Prediction-Error Identification of LPV Systems: Present and Beyond

Tóth, Roland; Heuberger, Psc Peter; Hof, van den Pmj Paul

doi:10.1007/978-1-4614-1833-7_2

Cited by 28 publications

(38 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Let H be a matrix whose vectors form a basis of the subspace  defined in (15), guaranteed to exist by Proposition 3. Let H ⟂ be a basis of the orthogonal subspace to .…”

Section: Proposition 2 For Any Choice Of Q(z) Fulfillingmentioning

confidence: 99%

See 1 more Smart Citation

Performance‐oriented quasi‐LPV modeling of nonlinear systems

Robles

Sala

Bernal

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Polytopic quasi-linear parameter-varying (quasi-LPV) models of nonlinear processes allow the usage linear matrix inequalities (LMIs) to guarantee some performance goal on them (in most cases, locally, over a so-called modeling region). In order to get a finite number of LMIs, nonlinearities are embedded on the convex hull of a finite set of linear models. However, for a given system, the quasi-LPV representations are not unique, yielding different performance bounds depending on the model choice. To avoid such drawback, earlier literature on the topic used annihilator-based approaches, which require gridding on the modeling region, and nonconvex BMI conditions for controller synthesis; optimal performance bounds are obtained, but with a huge computational burden. This paper proposes building a model by minimizing the projection of the nonlinearities onto directions, which are deleterious for performance.For a small modeling region, these directions are obtained from LMIs with the linearized model. Additionally, these directions will guide the selection of the polytopic embedding's vertices. The procedure allows gridding-free LMI controller synthesis, as in standard LPV setups, with a very reduced performance loss with respect to the aforementioned BMI+gridding approaches, at a fraction of the computational cost. KEYWORDS gain scheduling, linear matrix inequalities, linear-parameter-varying systems, quasi-LPV systems, robust control, Takagi-Sugeno systems 1230

show abstract

“…Let H be a matrix whose vectors form a basis of the subspace  defined in (15), guaranteed to exist by Proposition 3. Let H ⟂ be a basis of the orthogonal subspace to .…”

Section: Proposition 2 For Any Choice Of Q(z) Fulfillingmentioning

confidence: 99%

“…Alternatively, nonlinearities can also be embedded into the convex hull of polynomials, 12,13 amenable to convex sum-of-squares optimization, 14 but these approaches are intentionally out of the scope of this work. Identification-based LPV models 15 will also be left out of the present discussion.…”

Section: Introductionmentioning

confidence: 99%

Performance‐oriented quasi‐LPV modeling of nonlinear systems

Robles

Sala

Bernal

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Due to the linearity of the considered model (20), the one-step ahead predictor in the case of a generalized polynomial noise model has a similar form as in the LTI case under the commonly taken assumption of noise free measurement of the scheduling variable p. This facilitates the extension of the classical prediction error minimization approaches as discussed in [10,21,48].…”

Section: The Prediction Error Minimization Approachmentioning

confidence: 99%

“…the parameter vector Â under the constraint (22) leads to a classical nonlinear optimization problem that can be solved by gradient descent or pseudo-linear regression [21,48]. Note that other noise structures such as ARX, ARMAX, BJ, etc.…”

Section: The Prediction Error Minimization Approachmentioning

confidence: 99%

See 1 more Smart Citation

A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study

Bachnas

Tóth

Ludlage

et al. 2014

Journal of Process Control

110

View full text Add to dashboard Cite

a b s t r a c tModel-based control strategies are widely used for optimal operation of chemical processes to respond to the increasing performance demands in the chemical industry. Yet, obtaining accurate models to describe the inherently nonlinear, time-varying dynamics of chemical processes remains a challenge in most model-based control applications. This paper reviews data-driven, Linear Parameter-Varying (LPV) modeling approaches for process systems by exploring and comparing various identification methods on a high-purity distillation column case study. Several LPV identification methods that utilize input-output and series expansion model structures are explored. Two LPV identification perspectives are adopted: (i) the local approach, which corresponds to the interpolation of Linear Time-Invariant (LTI) models identified at different steady-state operating points of the system and (ii) the global approach, where a parametrized LPV model structure is identified directly using a global data set with varying operating points. For the local approach, various model interpolation schemes are studied under an Output Error (OE) noise setting, whereas in the global case, a polynomial parametrization based OE prediction error minimization approach, an Orthonormal Basis Functions (OBFs) based model estimator and a LeastSquare Support Vector Machine (LS-SVM) based non-parametric approach are investigated. Through extensive simulation studies, the aforementioned LPV identification approaches are analyzed in terms of the attainable model accuracy and local frequency response behavior of the obtained models. Recommendations are provided to achieve adequate choice between the methods for a particular process system at hand.

show abstract