Control Sets for Bilinear and Affine Systems
Fritz Colonius, Juliana Raupp, Alexandre J. Santana
TL;DR
This paper characterizes control sets for homogeneous bilinear and affine control systems using Lie algebra conditions and Diophantine approximation, addressing boundedness and unboundedness of control sets around equilibria.
Contribution
It introduces a Lie algebra rank condition for control sets in bilinear systems and analyzes control set boundedness in affine systems, extending classical control theory.
Findings
Control sets characterized via Lie algebra rank condition.
Unbounded control sets identified around equilibria in affine systems.
Application of Diophantine approximation to control set analysis.
Abstract
For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control systems, the control sets around the equilibria for constant controls are characterized with particular attention to the question when the control sets are unbounded.
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