Enforcing contraction via data
CoRR(2024)
摘要
We present data-based conditions for enforcing contractivity via feedback
control and obtain desired asymptotic properties of the closed-loop system. We
focus on unknown nonlinear control systems whose vector fields are expressible
via a dictionary of functions and derive data-dependent semidefinite programs
whose solution returns the controller that guarantees contractivity. When data
are perturbed by disturbances that are linear combination of sinusoids of known
frequencies (but unknown amplitude and phase) and constants, we remarkably
obtain conditions for contractivity that do not depend on the magnitude of the
disturbances, with imaginable positive consequences for the synthesis of the
controller. Finally, we show how to design from data an integral controller for
nonlinear systems that achieves constant reference tracking and constant
disturbance rejection.
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