Constraint Programming based Input Signal Design for System Identification

Abstract

Abstract The selection of appropriate input harmonics in a multi-harmonic signal for the identification of nonlinear systems leads to a nonlinear, combinatorial optimization problem. Lack of efficient optimization tools for solving such problems had previously led to the development of an explicit Integer Linear Programming (ILP) based lexicographic optimization formulation. However, the dimensionality of such a formulation increases considerably with an increase in the number of frequencies and the problem has been reported to become intractable for higher frequencies. In this article, we demonstrate the ability of Constraint Programming (CP) to efficiently model and solve the original nonlinear problem to guaranteed global optimality. We successfully demonstrate the ability of CP to determine the optimal solutions much faster and also solve problems that have so far remained intractable. In addition, we also show the ability of CP to determine all the multiple optimal solutions and near best optimal solutions in a single optimization run.