Convex relaxation approach to the identification of the Wiener-Hammerstein model

In this paper, an input/output system identification technique for the Wiener-Hammerstein model and its feedback extension is proposed. In the proposed framework, the identification of the nonlinearity is non-parametric. The identification problem can be formulated as a non-convex quadratic program (QP). A convex semidefinite programming (SDP) relaxation is then formulated and solved to obtain a sub-optimal solution to the original non-convex QP. The convex relaxation turns out to be tight in most cases. Combined with the use of local search, high quality solutions to the Wiener-Hammerstein identification can frequently be found. As an application example, randomly generated Wiener-Hammerstein models are identified.