Nonlinear discrete-time systems are shown to admit exact bilinear representations via separate RKHS lifts of state and input, with stabilization posed as optimization over conditional probability measures.
A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces
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abstract
We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled by Volterra series and their autoregressive variants, as well as systems admitting Hammerstein-type state-space realizations. We apply the proposed framework to the problem of data-driven modeling of such systems, i.e., when simulation or control objectives for an unknown system are carried out without an explicit system identification step. To that end, we link the behavioral approach to two data-driven modeling methods in a vector-valued RKHS: (1) minimum-norm interpolation and (2) subspace identification.
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2026 1verdicts
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Koopman Modeling and Stabilization of Discrete-Time Nonlinear Control Systems: Bilinearity on a Reproducing Kernel Hilbert Space
Nonlinear discrete-time systems are shown to admit exact bilinear representations via separate RKHS lifts of state and input, with stabilization posed as optimization over conditional probability measures.