Tracking control design for nonlinear polynomial systems via augmented error system approach and block pulse functions technique

summary:In this paper, tracking control design for a class of nonlinear polynomial systems is investigated by augmented error system approach and block pulse functions technique. The proposed method is based on the projection of the close loop augmented system and the associated linear reference model that it should follow over a basis of block pulse functions. The main advantage of using this tool is that it allows to transform the analytical differential calculus into an algebraic one relatively easy to solve. The developments presented have led to the formulation of a linear system of algebraic equations depending only on parameters of the feedback control. Once the control gains are determined by solving the latter optimization problem in least square sense, the practical stability of the closed loop augmented system is checked through given conditions. A double inverted pendulums benchmark is used to validate the proposed tracking control method