arXiv subjects

András Sasfi

Publications and source records attributed to András Sasfi.

5 recordsLinked to original sources

arXiv2026

Gaussian behaviors and stochastic data-driven control

We propose a stochastic behavioral modeling framework, termed Gaussian behaviors, which augments a deterministic linear time-invariant (LTI) behavior with a Gaussian noise component. We show that this notion is a tractable subclass of stochastic behaviors and encompasses classical parametric stochastic LTI state-space system models as special cases. Analogously to deterministic LTI behaviors, the framework enables simple and tractable stochastic data-driven control methods. To this end, we obtain a method for prediction by conditioning the Gaussian behavior on the known part of the trajectory, which is identified directly from the sample covariance of trajectory data. Building on this method, we develop predictive control formulations that optimize over feedforward or disturbance affine feedback policies. The resulting formulations are shown to be convex. We further derive a finite-sample confidence bound on the prediction accounting for both aleatoric and epistemic uncertainty, and incorporate it into a robust control method, for which a tractable convex upper bound is obtained. Within this framework, subspace predictive control is recovered when only the mean prediction is used, while data-enabled predictive control is shown to account for the prediction uncertainty in an optimistic fashion. Numerical case studies illustrate the benefits of the proposed methods.

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arXiv2026

Soft projections for robust data-driven control

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.

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arXiv2025

Gaussian behaviors: representations and data-driven control

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.

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arXiv2025

GREAT: Grassmannian REcursive Algorithm for Tracking & Online System Identification

This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems. The approach of representing linear systems by non-parametric subspace models has received significant interest in the field of data-driven control recently. This system representation enables us to provide rigorous guarantees for linear time-varying systems, which are difficult to obtain for parametric system models. The proposed method leverages optimization on the Grassmann manifold leading to the Grassmannian Recursive Algorithm for Tracking (GREAT). We view subspaces as points on the Grassmann manifold and adapt the estimate based on online data by performing optimization on the manifold. At each time step, a single measurement from the current subspace corrupted by a bounded error is available. The subspace estimate is updated online using Grassmannian gradient descent on a cost function incorporating a window of the most recent data. Under suitable assumptions on the signal-to-noise ratio of the online data and the subspace's rate of change, we establish theoretical guarantees for the resulting algorithm. More specifically, we prove an exponential convergence rate and provide an uncertainty quantification of the estimates in terms of an upper bound on their distance to the true subspace. The applicability of the proposed algorithm is demonstrated by means of numerical examples.

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arXiv2023

Robust adaptive MPC using control contraction metrics

We present a robust adaptive model predictive control (MPC) framework for nonlinear continuous-time systems with bounded parametric uncertainty and additive disturbance. We utilize general control contraction metrics (CCMs) to parameterize a homothetic tube around a nominal prediction that contains all uncertain trajectories. Furthermore, we incorporate model adaptation using set-membership estimation. As a result, the proposed MPC formulation is applicable to a large class of nonlinear systems, reduces conservatism during online operation, and guarantees robust constraint satisfaction and convergence to a neighborhood of the desired setpoint. One of the main technical contributions is the derivation of corresponding tube dynamics based on CCMs that account for the state and input dependent nature of the model mismatch. Furthermore, we online optimize over the nominal parameter, which enables general set-membership updates for the parametric uncertainty in the MPC. Benefits of the proposed homothetic tube MPC and online adaptation are demonstrated using a numerical example involving a planar quadrotor.

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