András Sasfi

András Sasfi, Ivan Markovsky, Alberto Padoan et al.

We propose a modeling framework for stochastic systems, termed Gaussian behaviors, that describes finite-length trajectories of a system as a Gaussian process. 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 noise. Gaussian behaviors can be estimated directly from observed data as the empirical sample covariance. 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 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.

András Sasfi, Jaap Eising, Florian Dörfler

We consider data-based predictive control based on behavioral systems theory. In the linear setting this means that a system is described as a subspace of trajectories, and predictive control can be formulated using a projection onto the intersection of this behavior and a constraint set. Instead of learning the model, or subspace, we focus on determining this projection from data. Motivated by the use of regularization in data-enabled predictive control (DeePC), we introduce the use of soft projections, which approximate the true projector onto the behavior from noisy data. In the simplest case, these are equivalent to known regularized DeePC schemes, but they exhibit a number of benefits. First, we provide a bound on the approximation error consisting of a bias and a variance term that can be traded-off by the regularization weight. The derived bound is independent of the true system order, highlighting the benefit of soft projections compared to low-dimensional subspace estimates. Moreover, soft projections allow for intuitive generalizations, one of which we show has superior performance on a case study. Finally, we provide update formulas for soft projectors enabling the efficient adaptation of the proposed data-driven control methods in the case of streaming data.