We propose a modeling framework for stochastic systems based on Gaussian
processes. Finite-length trajectories of the system are modeled as random
vectors from a Gaussian distribution, which we call a Gaussian behavior. The
proposed model naturally quantifies the uncertainty in the trajectories, yet it
is simple enough to allow for tractable formulations. We relate the proposed
model to existing descriptions of dynamical systems including deterministic and
stochastic behaviors, and linear time-invariant (LTI) state-space models with
Gaussian process and measurement noise. Gaussian behaviors can be estimated
directly from observed data as the empirical sample covariance under the
assumption that the measured trajectories are from independent experiments. The
distribution of future outputs conditioned on inputs and past outputs provides
a predictive model that can be incorporated in predictive control frameworks.
We show that subspace predictive control (SPC) is a certainty-equivalence
control formulation with the estimated Gaussian behavior. Furthermore, the
regularized data-enabled predictive control (DeePC) method is shown to be a
distributionally optimistic formulation that optimistically accounts for
uncertainty in the Gaussian behavior. To mitigate the excessive optimism of
DeePC, we propose a novel distributionally robust control formulation, and
provide a convex reformulation allowing for efficient implementation.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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