arXiv subjects

Chris Verhoek

Publications and source records attributed to Chris Verhoek.

23 records · Page 2Linked to original sources

arXiv2022

Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version

Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to the regions around the equilibrium points of these nonlinear systems. The incremental framework, based on the convergence of the system trajectories, removes this limitation. We investigate how stability and performance characterizations of nonlinear systems in the incremental framework are linked to dissipativity, and how general performance characterization beyond the $\mathcal{L}_2$-gain concept can be understood in this framework. This paper presents a matrix inequalities-based convex incremental dissipativity analysis for nonlinear systems via quadratic storage and supply functions. The proposed dissipativity analysis links the notions of incremental, differential, and general dissipativity. We show that through differential dissipativity, incremental and general dissipativity of the nonlinear system can be guaranteed. These results also lead to the incremental extensions of the $\mathcal{L}_2$-gain, the generalized $\mathcal{H}_2$-norm, the $\mathcal{L}_\infty$-gain, and passivity of nonlinear systems.

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arXiv2022

Deep-Learning-Based Identification of LPV Models for Nonlinear Systems

The Linear Parameter-Varying (LPV) framework provides a modeling and control design toolchain to address nonlinear (NL) system behavior via linear surrogate models. Despite major research effort on LPV data-driven modeling, a key shortcoming of the current identification theory is that often the scheduling variable is assumed to be a given measured signal in the data set. In case of identifying an LPV model of a NL system, the selection of the scheduling map, which describes the relation to the measurable scheduling signal, is put on the users' shoulder, with only limited supporting tools available. This choice however greatly affects the usability and complexity of the resulting LPV model. This paper presents a deep-learning-based approach to provide joint estimation of a scheduling map and an LPV state-space model of a NL system from input-output data, and has consistency guarantees under general innovation-type noise conditions. Its efficiency is demonstrated on a realistic identification problem.

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arXiv2022

LPV Modeling of the Atmospheric Flight Dynamics of a Generic Parafoil Return Vehicle

Obtaining models that can be used for control is of utmost importance to ensure the guidance and navigation of spacecraft, like a Generic Parafoil Return Vehicle (GPRV). In this paper, we convert a nonlinear model of the atmospheric flight dynamics of an GPRV to a Linear Parameter-Varying (LPV) description, such that the LPV model is suitable for navigation control design. Automated conversion methods for nonlinear models can result in complex LPV representation, which are not suitable for controller synthesis. We apply several state-of-the-art techniques, including learning based approaches, to optimize the complexity and conservatism of the LPV embedding for an GPRV. The results show that we can obtain an LPV embedding that approximates the complex nonlinear dynamics sufficiently well, where the balance between complexity, conservatism and model performance is optimal.

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arXiv2022

Data-Driven Predictive Control for Linear Parameter-Varying Systems

Based on the extension of the behavioral theory and the Fundamental Lemma for Linear Parameter-Varying (LPV) systems, this paper introduces a Data-driven Predictive Control (DPC) scheme capable to ensure reference tracking and satisfaction of Input-Output (IO) constraints for an unknown system under the conditions that (i) the system can be represented in an LPV form and (ii) an informative data-set containing measured IO and scheduling trajectories of the system is available. It is shown that if the data set satisfies a persistence of excitation condition, then a data-driven LPV predictor of future trajectories of the system can be constructed from the IO data set and online measured data. The approach represents the first step towards a DPC solution for nonlinear and time-varying systems due to the potential of the LPV framework to represent them. Two illustrative examples, including reference tracking control of a nonlinear system, are provided to demonstrate that the data-based LPV-DPC scheme, achieves similar performance as LPV model-based predictive control.

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arXiv2022

Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems

Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems'. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.

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