STABILITY AND CONVERGENCE ANALYSES OF AN ADAPTIVE GPC BASED ON STATE-SPACE MODELING

TitleSTABILITY AND CONVERGENCE ANALYSES OF AN ADAPTIVE GPC BASED ON STATE-SPACE MODELING
Publication TypeJournal Article
Year of Publication1995
AuthorsELSHAFEI, A. L., G. Dumont, and A. ELNAGGAR
JournalInternational Journal of Control
Volume61
Pagination193–210
ISSN0020-7179
Abstract

A generalized predictive controller (GPC) is derived based on a general state-space model. The equivalence of the predictive control problem to a perturbation problem is revealed. In the case of a small perturbation, the closed-loop poles are calculated with high accuracy. For the case of a general perturbation, an upper bound on the permissible perturbation norm is derived assuming an open-loop stable system. Both the plant-model match and plant-model mismatch cases are analysed. The controller is proven to be robust and an adaptive implementation is motivated. For open-loop stable systems, the convergence and stability of the control scheme are ensured by proper tuning of the control weight and prediction horizon. The results are applicable to a wide range of predictive controllers. The main contribution of this paper is not a new control algorithm, but new techniques to analyse the GPC as well as new stability and convergence results.

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