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ABSTRACT
As a system may evolve over time under the effects of external and internal influences, an entrance and an exit can be defined. When the exit depends linearly on the entrance, it is referred to as linear control. The basic concept for this type of control procedures is to determine an objective function that is linear and constraints that are linear matrix inequalities. This article presents the basic concepts of linear control and outlines the various parameters such as controllability, observability, canonical representation and model reduction, which make it possible to approach this concept.
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Claude BREZINSKI: Professor at Lille University of Science and Technology
INTRODUCTION
Many physical systems evolve over time as a result of external and internal influences. They behave like black boxes: they receive an input, it is then transformed according to certain laws (usually a differential equation) and an output is observed. The problem is to regulate the input, to control it in order to obtain the desired output. Modifying the input according to the output obtained is called feedback. In French, this word is translated as retour, or looping, or rétroaction. Control theory studies such dynamic systems. When the output depends linearly on the input, we speak of linear control. When the output depends linearly on the input, it is referred to as linear control.
The basic idea behind linear control methods is to express a control problem as an optimization problem with an objective function that is linear and constraints that are linear matrix inequalities.
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Numerical aspects of linear control
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Software
There are many different types of control software. Many of them are specific to a certain application, a certain field, such as the aerospace industry. Most of them are commercial and therefore not free.
The most widely used software packages are MATLAB → with a large number of toolboxes covering the majority of design, simulation and implementation methods...
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