LPV system identification using a separable least squares support vector machines approach

P. Lopes Dos Santos, T. P. Azevedo-Perdicoulis, J. A. Ramos, S. Deshpande, Daniel Rivera, J. L. Martins De Carvalho

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this article, an algorithm to identify LPV State Space models for both continuous-time and discrete-time systems is proposed. The LPV state space system is in the Companion Reachable Canonical Form. The output vector coefficients are linear combinations of a set of a possibly infinite number of nonlinear basis functions dependent on the scheduling signal, the state matrix is either time invariant or a linear combination of a finite number of basis functions of the scheduling signal and the input vector is time invariant. This model structure, although simple, can describe accurately the behaviour of many nonlinear SISO systems by an adequate choice of the scheduling signal. It also partially solves the problems of structural bias caused by inaccurate selection of the basis functions and high variance of the estimates due to over-parameterisation. The use of an infinite number of basis functions in the output vector increases the flexibility to describe complex functions and makes it possible to learn the underlying dependencies of these coefficients from the data. A Least Squares Support Vector Machine (LS-SVM) approach is used to address the infinite dimension of the output coefficients. Since there is a linear dependence of the output on the output vector coefficients and, on the other hand, the LS-SVM solution is a nonlinear function of the state and input matrix coefficients, the LPV system is identified by minimising a quadratic function of the output function in a reduced parameter space; the minimisation of the error is performed by a separable approach where the parameters of the fixed matrices are calculated using a gradient method. The derivatives required by this algorithm are the output of either an LTI or an LPV (in the case of a time-varying SS matrix) system, that need to be simulated at every iteration. The effectiveness of the algorithm is assessed on several simulated examples.

Original languageEnglish (US)
Article number7039778
Pages (from-to)2548-2554
Number of pages7
JournalUnknown Journal
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - 2014

Fingerprint

Least Squares Support Vector Machine
System Identification
Least-Squares Analysis
Support vector machines
Identification (control systems)
Output
Basis Functions
Coefficient
Scheduling
Nonlinear Function
Space Simulation
Linear Combination
Linear dependence
Invariant
Infinite Dimensions
Complex Functions
Gradient Method
State-space Model
Canonical form
Gradient methods

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Lopes Dos Santos, P., Azevedo-Perdicoulis, T. P., Ramos, J. A., Deshpande, S., Rivera, D., & Martins De Carvalho, J. L. (2014). LPV system identification using a separable least squares support vector machines approach. Unknown Journal, 2015-February(February), 2548-2554. [7039778]. https://doi.org/10.1109/CDC.2014.7039778

LPV system identification using a separable least squares support vector machines approach. / Lopes Dos Santos, P.; Azevedo-Perdicoulis, T. P.; Ramos, J. A.; Deshpande, S.; Rivera, Daniel; Martins De Carvalho, J. L.

In: Unknown Journal, Vol. 2015-February, No. February, 7039778, 2014, p. 2548-2554.

Research output: Contribution to journalArticle

Lopes Dos Santos, P, Azevedo-Perdicoulis, TP, Ramos, JA, Deshpande, S, Rivera, D & Martins De Carvalho, JL 2014, 'LPV system identification using a separable least squares support vector machines approach', Unknown Journal, vol. 2015-February, no. February, 7039778, pp. 2548-2554. https://doi.org/10.1109/CDC.2014.7039778
Lopes Dos Santos P, Azevedo-Perdicoulis TP, Ramos JA, Deshpande S, Rivera D, Martins De Carvalho JL. LPV system identification using a separable least squares support vector machines approach. Unknown Journal. 2014;2015-February(February):2548-2554. 7039778. https://doi.org/10.1109/CDC.2014.7039778
Lopes Dos Santos, P. ; Azevedo-Perdicoulis, T. P. ; Ramos, J. A. ; Deshpande, S. ; Rivera, Daniel ; Martins De Carvalho, J. L. / LPV system identification using a separable least squares support vector machines approach. In: Unknown Journal. 2014 ; Vol. 2015-February, No. February. pp. 2548-2554.
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