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Mathematics of Complexity and Dynamical Systems pp 755–770Cite as

Infinite Dimensional Controllability

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  • 388 Accesses

Article Outline

Glossary

Definition of the Subject

Introduction

First Definitions and Examples

Linear Systems

Nonlinear Systems

Some Other Problems

Future Directions

Bibliography

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Abbreviations

Infinite dimensional control system:

A infinite dimensional control system is a dynamical system whose state lies in an infinite dimensional vector space—typically a Partial Differential Equation (PDE)—and depending on some parameter to be chosen, called the control.

Exact controllability:

The exact controllability property is the possibility to steer the state of the system from any initial data to any target by choosing the control as a function of time in an appropriate way.

Approximate controllability:

The approximate controllability property is the possibility to steer the state of the system from any initial data to a state arbitrarily close to a target by choosing a suitable control.

Controllability to trajectories:

The controllability to trajectories is the possibility to make the state of the system join some prescribed trajectory by choosing a suitable control.

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Author information

Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

    Olivier Glass

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  1. Olivier Glass
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Glass, O. (2012). Infinite Dimensional Controllability. In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1806-1_46

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