Lecture

Nonlinear Systems: Equilibrium Points and Dynamics

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In course

ME-523: Nonlinear Control Systems

Les systèmes non linéaires sont analysés en vue d'établir des lois de commande. On présente la stabilité au sens de Lyapunov, ainsi que des méthodes de commande géométrique (linéarisation exacte). Divers exemples illustrent la théorie (exercices papier cra ...

Description

This lecture covers the analysis of nonlinear systems, focusing on equilibrium points and system dynamics. The instructor explains how to calculate equilibrium points and analyzes the behavior of systems around these points. Various examples illustrate the concepts, such as step responses and harmonic signal analysis.

Instructor

Philippe Müllhaupt

Expertise Nonlinear Control (Geometry and Algebra)Classical DynamicsRoboticsStatistics Mission Provide rigorous technical and scientific training in nonlinear control, classical mechanics, and statistical theory Current Work Research and teaching in the fields of control theory, statistics, dynamical systems, and general mechanics. Philippe Mullhaupt received his Diplôme d Education Ingï¿½nieur | Electricitï¿½ 1993 – 1993 EPFL DEA | Automatique et Traitement du Signal 199

Official source

Related concepts (26)

NP-completeness

In computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.

P-complete

In computational complexity theory, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be reduced to it by an appropriate reduction. The notion of P-complete decision problems is useful in the analysis of: which problems are difficult to parallelize effectively, which problems are difficult to solve in limited space. specifically when stronger notions of reducibility than polytime-reducibility are considered.

Complete lattice

In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known as a conditionally complete lattice. Specifically, every non-empty finite lattice is complete. Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra.

Complete partial order

In mathematics, the phrase complete partial order is variously used to refer to at least three similar, but distinct, classes of partially ordered sets, characterized by particular completeness properties. Complete partial orders play a central role in theoretical computer science: in denotational semantics and domain theory. A complete partial order, abbreviated cpo, can refer to any of the following concepts depending on context. A partially ordered set is a directed-complete partial order (dcpo) if each of its directed subsets has a supremum.

Socialist calculation debate

The socialist calculation debate, sometimes known as the economic calculation debate, was a discourse on the subject of how a socialist economy would perform economic calculation given the absence of the law of value, money, financial prices for capital goods and private ownership of the means of production. More specifically, the debate was centered on the application of economic planning for the allocation of the means of production as a substitute for capital markets and whether or not such an arrangement would be superior to capitalism in terms of efficiency and productivity.

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