Solving non convex Min-Max predictive controller

This paper focuses on robust predictive control (RPC) using uncertain Controlled Auto Regressive Integrated Moving Average (CARIMA) model. To take into account the uncertain behavior of physical process, the parametric uncertainties are considered. The proposed controller is based on worst case strategy. Consequently, the control law is obtained by resolution of a non convex min-max optimization problem. To overcome the drawbacks of classical optimization methods, a global deterministic optimization, Generalized Geometric Programming (GGP), is proposed. This technique is addressed to non convex polynomial problem which the case of most robust and nonlinear control system analysis and design problem. The efficiency of this technique is tested on benchmark functions and compared with LMI and genetic algorithms optimisation methods. Simulation results obtained with an uncertain process are also presented to illustrate the performance of the proposed controller.