Design of Robust Fractional Predictive Control using Global Optimization Approach

This paper provides a new approach to solve non-convex min-max predictive controller for fractional systems with real uncertain parameters. The Grünwald–Letnikov’s (GL) definition will be used as a fractional internal model to predict the plant future dynamic behavior. This definition consists in replacing the fractional order derivation operator of the adopted process representation by a discrete approximation. The controller parameters are obtained by resolving a min-max non-convex optimization problem. The resolution of this problem under constraints using a standard approach can give local solutions. Thus, we propose the use of the Genetic Algorithm (GA), which is a global optimization approach that consists to transforming the initial non-convex optimization problem to a convex one by means of variable transformations. The efficiency of the proposed robust fractional predictive controller is illustrated in simulation with an uncertain fractional system example.