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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- Infinite dimensional control system:
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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:
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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:
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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:
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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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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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