Lecture

Large Scale Stability in Dynamical Systems

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In course

COM-502: Dynamical system theory for engineers

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-t ...

Description

This lecture covers the concept of large scale stability in dynamical systems, focusing on the analysis of stability conditions and the behavior of interconnected systems. The instructor discusses the mathematical framework and key principles for understanding the stability of complex systems.

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Instructor

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.

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Related concepts (32)

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.

Dynamical systems theory

Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.

Behaviorism

Behaviorism (also spelled behaviourism) is a systematic approach to understanding the behavior of humans and other animals. It assumes that behavior is either a reflex evoked by the pairing of certain antecedent stimuli in the environment, or a consequence of that individual's history, including especially reinforcement and punishment contingencies, together with the individual's current motivational state and controlling stimuli. Although behaviorists generally accept the important role of heredity in determining behavior, they focus primarily on environmental events.

Applied behavior analysis

Applied behavior analysis (ABA), also called behavioral engineering, is a psychological intervention that applies empirical approaches based upon the principles of respondent and operant conditioning to change behavior of social significance. It is the applied form of behavior analysis; the other two forms are radical behaviorism (or the philosophy of the science) and the experimental analysis of behavior (or basic experimental laboratory research).

Complex system

A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe.

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