Linearized controller design for the output pdfs using square root based B-spline models

P. Kabore; H. Baki; H. Wang

doi:10.3182/20020721-6-es-1901.01149

Linearized controller design for the output pdfs using square root based B-spline models

P. Kabore, H. Baki, H. Wang

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper presents a linearized approach for the controller design of the shape of the output probability density functions for general stochastic systems. A square root approximation to the output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees the closed loop stability and realizes the perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.

Original language	English
Title of host publication	IFAC Proceedings Volumes (IFAC-PapersOnline)
Editors	Gabriel Ferrate, Eduardo F. Camacho, Luis Basanez, Juan. A. de la Puente
Publisher	IFAC Secretariat
Pages	467-472
Number of pages	6
Edition	1
ISBN (Print)	9783902661746
DOIs	https://doi.org/10.3182/20020721-6-es-1901.01149
State	Published - 2002
Externally published	Yes
Event	15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain Duration: Jul 21 2002 → Jul 26 2002

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Number	1
Volume	35
ISSN (Print)	1474-6670

Conference

Conference	15th World Congress of the International Federation of Automatic Control, 2002
Country/Territory	Spain
City	Barcelona
Period	07/21/02 → 07/26/02

Funding

The author would like to thank the financial support from the UK EPSRC grant (GB/K97721).

Keywords

B-splines neural networks
Dynamic stochastic systems
Lyapunov stability theory
Probability density function

Access to Document

10.3182/20020721-6-es-1901.01149

Cite this

Kabore, P., Baki, H., & Wang, H. (2002). Linearized controller design for the output pdfs using square root based B-spline models. In G. Ferrate, E. F. Camacho, L. Basanez, & J. A. de la Puente (Eds.), IFAC Proceedings Volumes (IFAC-PapersOnline) (1 ed., pp. 467-472). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 35, No. 1). IFAC Secretariat. https://doi.org/10.3182/20020721-6-es-1901.01149

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abstract = "This paper presents a linearized approach for the controller design of the shape of the output probability density functions for general stochastic systems. A square root approximation to the output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees the closed loop stability and realizes the perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.",

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Kabore, P, Baki, H & Wang, H 2002, Linearized controller design for the output pdfs using square root based B-spline models. in G Ferrate, EF Camacho, L Basanez & JA de la Puente (eds), IFAC Proceedings Volumes (IFAC-PapersOnline). 1 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. 1, vol. 35, IFAC Secretariat, pp. 467-472, 15th World Congress of the International Federation of Automatic Control, 2002, Barcelona, Spain, 07/21/02. https://doi.org/10.3182/20020721-6-es-1901.01149

Linearized controller design for the output pdfs using square root based B-spline models. / Kabore, P.; Baki, H.; Wang, H.
IFAC Proceedings Volumes (IFAC-PapersOnline). ed. / Gabriel Ferrate; Eduardo F. Camacho; Luis Basanez; Juan. A. de la Puente. 1. ed. IFAC Secretariat, 2002. p. 467-472 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 35, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Baki, H.

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N2 - This paper presents a linearized approach for the controller design of the shape of the output probability density functions for general stochastic systems. A square root approximation to the output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees the closed loop stability and realizes the perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.

AB - This paper presents a linearized approach for the controller design of the shape of the output probability density functions for general stochastic systems. A square root approximation to the output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees the closed loop stability and realizes the perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.

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KW - Dynamic stochastic systems

KW - Lyapunov stability theory

KW - Probability density function

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Linearized controller design for the output pdfs using square root based B-spline models

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Keywords

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