Controller Design for Polynomial Systems with Input Constraints

In this paper, a new optimization based design method for stabilization of polynomial systems with input constraints is presented. The method utilizes the sum of squares decomposition of polynomials and results in a nonpolynomial control law fulfilling amplitude constraints of the input. Consideration of input rate constraints can be included by extending the optimization problem. The resulting sum of squares optimization problems are bilinear. Thus, an iterative algorithm is used to obtain a solution. The applicability of the method is demonstrated by an example system, for which it turns out that the resulting controller exploits the given amplitude range very well and leads to better control performance than a polynomial controller.