Risk adjusted identification of a class of nonlinear systems

This paper addresses the problem of identification of a class of nonlinear systems from a set-membership standpoint. Specifically we consider structures consisting of the interconnection of a linear time invariant plant and a sector bound static nonlinearity. This structure includes as special cases, Hammerstein, Wiener and Hammerstein-Wiener systems. Our main result shows that, by pursuing a risk-adjusted approach, the problem can be reduced to a convex LMI optimization form that can be efficiently solved. In addition we provide a convergence analysis that points to an intrinsic limitation of any interpolatory algorithm. These results are illustrated with a simple example.