Authors:
Cristina Stoica
;
Pedro Rodríguez-Ayerbe
and
Didier Dumur
Affiliation:
Supélec, France
Keyword(s):
Model predictive control, Multivariable systems, Polytopic uncertainties, Robust control, LMIs, BMIs.
Related
Ontology
Subjects/Areas/Topics:
Adaptive Signal Processing and Control
;
Informatics in Control, Automation and Robotics
;
Signal Processing, Sensors, Systems Modeling and Control
Abstract:
An off-line technique enabling to robustify an initial Model Predictive Control (MPC) for multivariable systems via the convex optimization of a Youla parameter is presented. Firstly, a multivariable predictive controller is designed for a nominal system and then robustified towards unstructured uncertainties, while guaranteeing stability properties over a specified polytopic domain of uncertainties. This condition leads to verify a Bilinear Matrix Inequality (BMI) for each vertex of the polytopic domain. This BMI can be mathematically relaxed to semi-definite programming (SDP) using a Sum of Squares (SOS) strategy, with a significant increase of the number of scalar decision variables. To overcome this inconvenient, an alternative tractable sub-optimal solution for the BMI is proposed, based on the elaboration of a stable solution obtained by minimization of the complementary sensitivity function.