Application of SVM to Lyapunov function approximation

This paper proposes a novel technique to approximate Lyapunov functions for discrete time autonomous systems using a special form of support vector machine (SVM). We assume that a Lyapunov function can be accurately approximated by a polynomial of arbitrary degree on a finite set of points from trajectories of the closed-loop system. We transform the original problem of linearly constrained quadratic optimization into an equivalent dual problem. For computational tractability, we apply an iterative decomposition of the dual problem. We illustrate our technique on two examples