Application of rank-constrained optimisation to nonlinear system identification

Nonlinear System identification has a rich history spanning at least 5 decades. A very flexible approach to this problem depends upon the use of Volterra series expansions. Related work includes Hammerstein models, where a static nonlinearity is followed by a linear dynamical system, and Wiener models, where a static nonlinearity is inserted after a linear dynamical model. A problem with these methods is that they inherently depend upon series type expansions and hence it is difficult to know which terms should be included. In this paper we present a possible solution to this problem using recent results on rank-constrained optimization. Simulation results are included to illustrate the efficacy of the proposed strategy.