Kernel Based Identification of Systems with Multiple Outputs Using Nuclear Norm Regularization
The class of nonlinear systems is much broader than that of linear systems. Hence, for the estimation of nonlinear systems a lot of system structures are still an active domain for research. Most established techniques for nonlinear system identification  formulate a nonlinear regression problem that is then solved by a variety of techniques, like wavelets, neural networks, or more recently, support vector machines and kernel-based methods. A common limitation for nonlinear regression techniques is that it is difficult to handle multiple outputs, and this is particularly true for most kernel-based estimation schemes. A frequently applied workaround is to estimate independent models for each individual output. This chapter introduces an advanced estimation scheme that is able to exploit dependencies between output variables. The technique is based on least-squares support vector machines  and a convex regularization term based on the nuclear norm .