<abstract xmlns="http://www.w3.org/1999/xhtml"><p>An off-line methodology has been developed to improve the robustness of an initial generalized predictive control (GPC) through convex optimization of the Youla parameter. However, this method is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and polytopic uncertainties. The basic idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a non convex quadratically constrained quadratic programming (QCQP) problem. Based on semidefinite programming (SDP), this problem is relaxed and solved. Therefore, the robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, we present a numerical example to demonstrate the proposed method.</p></abstract>

An off-line methodology has been developed to improve the robustness of an initial generalized predictive control (GPC) through convex optimization of the Youla parameter. However, this method is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and polytopic uncertainties. The basic idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a non convex quadratically constrained quadratic programming (QCQP) problem. Based on semidefinite programming (SDP), this problem is relaxed and solved. Therefore, the robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, we present a numerical example to demonstrate the proposed method.

Improved Robustness of Generalized Predictive Control for Uncertain Systems

Process Control Laboratory, Ecole Nationale Polytechnique, 10 av. Pasteur, Hassen Badi, 16200 El Harrach, Algiers, Algeria

Electric and Industrial Systems Laboratory, University of Sciences and Technology Houari Boumediene, Algiers BP. 32 El Alia, 16111 Bab Ezzouar, Algiers, Algeria

Journal of Electrical Engineering

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Improved Robustness of Generalized Predictive Control for Uncertain Systems"}

An off-line methodology has been developed to improve the robustness of an initial generalized predictive control (GPC) through convex optimization of the...

Improved Robustness of Generalized Predictive Control for Uncertain Systems

Published Online: Jan 31, 2015

Page range: 349 - 355

Received: Oct 26, 2012

DOI: https://doi.org/10.2478/jee-2014-0057

© 2015 Faculty of Electrical Engineering and Information Technology, Slovak University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.