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A GGP Approach to Solve Non Convex Min-max Predictive Controller for a Class of Constrained MIMO Systems Described by State-space Models

Amira Kheriji, Faouzi Bouani, and Mekki Ksouri
International Journal of Control, Automation, and Systems, vol. 9, no. 3, pp.452-460, 2011

Abstract : This paper proposes a new method to solve non convex min-max predictive controller for a class of constrained linear Multi Input Multi Output (MIMO) systems. A parametric uncertainty state space model is adopted to describe the dynamic behavior of the real process. Moreover, the output deviation method is used to design the j-step ahead output predictor. The control law is obtained by the resolution of a non convex min-max optimization problem under input constraints. The key idea is to transform the initial non convex optimization problem to a convex one by means of variable transformations. To this end, the Generalized Geometric Programming (GGP) which is a global deterministic optimization method is used. An efficient implementation of this approach will lead to an algorithm with a low computational burden. Simulation results performed on Multi Input Multi Output (MIMO) system show successful set point tracking, constraints satisfaction and good non-zero disturbance rejection.

Keyword : Constrained control, disturbance rejection, generalized geometric programming, MIMO systems, parametric uncertainty, predictive control, set point tracking, state space model.

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