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Item type:Publication, Access status: without files , Fast risk certification of candidate trajectories under uncertain time-varying constraints(2026-06-30); ; ; This paper studies the certification of a fixed candidate trajectory on a finite certification grid under parametric uncertainty. For each constraint-time pair, we define a scalar measure of constraint violation and aggregate the resulting pointwise chance constraints into a worst-case Value-at-Risk (VaR) margin. The goal is not to generate a new trajectory, but to assess online whether a trajectory produced by a planner or predictive controller is sufficiently safe on the certification grid. Direct evaluation requires repeated uncertainty propagation and is often too expensive for computationally demanding models. We therefore adopt an offline-online scheme: offline, a surrogate of the constraint violation map along the candidate trajectory is constructed using polynomial chaos expansion (PCE) when the uncertainty law is known, or kernel regression when only sampled input-output data are available; online, the surrogate is sampled to evaluate conservative VaR bounds at low computational cost. On the theoretical side, we derive a finite-sample upper bound for the grid-based VaR margin using empirical quantiles, the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality, and a union bound over all constraint-time pairs, without assuming a parametric family for the underlying violation distribution. We also show how a uniform surrogate error bound transfers to the certified VaR margin. The approach is illustrated on a crystallization population balance model, where the surrogate-based risk estimates track direct Monte Carlo results while substantially reducing online evaluation time.Publicationtype: Preprint53 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Wiener Chaos in kernel regression: toward untangling aleatoric and epistemic uncertaintyGaussian Processes (GPs) are a versatile method that enables different approaches toward learning for dynamics and control. Gaussianity assumptions appear in two dimensions in GPs: The positive semi-definite kernel of the underlying reproducing kernel Hilbert space is used to construct the covariance of a Gaussian distribution over functions, while measurement noise (i.e., data corruption) is usually modeled as i.i.d. additive Gaussians. In this note, we generalize the setting and consider kernel ridge regression with additive i.i.d. non-Gaussian measurement noise. To apply the usual kernel trick, we rely on the representation of the uncertainty via polynomial chaos expansions, which are series expansions for random variables of finite variance introduced by Norbert Wiener. We derive and discuss the analytic solution to the arising Wiener kernel regression. Considering a polynomial dynamic system as a numerical example, we show that our approach allows us to distinguish the uncertainty that stems from the noise in the data samples from the total uncertainty encoded in the GP posterior distribution.Publicationtype: Conference Paper24 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Towards safe Bayesian optimization with Wiener kernel regressionBayesian Optimization (BO) is a data-driven strategy for minimizing/maximizing black-box functions based on probabilistic surrogate models. In the presence of safety constraints, the performance of BO crucially relies on tight probabilistic error bounds related to the uncertainty surrounding the surrogate model. For the case of Gaussian Process surrogates and Gaussian measurement noise, we present a novel error bound based on the recently proposed Wiener kernel regression. We prove that under rather mild assumptions, the proposed error bound is tighter than bounds previously documented in the literature, leading to enlarged safety regions. We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.Publicationtype: Conference Paper25 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Towards data-driven multi-stage OPF(IEEE, 2025-06); ; ; ; The operation of large-scale power systems is usually scheduled ahead via numerical optimization. However, this requires models of grid topology, line parameters, and bus specifications. Classic approaches first identify the network topology, i.e., the graph of interconnections and the associated impedances. The power generation schedules are computed by solving a multi-stage optimal power flow (OPF) problem built around the model. In this paper, we explore the prospect of data-driven approaches to multi-stage optimal power flow. Specifically, we leverage recent findings from systems and control to bypass the identification step and to construct the optimization problem directly from data. We illustrate the performance of our method on a 118-bus system and compare it with the classical identification-based approach.Publicationtype: Conference Paper23 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Exploring the links between the fundamental lemma and kernel regressionGeneralizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.Publicationtype: Journal Article27