Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms
Name
2106.03589v3.pdf
Description
Accepted version
Size
1.96 MB
Format
Adobe PDF
Checksum (MD5)
bb0a5c867f6e64f4e05d040cc0314396
Author(s)
Boffi, Nicholas M.
Tu, Stephen
Slotine, Jean-Jacques
Date Issued
December 14, 2021
Publisher
IEEE|2021 60th IEEE Conference on Decision and Control (CDC)
Citation
Boffi, Nicholas M., Tu, Stephen and Slotine, Jean-Jacques. 2021. "Nonparametric Adaptive Control and Prediction: Theory and Randomized Algorithms." 00.
Version
Author's final manuscript
Abstract
— A key assumption in the theory of nonlinear
adaptive control is that the uncertainty of the system can
be expressed in the linear span of a set of known basis
functions. While this assumption leads to efficient algorithms,
it limits applications to very specific classes of systems. We
introduce a novel nonparametric adaptive algorithm that learns
an infinite-dimensional parameter density to cancel an unknown disturbance in a reproducing kernel Hilbert space.
Surprisingly, the resulting control input admits an analytical
expression that enables its implementation despite its underlying infinite-dimensional structure. While this adaptive input
is rich and expressive – subsuming, for example, traditional
linear parameterizations – its computational complexity grows
linearly with time, making it comparatively more expensive
than its parametric counterparts. Leveraging the theory of
random Fourier features, we provide an efficient randomized
implementation which recovers the computational complexity
of classical parametric methods while provably retaining the
expressiveness of the nonparametric input. In particular, our
explicit bounds only depend polynomially on the underlying
parameters of the system, allowing our proposed algorithms to
efficiently scale to high-dimensional systems. As an illustration
of the method, we demonstrate the ability of the algorithm to
learn a predictive model for a 60-dimensional system consisting
of ten point masses interacting through Newtonian gravitation.
Description
2021 60th IEEE Conference on Decision and Control (CDC) December 13-15, 2021. Austin, Texas
MIT Department
Massachusetts Institute of Technology. Nonlinear Systems Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-ShareAlike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/cdc45484.2021.9682907
