arXiv subjects

Sahand Kiani

Publications and source records attributed to Sahand Kiani.

5 recordsLinked to original sources

arXiv2026

RAIN-FIT: Learning of Fitting Surfaces and Noise Distribution from Large Data Sets

This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of features and a parametric description of the distribution of the noise, a computationally efficient method is described that estimates both the surface and the noise distribution parameters. In the provided examples, polynomial and sinusoidal basis functions were used. However, any chosen basis that satisfies the outlined conditions mentioned in the paper can be approximated as a combination of trigonometric, exponential, and/or polynomial terms, making the presented approach highly generalizable. The proposed algorithm exhibits linear computational complexity in the number of samples. Our approach requires no hyperparameter tuning or data preprocessing and effectively handles data in dimensions beyond 2D and 3D. The theoretical results demonstrating the convergence of the proposed algorithm have been provided. To highlight the performance of the proposed method, comprehensive numerical results are conducted, evaluating our method against state-of-the-art algorithms, including Poisson Reconstruction and the Neural Network-based Encoder-X, on 2D and 3D shapes. The results demonstrate the superiority of our method under the same conditions.

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arXiv2026

Willems' Fundamental Lemma with Large Noisy Fragmented Dataset

Willems' Fundamental Lemma enables parameterizing all trajectories generated by a Linear Time-Invariant (LTI) system directly from data. However, this lemma relies on the assumption of noiseless measurements. In this paper, we provide an approach that enables the applicability of Willems' Fundamental Lemma with a large noisy-input, noisy-output fragmented dataset, without requiring prior knowledge of the noise distribution. We introduce a computationally tractable and lightweight algorithm that, despite processing a large dataset, executes in the order of seconds to estimate the invariants of the underlying system, which is obscured by noise. The simulation results demonstrate the effectiveness of the proposed method.

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arXiv2025

Robust Data-Driven Invariant Sets for Nonlinear Systems

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute robust polytopic contractive sets for unknown nonlinear systems operating under persistent bounded process noise and state-input constraints. Rather than attempting to identify a single, potentially nominal model, we utilize a finite data set to construct a polytopic consistency set--a rigorous geometric boundary encapsulating all possible system dynamics compatible with the noisy measurements. The core contribution of this work extends an established sufficient condition for {\lambda} contractiveness into the data-driven setting. Crucially, we prove that enforcing this condition strictly over the vertices of the consistency set guarantees robust invariance.

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arXiv2025

Robust Data-Driven Receding Horizon Control

This paper presents a data-driven receding horizon control framework for discrete-time linear systems that guarantees robust performance in the presence of bounded disturbances. Unlike the majority of existing data-driven predictive control methods, which rely on Willem's fundamental lemma, the proposed method enforces set-membership constraints for data-driven control and utilizes execution data to iteratively refine a set of compatible systems online. Numerical results demonstrate that the proposed receding horizon framework achieves better contractivity for the unknown system compared with regular data-driven control approaches.

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arXiv2023

Learning Robust Model Predictive Control for Voltage Control of Islanded Microgrid

This paper proposes a novel control design for voltage tracking of an islanded AC microgrid in the presence of {nonlinear} loads and parametric uncertainties at the primary level of control. The proposed method is based on the Tube-Based Robust Model Predictive Control (RMPC), an online optimization-based method which can handle the constraints and uncertainties as well. The challenge with this method is the conservativeness imposed by designing the tube based on the worst-case scenario of the uncertainties. This weakness is amended in this paper by employing a combination of a learning-based Gaussian Process (GP) regression and RMPC. The advantage of using GP is that both the mean and variance of the loads are predicted at each iteration based on the real data, and the resulted values of mean and the bound of confidence are utilized to design the tube in RMPC. The theoretical results are also provided to prove the recursive feasibility and stability of the proposed learning based RMPC. Finally, the simulation results are carried out on both single and multiple DG (Distributed Generation) units.

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