Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems

Fuente: arXiv
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Main Authors: Verhoek, Chris, Tóth, Roland, Abbas, Hossam S.
Format: Preprint
Published: 2022
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author Verhoek, Chris
Tóth, Roland
Abbas, Hossam S.
author_facet Verhoek, Chris
Tóth, Roland
Abbas, Hossam S.
contents The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed-loop system. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation we formulate data-driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of the closed-loop system. The controllers are synthesized by solving a semi-definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system.
format Preprint
id arxiv_https___arxiv_org_abs_2211_17182
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems
Verhoek, Chris
Tóth, Roland
Abbas, Hossam S.
Systems and Control
The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed-loop system. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation we formulate data-driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of the closed-loop system. The controllers are synthesized by solving a semi-definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system.
title Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems
topic Systems and Control
url https://arxiv.org/abs/2211.17182