Tracking control synthesis of nonlinear polynomial systems

In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear state feedback is derived using orthogonal functions and Kronecker product. The main objective is to force the controlled system output to follow that of a linear reference model. The useful properties of the considered basis transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. The efficiency of the proposed control strategy is illustrated by a single-link flexible joint robot.