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Koopman operator extensions for control: bridging infinite input sequences and operator families
M. Haseli, I. Mezić, J. Cortés
Proceedings of the IEEE Conference on Decision and Control, Rio de Janeiro, Brazil, 2025, submitted

Abstract

This paper investigates the connections between two existing formal extensions of Koopman operator theory to general discrete-time control systems that are not necessarily control-affine. The frameworks, namely (i) Koopman operator via infinite input sequences and (ii) Koopman control family, encode the system behavior in fundamentally different ways and rely on different function spaces. In spite of this, we connect the frameworks by defining operations that allow to go from one function space to the other, and provide precise conditions that ensure the function spaces capture the same information. Moreover, we prove that under these conditions the formal approaches are equivalent in terms of encoding the state information and multi-step trajectories in function values.

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