Towards synthesis of polynomial controllers - a multi-affine approach
Nicolas Ribard, Rafael Wisniewski, Christoffer Sloth · VBN Forskningsportal (Aalborg Universitet) · 2016
In the paper, we strive to develop an algorithm that simultaneously computes a polynomial control and a polynomial Lyapunov function. This ensures asymptotic stability of the designed feedback system. The above problem is translated to a certificate of positivity. To this end, we use the representation of the given control system in Bernstein basis. Subsequently, the control synthesis problem is reduced to finite number of evaluations of a polynomial on vertices of cubes in the space of parameters representing admissible controls and Lyapunov functions.