arXiv subjects

K. J. A. Scheres

Publications and source records attributed to K. J. A. Scheres.

5 recordsLinked to original sources

arXiv2026

From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control

Willems' fundamental lemma has recently received an impressive amount of attention from the data-driven control community. In this paper, we formulate a version of this celebrated result based on frequency-domain data. In doing so, we bridge the gap between recent developments in data-driven control, and the readily-available techniques and expertise for non-parametric frequency-domain identification. We also generalize our results to combine multiple frequency-domain data sets to form a sufficiently rich data set. Building on these results, we propose a data-driven predictive control scheme based on measured frequency-domain data of the plant. This novel scheme provides a frequency-domain counterpart of the well-known data-enabled predictive control scheme DeePC based on time-domain data. Under appropriate conditions, the new frequency-domain data-driven predictive control (FreePC) scheme is equivalent to the corresponding DeePC scheme. We demonstrate the benefits of FreePC and the use of frequency-domain data in several examples and a numerical case study, including the ability to collect data in closed loop, computational benefits, and intuitive visualization of the data.

math.OC↗

arXiv2026

Solution Concepts and Existence Results for Hybrid Systems with Continuous-time Inputs

In many scenarios, it is natural to model a plant's dynamical behavior using a hybrid dynamical system influenced by exogenous continuous-time inputs. While solution concepts and analytical tools for existence and completeness are well established for autonomous hybrid systems, corresponding results for hybrid dynamical systems involving continuous-time inputs are generally lacking. This work aims to address this gap. We first formalize notions of a solution for such systems. We then provide conditions that guarantee the existence and forward completeness of solutions. Moreover, we leverage results and ideas from viability theory to present more explicit conditions in terms of various tangent cone formulations. Variants are provided that depend on the regularity of the exogenous input signals.

eess.SY↗

arXiv2024

Analysis of a Simple Neuromorphic Controller for Linear Systems: A Hybrid Systems Perspective

In this paper we analyze a neuromorphic controller, inspired by the leaky integrate-and-fire neuronal model, in closed-loop with a single-input single-output linear time-invariant system. The controller consists of two neuron-like variables and generates a spiking control input whenever one of these variables reaches a threshold. The control input is different from zero only at the spiking instants and, hence, between two spiking times the system evolves in open-loop. Exploiting the hybrid nature of the integrate-and-fire neuronal dynamics, we present a hybrid modeling framework to design and analyze this new controller. In the particular case of single-state linear time-invariant plants, we prove a practical stability property for the closed-loop system, we ensure the existence of a strictly positive dwell-time between spikes, and we relate these properties to the parameters in the neurons. The results are illustrated in a numerical example.

eess.SY↗

arXiv2024

Frequency-Domain Data-Driven Predictive Control

In this paper, we propose a data-driven predictive control scheme based on measured frequency-domain data of the plant. This novel scheme complements the well-known data-driven predictive control (DeePC) approach based on time series data. To develop this new frequency-domain data-driven predictive control (FreePC) scheme, we introduce a novel version of Willems' fundamental lemma based on frequency-domain data. By exploiting frequency-domain data, we allow recent direct data-driven (predictive) control methodologies to benefit from the available expertise and techniques for non-parametric frequency-domain identification in academia and industry. We prove that, under appropriate conditions, the new FreePC scheme is equivalent to the corresponding DeePC scheme. The strengths of FreePC are demonstrated in a numerical case study.

eess.SY↗

arXiv2024

A Unified Non-Strict Finsler Lemma

In this paper, we present a unified general non-strict Finsler lemma. This result is general in the sense that it does not impose any restrictions on the involved matrices and, thereby, it encompasses all existing non-strict versions of Finsler's lemma that do impose such restrictions. To further illustrate its usefulness, we showcase applications of the non-strict Finsler's lemma in deriving a structured solution to a special case of the non-strict projection lemma, and we use the unified non-strict Finsler's lemma to prove a more general version of the matrix Finsler's lemma.

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