NONPARAMETRIC IDENTIFICATION OF STATIC NONLINEARITIES IN A GENERAL INTERCONNECTED SYSTEM Kenneth Hsu †∗ Mareike Claassen ✸ ∗∗ Carlo Novara ◦ ∗∗∗ Pramod Khargonekar △ ∗∗∗∗ Mario Milanese ♯ ∗∗∗ Kameshwar Poolla ‡∗ ∗ University of California at Berkeley, USA ∗∗ Fullerton College, USA ∗∗∗ Politecnico di Torino, Italy ∗∗∗∗ University of Florida at Gainesville, USA Abstract: We are concerned with the identification of static nonlinear maps in a structured interconnected system. Structural information is often neglected in nonlinear system identification methods. We take advantage of a priori structural information and employ a nonparametric method of identification. We focus on the case where the linear part of the interconnection is known and only the static nonlinear components require identification. We propose an identification algorithm and explore its convergence properties. Copyright c 2005 IFAC Keywords: system identification, nonlinear systems, structured systems, convergence, nonparametric nonlinearities 1. INTRODUCTION This paper is concerned with identification prob- lems in interconnected nonlinear systems. These problems are of considerable importance in the con- text of control, simulation, and design of complex systems. There is available limited past work on the iden- tification of such systems on a case-by-case basis. These include studies of Hammerstein and Wiener systems (Billings and Fakhouri, 1978),(Narendra and Gallman, 1966),(Pawlak, 1991). However, many of the simplest problems here remain open. For instance, the systematic inclusion of a priori struc- tural information has been limited by the lack of a 1 Supported in part by NSF under Grant ECS 03-02554. email: † ken@jagger.me.berkeley.edu ✸ mclaassen@fullcoll.edu ◦ carlo.novara@polito.it △ pramod@ufl.edu ♯ mario.milanese@polito.it ‡ poolla@jagger.me.berkeley.edu paradigm that is sufficiently general to incorporate such information. We believe that the development of generalizations such as linear fractional transformations (LFT’s) in the control systems literature (Packard and Doyle, 1993),(Safonov, 1982), together with the advent of powerful, inexpensive computational resources offer the promise of significant advances in system identification for complex nonlinear systems. Much of the available literature treats nonlinear system identification problems in extreme general- ity, for example using Volterra kernel expansions, neural networks, or radial basis function expan- sions (Billings and Fakhouri, 1978),(Boutayeb et al., 1993),(Johansen, 1996),(Sjoberg et al., 1995). However, it is our conviction that a completely gen- eral theory of nonlinear system identification will have little material impact on the many practical problems that are of interest. We believe that it is more beneficial to study specific classes of nonlinear system identification problems, devise appropriate systematic algorithms, and to study the behavior of