Affine linear parameter‐varying embedding of non‐linear models with improved accuracy and minimal overbounding

Sadeghzadeh, Arash; Sharif, Bardia; Tóth, Roland

doi:10.1049/iet-cta.2020.0474

Cited by 13 publications

(14 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For reducing the conservativeness and complexity of the converted LPV model obtained in Section 2, we will briefly introduce the PCA method developed in Sadeghzadeh et al (2020) and the DNN approach from Koelewijn and Tóth (2020) in this section. These methods will be applied to the GPRV LPV model in Section 4.…”

Section: Scheduling Reduction Methodsmentioning

confidence: 99%

“…The PCA-based scheduling dimension reduction method is based on Sadeghzadeh et al (2020), which is an improved version of (Kwiatkowski and Werner, 2008). The idea of the PCA method is to extract dominant components, i.e., the principle components, of the model variations that contribute most to the system behavior along typical operational trajectories of the system.…”

Section: Pca-based Scheduling Dimension Reductionmentioning

confidence: 99%

“…However, only a limited number of methods have been derived to optimize the scheduling complexity in the conversion process, like the family of Principle Component Analysis (PCA) methods (Kwiatkowski and Werner, 2008;Rizvi et al, 2016;Sadeghzadeh et al, 2020) and learningbased scheduling reduction methods discussed in Rizvi et al (2018); Koelewijn and Tóth (2020).…”

Section: Introductionmentioning

confidence: 99%

“…To make this model suitable for LPV control, as a main contribution of the paper, we develop a global embedding of these dynamics in terms of an LPV representation, where both the conservativeness and complexity of the embedding are optimized. For this purpose, we apply and compare two data-based scheduling dimension reduction methods: (i) the PCA method in (Sadeghzadeh et al, 2020) that is the current state-of-the-art method in the PCA family of reduction techniques and the (ii) Deep Neural Network (DNN) method from (Koelewijn and Tóth, 2020) that has been reported to perform the best among the learning based methods. The accuracy of the obtained LPV models with various complexity levels is analyzed in simulation studies with the original model.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Lange¹,

Verhoek²,

Preda³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Scheduling Reduction Methodsmentioning

confidence: 99%

Section: Pca-based Scheduling Dimension Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Lange¹,

Verhoek²,

Preda³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Furthermore, P is chosen as the smallest convex set in a given complexity class (n-vertex polytope, hyper-ellipsoid, etc.) such that ψ(X p , U p ) ⊆ P to minimize the conservativeness of the representation, see [16,26].…”

Section: Incremental Synthesismentioning

confidence: 99%

Nonlinear Tracking and Rejection using Linear Parameter-Varying Control

Koelewijn¹,

Tóth²,

Nijmeijer³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The Linear Parameter-Varying (LPV) framework has been introduced with the intention to provide stability and performance guarantees for analysis and controller synthesis for Nonlinear (NL) systems via convex methods. By extending results of the Linear Time-Invariant framework, mainly based on quadratic stability and L2-gain performance, it was assumed that they generalize tracking and disturbance rejection guarantees for NL systems. But as we show through examples, the notion of L2gain stability and performance is not sufficient in order to satisfy the desired guarantees in case of tracking and disturbance rejection. We propose to solve this problem by the application of incremental stability and performance, which does indeed ensure these specifications. A novel approach is proposed to synthesize and realize an LPV controller which is able to guarantee incremental stability and performance for NL systems via convex optimization. Through examples, the presented method is compared to standard L2-gain optimal LPV controller design, showing significant performance improvements. Finally, the approach is experimentally verified on an unbalanced disc setup, demonstrating the shortcomings of standard L2-gain optimal LPV controllers.

show abstract

Simultaneous design of robust gain‐scheduled static output‐feedback controller and scaling matrices for linear parameter varying systems with inexact scheduling parameters

Niu,

Lu,

2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This article presents a design method of the robust gain‐scheduled static output‐feedback controller exploiting inexact measured scheduling parameters for multi‐affine linear parameter‐varying systems with structured uncertainty blocks. Performance scaling matrices are introduced in the design process to reduce conservatism. By introducing auxiliary variables and properly utilizing projection lemma, a parameter‐dependent linear matrix inequality with a single line search parameter is derived to synthesize the static output‐feedback controller gains and scaling matrices simultaneously. Based on vertices of the convex polytope covering the admissible region of scheduling parameters and inexact ones, the given parameter‐dependent synthesis condition is further expressed as a set of linear matrix inequalities at the vertices of the polytope to guarantee the robustness against inaccurate scheduling parameters. Several examples show the effectiveness of the proposed algorithm.

show abstract

Affine linear parameter‐varying embedding of non‐linear models with improved accuracy and minimal overbounding

Cited by 13 publications

References 40 publications

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

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

Nonlinear Tracking and Rejection using Linear Parameter-Varying Control

Simultaneous design of robust gain‐scheduled static output‐feedback controller and scaling matrices for linear parameter varying systems with inexact scheduling parameters

Contact Info

Product

Resources

About