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Off-line robustification of Generalized Predictive Control for uncertain systems

Otmane K. K., Bali N., Nezli L.

Archives of Control Sciences

2014

Vol. 24, no. 4

499--513

An off-line methodology was proposed for enhancing the robustness of an initial Generalized Predictive Control (GPC) by convex optimization of the Youla parameter. However, this procedure of robustification 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 structured polytopic uncertainties. The main 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 set of non convex quadratic constraints. The globally optimal solution is found by means of the GloptiPoly3 software. Therefore, this robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, an illustrative example is given.

On the H2 , L2 and H∞, L∞ optimality of some two-degree of freedom control systems

Keviczky L., Banyasz C.

Systems Science

2007

Vol. 33, no 3

39-49

The sensitivity function in a generic two-degree of freedom (TDOF) control system can be decomposed into three major parts: design-, realizability- and modeling-loss. This decomposition opens new ways for practical optimization of TDOF systems and helps the construction of new algorithms for robust identification and control. The paper investigates the optimality of the second term in different norm spaces.

Robust Predictive Control Using a Time-Varying Youla Parameter

Van den Boom T. J. J., De Vries R. A. J.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 1

101-128

In this paper, a standard predictive control problem (SPCP) is formulated, which consists of one extended process description with a feedback uncertainty block. The most important finite horizon predictive control problems can be seen as special realizations of this SPCP. The SPCP and its solution are given in a state-space form. The objective of the controller is a nominal performance subject to signal constraints and robust stability with respect to a 1-norm bounded model uncertainty. The optimal controller consists of a feedforward part for nominal signal tracking and a feedback part for disturbance rejection and model error compensation. The feedforward part is realized by the predictive controller for the nominal disturbance-free case. The feedback part of the controller is realized by using the Youla parametrization. The Youla parameter is optimized at every sample time in a receding horizon setting to cope with signal constraints and (robust stability) constraints on the operator itself.