Canonical duality approach for non-linear dynamical systems

Abstract

This paper presents a canonical dual approach for solving a non-linear population growth problem governed by the well-known logistic equation. Using the finite difference and least squares methods, the non-linear differential equation is first formulated as a non-convex optimization problem with unknown parameters. We then prove that by the canonical duality theory, this non-convex problem is equivalent to a concave maximization problem over a convex feasible space, which can be solved easily to obtain a global optimal solution to this challenging problem. Several illustrative examples are presented.