapter 8, where the useful concept of asymptotic exponential cone of a Metzler matrix (an ordered set of Metzler matrices) is first defined and then fully characterized.
Results pertaining to a different stream of research 1 are included in the chapters 9 and 10.
More specifically, in Chapter 9 the case when a traditional Linear Time Invariant plant is controlled by a switching multicontroller whose transfer function may commute among different ones, each of them stabilizing the system, is considered. In particular, we focus our interest on the design of
the function, called Reset Map, ruling the update of the multicontroller state vector at every switching time. It turns out that a proper choice of it may deeply improve the controlled system transient behaviour.
The application of the same principles is then suggested in Chapter 10 in the context of non-switching reset controllers. The result presented within this chapter represents a substantial enhancement with respect to the traditional
approach which is known in the literature under the name of Reset Control Strategy.
The Appendix, besides a series of technical results which are preliminary to those presented in this thesis, features an extensive contribution to the study of the exponential of a Metzler matrix. This topic has been initially addressed as a mathematical mean for solving certain specific problems within
the setting of positive switched systems. Indeed, the analysis of reachability property for continuous-time positive switched systems requires a deep knowledge of the behaviour of these exponential matrices. For this reason, we decided to include the results in the Appendix. However, we believe that they deserve some interest by themselves, as their significance and extension
exceed by far what we needed for their initial application
Controllability and reachability of switched positive systems
No full textIn this paper controllability and reachability
properties for continuous-time switched positive systems are
introduced. Controllability is explored and ruled out, while
some preliminary characterizations of reachability are provided.
In particular, monomial reachability (which represents
a necessary condition for reachability) is fully investigated.
Finally, by focusing on the class of switched positive systems
which commute among n single-input n-dimensional systems,
we provide necessary and sufficient conditions for their
reachability
On the zero pattern properties and asymptotic behavior of continuous-time positive system trajectories
No full textIn this paper, the zero pattern properties and the asymptotic evolution of the trajectories of
a continuous-time positive system are investigated. To this end, we need to introduce some new tools and
to derive some new results, within the broad research area of nonnegative matrix theory, which enable use
to explore the zero pattern and the elementary modes of the exponential of a Metzler matrix. Specifically, a
normal form for the exponential of a Metzler matrix is provided, and the concept of echelon basis (consisting
of eigenvectors and generalized eigenvectors of the Metzler matrix) is introduced. By making use of these two
ingredients, a detailed result about the dominant mode of each single block appearing in the normal form of
the exponential matrix is provided. This allows to obtain a “modal decomposition” of the exponential matrix,
emphasizing the column dominant modes. As a result, the zero pattern as well as the asymptotic behavior of
every free state evolution, depending on the zero pattern of the initial state, can be easily determined
Reachability properties of discrete-time positive switched systems
No full textAbstract—In this paper, reachability properties of discretetime
positive switched systems are investigated. Sufficient
conditions for positive reachability to hold, together with
interesting examples, disproving some of the most natural conjectures,
are provided. The concept of monomial reachability,
which represents a necessary condition for reachability, is then
explored, and a tight upper bound on the length of the shortest
switching sequence which allows to reach a monomial vector
is provided
A fault-tolerant approach to the control of multibody mechanisms with flexible links
No full textIn this article a fault-tolerant control technique
for flexible-link multibody mechanisms is proposed, and described
in detail for the case of a planar four-bar mechanism,
lying on a horizontal plane.When no fault occurs, the feedback
control law is an adaptive PD controller, which makes use of
the crank angle measure provided by an encoder and of the
link curvatures provided by two strain gauges. When a fault
occurs in one or both strain gauges, a fault detection and
identification algorithm allows to detect the faulty device. The
faulty signal is then replaced either with a previously stored
waveform or with an estimate of the link curvature.
The resulting controlled system simple stability is formally
proved by means of a model-independent energy-based approach.
The controller performances are tested in simulation
On the reachability properties of continuous-time positive switched systems
No full textIn this paper we address the reachability of
continuous-time positive switched systems. In detail, we first
provide the reachability definition and a necessary condition
for its existence. We then fully explore the “pattern reachability”
problem, namely the problem of reaching, for every
subset S of {1, 2, . . . , n}, at least one nonnegative state vector
whose nonzero entries are exactly those corresponding to the
elements of S. Finally, for the class of n-dimensional singleinput
systems switching among n subsystems, necessary and
sufficient conditions for reachability are given
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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