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Lecture

Control Theory Fundamentals

In course

MATH-301: Ordinary differential equations

Ce cours donne une introduction rigoureuse au principaux thèmes de la théorie des équations différentielles ordinaires (EDO). Les EDO sont fondamentales pour l'étude des systèmes dynamiques et des équations aux dérivées partielles. Des applications dans ce ...

Description

This lecture covers the basics of control theory, focusing on symmetric matrices, propagators, and invertibility. It explains the concept of controllability, providing proofs and examples to illustrate the theory. The lecture also delves into the controllability of systems and the implications of invertibility.

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Instructors (2)

François Samer Genoud

2000-2005 Etudes en Physique à l'EPFL dont une année d'échange à Zürich (ETH, 2002-2003). 2005 Diplôme de Physicien EPF (Master) en physique mathématique, sous la direction du Prof. C.-E. Pfister. 2005-2008 Doctorat sous la direction du Prof. C.A. Stuart, sur l'étude de certaines équations de Schrödinger non-linéaires, en particulier de questions liées à l'existence et la stabilité orbitale d'ondes stationnaires. 2009-2010 Chercheur postdoc FNS à OxPDE, Université d'Oxford. 2010-2013 Chercheur postdoc à l'Université Heriot-Watt, Edimbourg. 2013-2014 Chercheur postdoc à l'Université de Vienne. 2015-2017 Professeur Assistant à TU Delft. 2017-2018 Professeur Associé à l'Université libre de Bruxelles. 2018- Directeur du CMS Domaines d'intérêt scientifique: analyse non-linéaire, calcul des variations, équations aux dérivées partielles, physique mathématique et physique théorique en général.

Joachim Krieger

Official source

Related concepts (32)

Control theory

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.

Optimal control

Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.

Controllability

Controllability is an important property of a control system and plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem. Roughly, the concept of controllability denotes the ability to move a system around in its entire configuration space using only certain admissible manipulations. The exact definition varies slightly within the framework or the type of models applied.

Control system

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation.

Control engineering

Control engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance.

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