Dynamic Mode Decomposition with Control Liouville Operators
Joel A. Rosenfeld, Rushikesh Kamalapurkar
Abstract
This manuscript provides a theoretical foundation for the Dynamic Mode Decomposition (DMD) of control affine dynamical systems through vector valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville operators and control occupation kernels are introduced to separate the drift dynamics from the control effectiveness components. Given a known feedback controller that is represented through a multiplication operator, a DMD analysis may be performed on the composition of these operators to make predictions concerning the system controlled by the feedback controller.
Topics & Concepts
Dynamic mode decompositionMultiplication operatorController (irrigation)Control theory (sociology)Kernel (algebra)Operator (biology)MathematicsAffine transformationMultiplication (music)DecompositionHilbert spaceOperator theoryControl (management)Computer sciencePure mathematicsAlgebra over a fieldArtificial intelligenceChemistryMachine learningAgronomyOrganic chemistryTranscription factorGeneBiochemistryCombinatoricsRepressorBiologyModel Reduction and Neural NetworksHydraulic and Pneumatic SystemsProbabilistic and Robust Engineering Design