Model predictive control of differentially flat systems using Haar wavelets

A dynamical system is differentially flat if it is Lie-Bäcklund (L-B) equivalent to a free dynamical system which has dimension equal to that of the input of the original system. By the virtue of differential flatness, the classical nonlinear model predictive control optimization problem can be reduced to a lower dimensional nonlinear programming problem with respect to the flat outputs. A novel computational method based on Haar wavelets in the time-domain for solving the resulting nonlinear programming problem is developed to obtain an approximation of the optimal flat output trajectory. The Haar wavelet integral operational matrix is utilized to transform the nonlinear programming problem to a finite dimensional nonlinear static optimization problem. Thus, the proposed approach utilizes flatness as a structural property of nonlinear systems, and the convenient mathematical properties of Haar wavelets to develop an efficient computational algorithm for nonlinear model predictive control of differentially flat systems.