Abstract
A novel robust model predictive control (RMPC) scheme is developed for uncertain nonlinear systems. To the RMPC design, firstly, the uncertain system would be described using a linear fractional transformation (LFT). Then, regarding the system’s uncertainties and control limitations, a linear matrix inequality (LMI) based control strategy is addressed to translate the RMPC synthesis into a minimization problem. Thus the controller’s gains are automatically updated at some time-instants by the solution of such optimization problem. Finally, the outcomes are numerically applied in some control examples. The simulation results show the effectiveness of the suggested robust predictive controller in comparison to similar RMPC techniques.
Highlights
The control issue of dynamical systems is increasingly affected by uncertain and unknown terms
The uncertainties may be raised from several sources. b) All unknown expressions would be treated as a single uncertain term. c) The conventional description formula can be counted as a particular form of the linear fractional transformation (LFT) model
Wide variations of the uncertain systems would be covered using the LFT tool. This methodology has been applied to the linear time-invariant (LTI) systems described via a transfer function [2]
Summary
The control issue of dynamical systems is increasingly affected by uncertain and unknown terms. Some LFT based control methods have been addressed to uncertain linear systems. The classical MPCs are mainly developed for the discrete-time representation [12] They may be used in closed-form or require to solve an on-line optimization problem. Many attempts to the RMPC design, based on the LMI, have been reported in the literature The works in this field focused primarily on the non-LFT models, as well as the tubes [14, 15], norm bounded uncertainty [16], and the constrained ones [17, 18]. Compared to the other control approaches, the key contribution and novelties of the method may be summarized as follows: a) All uncertain terms of the dynamical system are formulated via the LFT model.
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