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<!DOCTYPE html>
<html lang="en">
<head>
<title>Marco Tulio Angulo</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="author" content="owwwlab.com">
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<!-- Profile/logo section-->
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<div class="title">
<h2>Marco Tulio Angulo</h2>
<h3>creating science, exploring human being </h3>
<!--<h3> CCNR <br> Northeastern University</h3>
<h3> Brigham and Women's Hospital <br> Harvard Medical School</h3> -->
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<!-- Main navigation-->
<div id="main-nav">
<ul id="navigation">
<li>
<a href="#biography">
<i class="fa fa-user"></i>
<div class="text">About Me</div>
</a>
</li>
<li>
<a href="#research">
<i class="fa fa-book"></i>
<div class="text">Research</div>
</a>
</li>
<li>
<a href="#publications">
<i class="fa fa-edit"></i>
<div class="text">Publications</div>
</a>
</li>
<!--<li>
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<div class="text">Contact Me</div>
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</li>
<li class="external">
<a href="resume-MarcoTulioAngulo.pdf">
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<!-- Sidebar footer -->
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<div id="copyright">to search for the pearl, it is best to calm the waves</div>
</div>
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</div>
</div>
</div>
<div id="main">
<div id="biography" class="page home" data-pos="home">
<div class="pageheader">
<div class="headercontent">
<div class="section-container">
<div class="row">
<div class="col-sm-2 visible-sm"></div>
<div class="col-sm-8 col-md-5">
<div class="biothumb">
<img alt="image" src="img/personal/personal-big.png" class="img-responsive">
<div class="overlay">
<ul class="list-unstyled">
<li>Understanding, diagnosing and controlling complex systems
by blending control theory, system identification, dynamical systems theory and networks science. </li>
</ul>
</div>
</div>
</div>
<div class="clearfix visible-sm visible-xs"></div>
<div class="col-sm-12 col-md-7">
<h3 class="title">Bio</h3>
<p>
I was born in Mexico City in 1985. I got my Dr.Eng. degree in Automatic Control in 2012 from <a href="https://www.unam.mx">UNAM</a>, México, under the supervision of
<a href="http://verona.fi-p.unam.mx/~lfridman/">Leonid Fridman</a> and <a href="http://www.iingen.unam.mx/es-mx/Investigacion/Coordinacion/ElectricayComputacion/Lists/ElectricaYComputacion1/DispForm.aspx?ID=51">Jaime A. Moreno</a>.
</p>
<p>
Since 2014, I am a Postdoctoral Research Associate at the <a href="http://www.barabasilab.com/people.php">Center for Complex Network Research</a> (CCNR), Northeastern University, under the supervision of <a href="http://www.barabasi.com">Albert-László Barabási</a>.
Since 2015, I also have an appointment as Sponsored Staff Collaborator in the <a href="http://brighamandwomens.org/research/depts/medicine/channing/default.aspx">Channing Division of Network Medicine</a>, Brigham and Women's Hospital and Harvard Medical School working under the supervision of <a href="http://scholar.harvard.edu/yyl/home">Yang-Yu Liu</a>. During my stay in Boston, I have been much influenced by <a href="http://web.mit.edu/nsl/www/">Jean-Jacques Slotine</a> also.
</p>
<p>My research sits at the intersection of <b>control theory</b>, <b>system identification</b>, <b>dynamical system theory</b> and <b>network science</b>.
Inspired by these disciplines, my <b>research program</b> aims to develop mathematically rigorous theory in order to understand, diagnose and control complex networked systems in engineering, biology and medicine.
</p>
<p> My <b>current efforts</b> focus on the diagnosis of complex systems, the fundamental limitations of network reconstruction, the interplay between network structure and functionality of complex systems, optimization of uncertain systems, observability and observer design for uncertain systems, and robust control with emphasis on discontinuous algorithms.
</p>
<p>
<span class="label label-warning">I am applying for jobs!</span> <a href="resume-MarcoTulioAngulo.pdf">CV</a> and <a href="ResearchStatement-v1.pdf">Research Statement</a>.
</p>
</div>
</div>
</div>
</div>
</div>
<div class="pagecontents">
<div class="section color-1">
<div class="section-container">
<div class="row">
<div class="col-md-5 col-md-offset-1">
<div class="title text-center">
<h3>Academic Positions</h3>
</div>
<ul class="ul-dates">
<li>
<div class="dates">
<span>Present</span>
<span>2015</span>
</div>
<div class="content">
<h4>Sponsored Staff Collaborator</h4>
<p><em>Brigham and Women’s Hospital, Harvard Medical School.</em>Channing Division of Network Medicine, Boston, MA.</p>
</div>
</li>
<li>
<div class="dates">
<span>Present</span>
<span>2014</span>
</div>
<div class="content">
<h4>Postdoctoral Research Associate</h4>
<p><em>Center for Complex Network Research. </em>Northeastern University, Boston, MA.</p>
</div>
</li>
<li>
<div class="dates">
<span>2013</span>
<span>2012</span>
</div>
<div class="content">
<h4>Full-time Professor</h4>
<p><em>Faculty of Engineering</em>, UAQ, México.</p>
</div>
</li>
</ul>
</div>
<div class="col-md-5">
<div class="title text-center">
<h3>Education</h3>
</div>
<ul class="ul-card">
<li>
<div class="dy">
<span class="degree">Dr.Eng.</span>
<span class="year">2012</span>
</div>
<div class="description">
<p class="waht">Dr.Eng. in Automatic Control</p>
<p class="where">UNAM, México</p>
</div>
</li>
<li>
<div class="dy">
<span class="degree">M.Eng.</span><span class="year">2009</span>
</div>
<div class="description">
<p class="waht">Master in Electrical Engineering/Automatic Control</p>
<p class="where">UNAM, México</p>
</div>
</li>
<li>
<div class="dy">
<span class="degree">B.Sc.</span><span class="year">2007</span>
</div>
<div class="description">
<p class="waht">Bachelor degree in Automation and Mechatronic systems</p>
<p class="where">UAQ, México</p>
</div>
</li>
</ul>
</div>
</div>
</div>
</div>
<div class="section color-2">
<div class="section-container">
<div class="row">
<div class="col-md-10 col-md-offset-1">
<div class="title text-center">
<h3>Selected honors and awards</h3>
</div>
<ul class="timeline">
<li class="open">
<div class="date">2014</div>
<div class="circle"></div>
<div class="data">
<div class="subject">Member of the Mexican National System of Researchers, Level 1</div>
<div class="text row">
<div class="col-md-10">
Sistema Nacional de Investigadores (National System of Researchers) or SNI is a governmental agency established in Mexico in 1984, to promote both the quantity and quality of research in Mexico, especially in the sciences.
</div>
</div>
</div>
</li>
<li>
<div class="date">2014-2015</div>
<div class="circle"></div>
<div class="data">
<div class="subject">Grant from the Mexican National Council of Science and Technology for postdoctoral studies</div>
<div class="text row">
<div class="col-md-10">
The National Council of Science and Technology (abbreviated CONACyT) is Mexico's entity in charge of the promotion of scientific and technological activities, setting government policies for these matters, and granting scholarships for postgraduate studies. It is the equivalent of USA's National Science Foundation or Argentina's CONICET. It is officially designated as a decentralized public agency of Mexico's federal government.
</div>
</div>
</div>
</li>
<li>
<div class="date">2012</div>
<div class="circle"></div>
<div class="data">
<div class="subject">Dr. Eng degree with summa cum laude</div>
<div class="text row">
<div class="col-md-10">
Honorific mention in the defense of my thesis.
</div>
</div>
</div>
</li>
<li>
<div class="date">2010</div>
<div class="circle"></div>
<div class="data">
<div class="subject">Alfonso Caso Medal</div>
<div class="text row">
<div class="col-md-10">
Given to the most distinguished graduate of the Master program.
</div>
</div>
</div>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
<div id="research" class="page">
<div class="pageheader">
<div class="headercontent">
<div class="section-container">
<h2 class="title">Research Summary</h2>
<div class="row">
<div class="col-md-8">
<p> I have broad research interesets in the intersection of <strong>control theory</strong>, <b>system identification</b>, <b>dynamical systems theory</b> and <b>network science</b>. Based on these disciplines, I aim to develop mathematically rigorous theory in order to understand, diagnose and control complex networked systems in engineering, biology and medicine. </p>
<p>
</div>
<!--<div class="col-md-4">
<div class="subtitle text-center">
<h3>Interests</h3>
</div>
<ul class="ul-boxed list-unstyled">
<li>Time, Money and Happiness</li>
<li>The Power of Story</li>
<li>Building Innovative Brands</li>
<li>Cultural Psychology</li>
<li>Emotions, Goals, and Health</li>
<li>computer-aided design</li>
</ul>
</div>-->
</div>
</div>
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<h3>Laboratory Personel</h3>
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<h3>David A. Doe</h3>
<h4>Postdoctoral fellow</h4>
<a href="#" class="btn btn-info">+ Follow</a>
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<h3>James Doe</h3>
<h4>Postdoctoral fellow</h4>
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<h3>Nadja Sriram</h3>
<h4>Postdoctoral fellow</h4>
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<h3>Davide Doe</h3>
<h4>Research Assistant</h4>
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<h4>Summer Intern</h4>
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<h3>James Doe</h3>
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<h3>Great lab Personel!</h3>
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<h3>Network structure and functionality of complex systems</h3>
<p>Do the microscopic and macroscopic organization properties of complex systems provide functional advantages for the dynamics running on top of them? </p>
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<p>Real networks such as gene regulatory networks or the World-Wide-Web have specific (macroscopic) organization properties like scale-free degree distribution and (microscopic) properties like network motifs. Do these organization properties provide functional advantages when dynamics are considered?</p>
<p>Combining contraction theory —a recent method to analyze stability of nonlinear systems— with a simple model reduction methodology, my collaborators and I have recently shown that the microscopic organization of real biological networks represented by their network motifs best favor the stability of the whole network. In addition, we have also shown that the macroscopic organization of real networks (i.e., scale-free degree distribution) provides functional advantages in terms of emergence of new behavior in the limit of an infinite number of agents (i.e., the so-called ‘thermodynamic limit’). Understanding how new behavior emerges from aggregating simple agents remains a fundamental problem in modern physics, with deep branches that extend to biology, technology and the nature of consciousness. By deriving new asymptotics for the eigenvectors of random graphs in the thermodynamic limit, we characterize conditions for the emergence of new behavior in the sense that the mean behavior of the ther- modynamic limit cannot be approximated by the dynamics of a single agent. With these conditions, we show that networks with power-law degree distribution favor the emergence of new behavior. However, new behavior does not emerge in networks with other degree distributions (such as Erdös-Renyi, small-world or lattice networks)
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<h3>Fundamental limitations of network reconstruction</h3>
<p>What are the limits of the properties of a network that can be reconstructed from given temporal data of the system?</p>
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<p>
Network reconstruction (NR) aims to infer some property of the interaction matrix (i.e., interconnection network) of a networked system from measuring the temporal response of its nodes. Properties of interest include its sign-pattern (i.e., if interactions are inhibitory or excitatory), its connectivity (i.e., if there is an interaction or not) or the degree-sequence (i.e., number of incoming/outgoing interactions per node). Indeed, a key observation of network science is that fundamental properties of complex systems —from stability and epidemic thresholds to observability and controllability— can be determined from these properties without knowing the interaction matrix itself. Consequently, NR is being increasingly used in fields as diverse as biology, medicine or engineering, allowing us to understand, diagnose and control complex networked systems. Yet, NR remains an outstanding challenge after a decade of extensive studies. Most existing NR algo- rithms do not perform significantly better than random guesses and can even provide contradictory results for relatively simple systems. Most of these problems originate from a simple fact: our lack of understanding of the fundamentals limitations of NR, making impossible to decide if an algorithm fails due to its design limitations or due to the limitations imposed by the available data and our uncertainty about the system dynamics.
</p>
<p>By extending the notion of distinguishability —originated in system identification theory— and its analysis to consider uncertain dynamics, my collaborators and I have recently derived necessary and suf- ficient conditions to solve the NR problem. These conditions characterize how uncertain can we be about the system dynamics, and how informative does the measured temporal data need to be. Our results allows us to find the advantages and disadvantages of NR with respect to traditional parameter identification methods. We prove that NR is useful to decrease the required knowledge about the system dynamics. But, counterintuitively, NR generically requires the same the information from the measured data regardless of the property to reconstruct (e.g., degree sequence or the interaction matrix itself). Revealing these fundamental limitations shed light on designing better network reconstruction algorithms with practical improvements over existing methods.</p>
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<h3>Optimization of uncertain systems</h3>
<p>It is possible to optimize nonlinear systems with unknown dynamics and without access to all their state variables.</p>
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<p>
Traditional optimal control methodologies are not robust: they strongly rely on a model of the system, and cannot guarantee that optimality is preserved under uncertainties.
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<p>In progress.</p>
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<h3>Performance tradeoffs in the design of discontinuous algorithms</h3>
<p>Discontinous algorithms for control and observation are, at the same time, very robust (i.e., exact) to disturbances and very sensitive to measurement noises. Understanding the fundamental limits of this tradeoff reveals how to improve their performance.
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In progress.
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<h4 class="pubtitle">Network motifs emerge from interconnections that favour stability</h4>
<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Yang-Yu Liu and Jean-Jacques Slotine</div>
<div class="pubcite"><span class="label label-success">Journal Paper</span> Nature Physics, Volume 11, 848–852 (2015).</div>
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<h4>Abstract</h4>
<p>The microscopic principles organizing dynamic units in complex networks—from proteins to power generators—can be understood in terms of network ‘motifs’: small interconnection patterns that appear much more frequently in real networks than expected in random networks. When considered as small subgraphs isolated from a large network, these motifs are more robust to parameter variations, easier to synchronize than other possible subgraphs, and can provide specific functionalities. But one can isolate these subgraphs only by assuming, for example, a significant separation of timescales, and the origin of network motifs and their functionalities when embedded in larger networks remain unclear. Here we show that most motifs emerge from interconnection patterns that best exploit the intrinsic stability characteristics at different scales of interconnection, from simple nodes to whole modules. This functionality suggests an efficient mechanism to stably build complex systems by recursively interconnecting nodes and modules as motifs. We present direct evidence of this mechanism in several biological networks.</p>
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<h4 class="pubtitle">
Fundamental limitations of network reconstruction
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<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Jaime A. Moreno, Gabor Lippner, Albert-László Barabási and Yang-Yu Liu</div>
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<span class="label label-primary">ArXiv Preprint</span> arXiv:1508.03559, 2015.
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<h4>Abstract</h4>
Network reconstruction helps us understand, diagnose and control complex networked systems by inferring properties of their interaction matrices, which characterize how nodes in the system directly interact with each other. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations on which properties of the interaction matrix can be inferred from given temporal data of individual nodes remain unknown. Here we reveal these fundamental limitations by deriving the necessary and sufficient conditions to reconstruct any property of the interaction matrix. These conditions characterize how uncertain can we be about the coupling functions between nodes in the net- work, and how informative does the measured temporal data need to be; rendering two classes of fundamental limitations of network reconstruction. The first class implies a natural trade-off: the more information we want to reconstruct the more certain we need to be about the coupling functions. Consequently, reconstructing less information —such as adjacency pattern instead of edge weights— helps us decrease the needed knowledge of the system dynamics. The second class originates from the measured temporal data only and produce a rather counterintuitive limitation: even if we know the coupling functions exactly, reconstructing any property of the interaction matrix is as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data. To circumvent this limitation, we show that prior knowledge of the interaction matrix —such as bounds on the edge weights— can be very helpful. Revealing these fundamental limitations shed light on designing better network reconstruction algorithms with practical improvements over existing methods.
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<h4 class="pubtitle">Nonlinear extremum seeking inspired on second order sliding modes</h4>
<div class="pubauthor"><strong>Marco Tulio Angulo</strong></div>
<div class="pubcite"><span class="label label-success">Journal Paper</span> Automatica 57 (2015), pp. 51–55. issn: 0005-1098.</div>
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<h4>Abstract</h4>
<p>We present a new Extremum Seeking algorithm that uses Super-Twisting like nonlinear terms in order to improve its precision. In addition, the algorithm is combined with Second Order Sliding Mode observers to build an optimization framework for uncertain dynamic systems in which the variable to optimize is not measured and needs to be estimated. The relevance of the proposed framework is illustrated in the problem of biomass optimization of a biological reactor with uncertain kinetics.
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<h4 class="pubtitle">
Estimating rotor parameters in induction motors using high-order sliding mode algorithms
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<div class="pubauthor"><strong>Marco Tulio Angulo</strong> and Valentin Carrillo-Serrano</div>
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<span class="label label-success">Journal Paper</span> Control Theory and Applications, IET 9(4), pp. 574-578, 2014.
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<h4>Abstract</h4>
<p>A good estimate of the rotor's parameters is essential in high-performance control of induction motors. It is shown that the structural impediment that prevents applying a usual adaptive observer to estimate these parameters is that the relative degree between the measured output and the unknown parameters is not one. Then, the high-order sliding mode differentiator is used to circumvent this restriction allowing the construction of a usual adaptive observer. Simulation results are presented to illustrate the performance of the proposed observer under ideal conditions and in the presence of measurement noises.</p>
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<h4 class="pubtitle">
Output-feedback finite-time stabilization of disturbed feedback linearizable nonlinear systems
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<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Leonid Fridman and Jaime A. Moreno</div>
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<span class="label label-success">Journal Paper</span> Automatica 49.9 (2013), pp. 2767–2773. issn: 0005-1098, 2013
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<h4>Abstract</h4>
<p>A novel methodology for designing multivariable High-Order Sliding-Mode (HOSM) controllers for disturbed feedback linearizable nonlinear systems is introduced. It provides for the finite-time stabilization of the origin of the state-space by using output feedback. Only the additional assumptions of algebraic strong observability and smooth enough matched disturbances are required. The control problem is solved in two consecutive steps: firstly, designing an observer based on the measured output and, secondly, designing of a full-state controller computed from a new virtual output with vector relative degree. The introduced notion of algebraic strong observability allows recovering the state of the system using the measured output and its derivatives. By estimating the required derivatives through the HOSM differentiator, a finite-time convergent observer is constructed.</p>
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<h4 class="pubtitle">
On functional observers for linear systems with unknown inputs and HOSM differentiators
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<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Jaime A. Moreno and Leonid Fridman</div>
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<span class="label label-success">Journal Paper</span> Journal of the Franklin Institute (2013), issn: 0016-0032, 2013
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<h4>Abstract</h4>
<p>The problem of constructing functional observers for linear systems with unknown inputs is considered. Necessary and sufficient conditions for the existence of a proper observer (without differentiations) are revisited. A simple and explicit form of a functional observer is presented. It is shown that when such observer is not proper, it is still possible to use the High-Order Sliding Mode differentiator to implement it. Nevertheless, in such case, additional conditions on the system and the unknown input are required.</p>
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<h4 class="pubtitle">
Robust exact uniformly convergent arbitrary order differentiator
</h4>
<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Jaime A. Moreno and Leonid Fridman</div>
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<span class="label label-success">Journal Paper</span> Automatica 49.8 (2013), pp. 2489–2495.
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<h4>Abstract</h4>
<p>An arbitrary order differentiator that, in the absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n−1) times is that its n-th derivative is uniformly bounded by a known constant. The proposed differentiator switches from a newly designed uniform differentiator to the classical High-Order Sliding Mode (HOSM) differentiator. The Uniform part drives the differentiation error trajectories into a compact neighborhood of the origin in a time that is independent of the initial differentiation error. Then, the HOSM differentiator is used to bring the differentiation error to zero in finite-time.</p>
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<h4 class="pubtitle">
Output-feedback finite-time stabilization of disturbed LTI systems
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<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Leonid Fridman, and Arie Levant.</div>
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<span class="label label-success">Journal Paper</span> Automatica 48.4 (2012), pp. 606–611. issn: 0005-1098.
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<h4>Abstract</h4>
<p>Semi-global finite-time exact stabilization of linear time-invariant systems with matched disturbances is attained using a dynamic output feedback, provided the system is controllable, strongly observable and the disturbance has a bound affine in the state norm. The novel non-homogeneous high-order sliding-mode control strategy is based on the gain adaptation of both the controller and the differentiator included in the feedback. A robust criterion is developed for the detection of differentiator convergence to turn on the controller at a proper time.</p>
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<h4 class="pubtitle">
Robust exact finite-time output based control using high-order sliding modes
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<div class="pubauthor"><strong>Marco Tulio Angulo</strong>, Leonid Fridman, and Arie Levant.</div>
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<span class="label label-success">Journal Paper</span> International Journal of Systems Science 42.11 (2011), pp. 1847–1857. issn: 0020-7721.
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<div class="pubdetails">
<h4>Abstract</h4>
<p>Linear time-invariant systems with matched perturbations are exactly stabilized in finite time by means of dynamic output-feedback control under the assumptions of a permanent complete vector relative degree and bounded perturbations. The approach makes use of global high-order sliding-mode controllers and differentia- tors. A criterion of the differentiator convergence is developed for the detection of a proper time of turning on the controller. A gain adaptation strategy is proposed for both controller and differentiator. The performance with noisy discrete sampling is studied.</p>
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<h4 class="pubtitle">
Applications of the strong approximability property to a class of affine switched systems and to relaxed differential equations with affine structure
</h4>
<div class="pubauthor">Vadim Azhmyakov and <strong>Marco Tulio Angulo</strong>.</div>
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<span class="label label-success">Journal Paper</span> International Journal of Systems Science 42.11 (2011), pp. 1899–1907. issn: 0020-7721.
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<h4 class="pubtitle">Second Order Sliding Mode Algorithms for the Reconstruction of Leaks</h4>
<div class="pubauthor"><strong>Marco Tulio Angulo</strong> and C. Verde </div>
<div class="pubcite"><span class="label label-warning">Conference Papers</span> 2013 Conference on Control and Fault-Tolerant Systems (SysTol), pp. 566 - 571, Nice, France.</div>
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<h4>Abstract</h4>
<p>A framework for leak reconstruction in pipelines using second-order sliding mode is presented. Two cases are considered. In the case of a single leak, the necessary and sufficient condition that allows estimating the position of the leak is determined and discussed. Under such a condition, an algorithm that determines the position and flow of the leak in finite-time is introduced. In the case of two leaks with known positions, a finite-time estimation of the leaks flow is obtained. Experimental results for this second case are presented, together with a comparison of the performance of first and second-order sliding mode algorithms.</p>
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<h4 class="pubtitle">Identification and observation in the anode line of PEM fuel cell stacks</h4>
<div class="pubauthor">C. Kunusch, J. A. Moreno and <strong>M. T. Angulo</strong> </div>
<div class="pubcite"><span class="label label-warning">Conference Papers</span> 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), Florencia, Italy, 2013.</div>
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<h4>Abstract</h4>
<p> In this work, some potential identifica- tion/observation problems that arise in the anode line of a typical Polymer Electrolyte Membrane (PEM) fuel cell based system are highlighted and then solved. They involve estimating the hydrogen input flow at the stack anode and the water transport across the membrane. It is argued that estimating the membrane water transport is of special interest since it gives relevant information on the actual performance and state of the fuel cell. Both problems are solved by constructing robust observers and parameter identification algorithms based on the Generalized Super-Twisting Algorithm.</p>
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