A method based on the Monte Carlo optimization schemes for the control of nonlinear polynomial systems

The present work proposes a new method to the problem of implementation of Input-State feedback linearization. Such method is based on the search of a diffeomorphism which transforms the original nonlinear system into a linear one in the controllable canonical form with an external reference input, and the subsequent using of linear pole-placement techniques. The problem is solved without need of the differential geometric complexity of the feedback linearization technique. It is based however, on an analytical method using the development in to generalized Taylor series of vectorial nonlinear functions and Kronecker product tools. The algebraic developments, we present in this paper, use the Monte Carlo optimization method to choose the best parameters of the polynomial feedback control in order to ensure the effectiveness of the diffeomorphism. A simulation study is synthesized to show the effectiveness of the proposed approach. Key–Words: Nonlinear system control, Input-State feedback linearization, Analytic representations, Kronecker product, Monte Carlo optimization.