A Kernel-Based PCA Approach to Model Reduction of Linear Parameter-Varying Systems

Rizvi, Syed Z.; Mohammadpour, Javad; Tóth, Roland; Meskin, Nader

doi:10.1109/tcst.2016.2517126

Cited by 33 publications

(29 citation statements)

References 14 publications

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“…1. This system is compactly denoted as Σ e (θ) = Σ(θ)−Σ(θ r ) where θ r is defined in (11). As such, Σ e (θ) is viewed as an error system in the parameter θ only.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

“…All these works are confined to state reduction without considering the problem to reduce the number of parameters. Approaches which consider parameter reduction either require typical trajectories of the parameter [11], lack interpretation or are limited in application [12]. The development of more general parameter reduction techniques can significantly improve the efficiency of simulations, often without loss of generality, as was shown in [13].…”

Section: Introductionmentioning

confidence: 99%

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Model reduction for linear parameter-varying systems through parameter projection

Schouten

Lou

Weiland

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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For affine linear parameter-varying (LPV) systems, this paper develops two parameter reduction methods for reducing the dimension of the parameter space. The first method achieves the complexity reduction by transforming the affine LPV system into a parameter-ordered form and establishing an affine upper bound of the system Gramians, which is extended to time-varying rate-bounded parameters. The second method is based on considering the sensitivity function of the transfer function and time evolution equations. Both methods are applied to an academic example and a thermal model. Simulation results together with some analysis are given. * Accepted by 58 th IEEE Conference on Decision and Control.

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“…1. This system is compactly denoted as Σ e (θ) = Σ(θ)−Σ(θ r ) where θ r is defined in (11). As such, Σ e (θ) is viewed as an error system in the parameter θ only.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model reduction for linear parameter-varying systems through parameter projection

Schouten

Lou

Weiland

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…• PCA-based approaches: they aim at determining operational trajectories of the plant and reshape the hyper-box representing the parameter range, such that it matches the given operating points as closely as possible. This is done by means of a procedure based on principal component analysis (PCA) (Kwiatkowski and Werner, 2008;Rizvi et al, 2016;Jabali and Kazemi, 2017).…”

Section: Introductionmentioning

confidence: 99%

An Lmi–Based Heuristic Algorithm for Vertex Reduction in LPV Systems

Sanjuan

Rotondo

Nejjari

et al. 2019

International Journal of Applied Mathematics and Computer Science

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The linear parameter varying (LPV) approach has proved to be suitable for controlling many non-linear systems. However, for those which are highly non-linear and complex, the number of scheduling variables increases rapidly. This fact makes the LPV controller implementation not feasible for many real systems due to memory constraints and computational burden. This paper considers the problem of reducing the total number of LPV controller gains by determining a heuristic methodology that combines two vertices of a polytopic LPV model such that the same gain can be used in both vertices. The proposed algorithm, based on the use of the Gershgorin circles, provides a combinability ranking for the different vertex pairs, which helps in solving the reduction problem in fewer attempts. Simulation examples are provided in order to illustrate the main characteristics of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

“…It is important to emphasize that our aim is to reduce the dimension of the state vector and not of the scheduling variable. The latter problem is fundamentally different and is addressed in, eg, Kwiatkowski and Werner 6 and Rizvi et al 7 Model order reduction for linear time-invariant (LTI) systems is a well-studied topic, see, eg, Antoulas 8 and the references therein. The same problem for LPV systems was first addressed in Wood, 9,10 where the concept of Int J Numer Meth Engng.…”

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confidence: 99%

Model reduction for LPV systems based on approximate modal decomposition

Luspay

Péni

Gozse

et al. 2017

Numerical Meth Engineering

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The paper presents a novel model order reduction technique for large-scale linear parameter varying (LPV) systems. The approach is based on decoupling the original dynamics into smaller dimensional LPV subsystems that can be independently reduced by parameter varying reduction methods. The decomposition starts with the construction of a modal transformation that separates the modal subsystems. Hierarchical clustering is applied then to collect the dynamically similar modal subsystems into larger groups. The subsystems formed from the groups are then independently reduced. This approach substantially differs from most of the previously proposed LPV model reduction techniques, since it performs manipulations on the LPV model and not on a set of linear time-invariant (LTI) models defined at fixed scheduling parameter values. Therefore the model interpolation, which is the most challenging part of most reduction techniques, is avoided. The applicability of the developed algorithm is thoroughly investigated and demonstrated by numerical case studies.

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A Kernel-Based PCA Approach to Model Reduction of Linear Parameter-Varying Systems

Cited by 33 publications

References 14 publications

Model reduction for linear parameter-varying systems through parameter projection

Model reduction for linear parameter-varying systems through parameter projection

An Lmi–Based Heuristic Algorithm for Vertex Reduction in LPV Systems

Model reduction for LPV systems based on approximate modal decomposition

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