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Course# COM-502: Dynamical system theory for engineers

Summary

Linear and nonlinear dynamical systems are found in all fields of science and engineering. After a short review of linear system theory, the class will explain and develop the main tools for the qualitative analysis of nonlinear systems, both in discrete-time and continuous-time.

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Instructor

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Patrick Thiran

Patrick Thiran is a full professor in network and systems theory at the School of Computer and Communication Sciences at EPFL. He holds an electrical engineering degree from the Université Catholique de Louvain, Louvain-la-Neuve, Belgium, an M.Sc. degree in electrical engineering from the University of California at Berkeley, USA, and he received the PhD degree from EPFL, in 1996. He became an adjunct professor in 1998, an assistant professor in 2002, an associate professor in 2006 and a full professor in 2011. He was with Sprint Advanced Technology Labs in Burlingame, California, in 2000-01.
His research interests are in communication and social networks, performance analysis and stochastic models. He is currently active in the analysis and design of wireless and PLC networks (scaling laws, medium access control), in network monitoring (network tomography, multi-layer networks), and data-driven network science. He also contributed to network calculus and to the theory of locally coupled neural networks and self-organizing maps.
He served as an associate editor for the IEEE Transactions on Circuits and Systems in 1997-99 and for the IEEE/ACM Transactions on Networking in 2006-10. He is currently on the editorial board of the IEEE Journal on Selected Areas in Communication. He is/was on the program committee of different conferences in networking, including ACM Sigcomm, Sigmetrics, IMC, CoNext and IEEE Infocom. He was TPC chair of AMC IMC 2011 and CoNext 2012. He is a Fellow of the Belgian American Educational Foundation and of the IEEE. He received the 1996 EPFL Doctoral Prize and the 2008 Crédit Suisse Teaching Award.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 2)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Lectures in this course (35)

Dynamical Systems for EngineersCOM-502: Dynamical system theory for engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Introduction to Dynamical System Theory for EngineersCOM-502: Dynamical system theory for engineers

Covers trajectory, solution, and orbit of dynamical systems for engineers.

Introduction to Dynamical System TheoryCOM-502: Dynamical system theory for engineers

Introduces dynamical system theory for engineers, covering trajectories, orbits, and solutions.

Dynamical System Theory for Engineers: IntroductionCOM-502: Dynamical system theory for engineers

Introduces dynamical system theory for engineers, covering system behavior, stability, and invariant sets.

Stability of Discrete Time Periodic SolutionsCOM-502: Dynamical system theory for engineers

Covers the stability of discrete time periodic solutions and their properties.

Related concepts (567)

Geometric data analysis

Geometric data analysis comprises geometric aspects of , pattern analysis, and shape analysis, and the approach of multivariate statistics, which treat arbitrary data sets as clouds of points in a space that is n-dimensional.

Floquet theory

Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form with a piecewise continuous periodic function with period and defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to , gives a canonical form for each fundamental matrix solution of this common linear system. It gives a coordinate change with that transforms the periodic system to a traditional linear system with constant, real coefficients.

Qualitative research

Qualitative research is a type of research that aims to gather and analyse non-numerical (descriptive) data in order to gain an understanding of individuals' social reality, including understanding their attitudes, beliefs, and motivation. This type of research typically involves in-depth interviews, focus groups, or observations in order to collect data that is rich in detail and context. Qualitative research is often used to explore complex phenomena or to gain insight into people's experiences and perspectives on a particular topic.

Discrete time and continuous time

In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next.

Calculus

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves.