Robust positive invariance and ultimate boundedness of nonlinear systems

In this article the problem of characterizing sets, described by vector nonlinear inequalities of the form v(x) = w, as robustly positively invariant and targets of uniformly ultimate bounded nonlinear systems is investigated. The class of general parameter uncertain continuous-time dynamical systems affected by exogenous disturbances is considered. The approach is based on establishing an associated monotone nonlinear comparison system. A numerical example is presented to illustrate the approach

Modélisation et contrôle de systèmes électriques de puissance avec propriétés de stabilité

To deal with nonlinear, large scale, multidomain, systems, as power systems are, we have witnessed in the last few years an increasing interest in energy–based modeling, analysis and controller design techniques. Energy is one of the fundamental concepts in science and engineering practice, where it is common to view dynamical systems as energy-transformation devices. This perspective is particularly useful in studying complex nonlinear systems by decomposing them into simpler subsystems which, upon interconnection, add up their energies to determine the full systems behavior. This is obviously the most natural and intuitive language to represent power systems. In particular, the use of port–Hamiltonian (pH) systems has been already proven highly successful in many applications, namely for mechanical, electrical and electromechanical systems. The port-Hamiltonian systems paradigm theremore provides a solid foundation, which suggests new ways to look at power systems analysis and control problems.Based on this framework, this thesis is structured in three main steps.1 - Modelling of a generalized class of electric power systems, based on graph theory and port-Hamiltonian representation of the individual components.2 - Modelling, analysis and control of multiterminal hvdc transmission systems. With the intention to bridge the gap between theory and applications, one of the main concerns is to establish connections between existing engineering solutions, usually derived via ad hoc considerations, and the solutions stemming from theoretical analysis.3 - Additional contributions of the author in other fields of electric power systems, including traditional ac power systems an microgrids.Pour traiter les systèmes non linéaires, à grande échelle, multi-domaine tels que les systèmes électriques de puissance, nous avons remarqué dans les dernières années un intérêt croissant pour les techniques de modélisation, analyse et contrôle basées sur la notion d'énergie. L'énergie est en fait un concept fondamental en science et en ingénierie, où typiquement les systèmes dynamiques sont regardés comme des dispositifs de transformation d'énergie. Cette perspective est particulièrement utile pour étudier des systèmes non linéaires assez complexes, qui peuvent être décomposés en sous-systèmes plus simples, caractérisés au niveau énergétique, et qui, à travers leurs interconnexions, déterminent le comportement global du système tout entier. Il représente bien évidemment le langage le plus naturel et intuitif pour représenter les systèmes électriques de puissance. En particulier, l'utilisation de systèmes Hamiltoniens à Ports a eu un impact très fort dans différentes applications, plus précisément dans le cas de systèmes mécaniques, électriques et électromécaniques. Dans ce contexte alors, l'approche Hamiltonien à Ports représentent sans doute une base solide qui montre une nouvelle fac{c}on d'aborder les problèmes d'analyse et contrôle de systèmes électriques de puissance. Basée sur cette approche, la thèse est structurée en trois étapes fondamentales:1 - Modélisation d'une classe très générale de systèmes électriques de puissance, basée sur la théorie des graphes et la formulation en Systèmes Hamiltoniens à Ports des composantes.2 - Modélisation, analyse et commande de systèmes de transmission de courant continu haute tension. Avec l'intention de construire un pont entre la théorie et les éventuelles applications, un des objectifs fondamentaux consiste à établir des relations évidentes entre les solutions adoptées dans la pratique et les solutions obtenues à travers une analyse mathématique précise.3 - Travaux apparentés de l'auteur, dans différents domaines des systèmes électriques de puissance: systèmes ac conventionnels et micro réseaux

Getting noncooperative agents to cooperate:nudging and dynamic interventions

Due to the strong interconnection between modern engineering systems and their users, performance of these systems heavily rely on the user behavior. Therefore, uncoordinated user behavior can deteriorate the overall performance and entail undesired outcomes. To address this problem, this thesis studies the problem of designing suitable interventions that provide coordination among noncooperative agents/players. We investigate the development of suitable interventions in several setups and propose mechanisms that achieve a desired outcome. The first part of the thesis focuses on altering the aggregative behavior of noncooperative price-taking agents towards a desired stationary or temporal behavior. We address this problem by introducing a nudge framework, where a system regulator modifies the behavior of the agents by providing a price prediction signal. In the second part of the thesis, we focus on designing intervention mechanisms that steer the actions of noncooperative players in network games to the social optimum. We investigate different cases based on the knowledge of the system regulator on the game as well as constraints on the actions and interventions. The third part of the thesis deals with the problem of Nash equilibrium seeking in aggregative games. We develop a distributed algorithm where the players communicate to their neighboring players. The robustness and privacy preserving properties of the algorithm are also analyzed

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Foundations of Mechanics, Second Edition

Preface to the Second Edition. Since the first edition of this book appeared in 1967, there has been a great deal of activity in the field of symplectic geometry and Hamiltonian systems. In addition to the recent textbooks of Arnold, Arnold-Avez, Godbillon, Guillemin-Sternberg, Siegel-Moser, and Souriau, there have been many research articles published. Two good collections are "Symposia Mathematica," vol. XIV, and "Géométrie Symplectique el Physique Mathématique," CNRS, Colloque Internationaux, no. 237. There are also important survey articles, such as Weinstein [1977b]. The text and bibliography contain many of the important new references we are aware of. We have continued to find the classic works, especially Whittaker [1959], invaluable. The basic audience for the book remains the same: mathematicians, physicists, and engineers interested in geometrical methods in mechanics, assuming a background in calculus, linear algebra, some classical analysis, and point set topology. We include most of the basic results in manifold theory, as well as some key facts from point set topology and Lie group theory. Other things used without proof are clearly noted. We have updated the material on symmetry groups and qualitative theory, added new sections on the rigid body, topology and mechanics, and quantization, and other topics, and have made numerous corrections and additions. In fact, some of the results in this edition are new. We have made two major changes in notation: we now use f^* for pull-back (the first edition used f[sub]*), in accordance with standard usage, and have adopted the "Bourbaki" convention for wedge product. The latter eliminates many annoying factors of 2. A. N. Kolmogorov's address at the 1954 International Congress of Mathematicians marked an important historical point in the development of the theory, and is reproduced as an appendix. The work of Kolmogorov, Arnold, and Moser and its application to Laplace's question of stability of the solar system remains one of the goals of the exposition. For complete details of all tbe theorems needed in this direction, outside references will have to be consulted, such as Siegel-Moser [1971] and Moser [1973a]. We are pleased to acknowledge valuable assistance from Paul Chernoff, Wlodek Tulczyjew, Morris Hirsh, Alan Weinstein, and our invaluable assistant authors, Richard Cushman and Tudor Ratiu, who all contributed some of their original material for incorporation into the text. Also, we are grateful to Ethan Akin, Kentaro Mikami, Judy Arms, Harold Naparst, Michael Buchner, Ed Nelson, Robert Cahn, Sheldon Newhouse, Emil Chorosoff, George Oster, André Deprit, Jean-Paul Penot, Bob Devaney, Joel Robbin, Hans Duistermaat, Clark Robinson, John Guckenheimer, David Rod, Martin Gutzwiller, William Satzer, Richard Hansen, Dieter Schmidt, Morris Kirsch, Mike Shub, Michael Hoffman, Steve Smale, Andrei Iacob, Rich Spencer, Robert Jantzen, Mike Spivak, Therese Langer, Dan Sunday, Ken Meyer, Floris Takens, [and] Randy Wohl for contributions, remarks, and corrections which we have included in this edition. Further, we express our gratitude to Chris Shaw, who made exceptional efforts to transfom our sketches into the graphics which illustrate the text, to Peter Coha for his assistance in organizing the Museum and Bibliography, and to Ruthie Cephas, Jody Hilbun, Marnie McElhiney, Ruth (Bionic Fingers) Suzuki, and Ikuko Workman for their superb typing job. Theoretical mechanics is an ever-expanding subject. We will appreciate comments from readers regarding new results and shortcomings in this edition. RALPH ABRAHAM, JERROLD E. MARSDEN</p

On modeling and control of multilevel converters and PLL algorithms.

Tesis (Doctorado en Control y Sistemas Dinámicos)"The present thesis is focuses in the study of the multilevel converters and the the phaselocked loop algorithms. In the first five chapters, two of the main topologies of multilevel converters are studied, namely, diode clamped multilevel converter (NPC) and cascaded H-bridge multilevel converter (HB). First, a model is obtained that described the dynamics of the three level NPC converter used in a synchronous rectifier application. The highly nonlinear model, originally in abc-coordinates, is also expressed in its ®¯°-coordinates. Special attention is given to the °-component of the control input, which represents a degree of freedom crucial for the balancing of the capacitors voltages. Then, based on this model, it is presented an adaptive controller that guarantees regulation and balance of the output capacitors voltages, as well as a close to unity power factor. Next, the modeling and the control design processes are presented for a cascade H-bridge single-phase multilevel converter used as a shunt active filter. Crucial for the developments is the transformation of the model in terms of the sum and the difference of the squares of the capacitors voltages. Moreover, it is shown that, while the current tracking problem and the regulation problem depend on the sum of the injected voltages, the balance depends on the difference between them. It is also presented a controller for the cascade H-bridge three-phase multilevel converter used as a shunt active filter. Based on the proposed mathematical model, the controller is designed to compensate harmonic distortion and reactive power due to a nonlinear distorting load. Simultaneously, the controller guarantees regulation and balance of all capacitor voltages. The idea behind the controller is to allow distortion of the current reference during the transients to guarantee regulation and balance of the capacitors voltages. The chapters 6 and 7 of the thesis deals with the design of phase-locked loop (PLL) algorithms. Although PLLs have been widely used in many electronic applications, the PLL presented here is of special interest in the synchronization of power electronic equipment coupled with the electric network. In particular, the presented PLL has been designed to work in fixed reference frame coordinates, and thus the proposed algorithm is referred as fixed reference frame PLL (FRF-PLL).

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement

Conceptual modelling and systems theory with an application using real options analysis - Volume 1

This thesis introduces an abstract conceptualization of the notion of the system and examines its relations to the various issues relating to the problem of conceptual modelling and its links to the development of formal models and control/information architectures. The overall effort is placed on creating a basis that will help to move from a purely conceptual level of describing a system to a more formal one, enabling decision making and driving the analysis away from experience and intuition. The major drive is the development of a basis of general system theory in a way that expresses all aspects which are relevant to conceptualisation, modelling and control of processes, but are so general to provide a meaningful framework for general processes. For that purpose, a general systemic framework, suitable for discussing a number of important issues arising in the analysis and design of processes, is introduced. A particular case study-the future projection of prices of electricity, generated by gas and nuclear in the UK- has been used in this thesis to enable the conceptualisation process, as well as initiate the decision making process with the use of Real Options analysis. Through this application, a spherical understanding of the requirements needed for the purpose of modelling analysis and decision making was acquired

System Concepts and Formal Modelling Methods for Business Processes

The major quality breakthrough of the 1980s was the realisation by management that business and manufacturing processes are the key to customer service and organisational performance. This thesis is concerned with the overall problem of modelling of business processes. Of special interest is the study of business processes through an interdisciplinary approach that cuts across the boundaries of management and information technology. The overall effort is placed on being able to move from a purely conceptual level of describing a business process to a more formal one, enabling decision making, and driving the analysis away from experience, intuition, and informal debate. The extended review and presentation of the various modelling methodologies given here, serve as a guide to their basic concepts and capabilities. A particular case study - the management of the human resources in a consulting company - has been used in this thesis to enable the evaluation of the modelling techniques. Hence, models have been produced, as well as simulation results to indicate the limitations, the advantages and the information gained. Through this application, the understanding of requirements for modelling analysis and decision making of business processes was acquired. Particularly, two very important techniques were investigated. System Dynamics and Petri nets provide the answers when process models are geared to deliver not only qualitative but also quantitative results. However, Petri nets provide the mathematical notation and the plethora of analysis tools needed for the validation, verification, and performance analysis of the model. Additionally, two different simulation software packages were used, based on these methodologies; Ithink®, which is based on System Dynamics, and Alpha/Sim®, based on Petri nets theory. The model produced in the case study depicts perfectly the capabilities of the two techniques. Petri nets is not the total business modelling solution, it can be complemented by other methods, such as System Dynamics and discrete-time modelling as shown in Chapter 6. The feasibility of all these modelling techniques lies entirely on the analyst, who should use them alternately to satisfy the requirements of the problem