Kernel-based identification of non-causal systems with application to inverse model control

Models of inverse systems are commonly encountered in control, e.g., feedforward. The aim of this paper is to address several aspects in identification of inverse models, including model order selection and dealing with unstable inverse systems that originate from inverting non-minimum phase dynamics. A kernel-based regularization framework is developed for identification of non-causal systems. It is shown that ‘unstable’ models can be viewed as bounded, but non-causal, operators. As the main contribution, a range of the required kernels for non-causal systems is developed, including non-causal stable spline kernels. Benefits of the approach are confirmed in an example, including non-causal feedforward control for non-minimum phase systems.