Nonlinear GMV control for unstable state dependent multivariable models

Abstract

A nonlinear generalized minimum variance control law is derived for systems represented by an input-output state dependent nonlinear subsystem that may be open-loop unstable. The solution is obtained using a model for the multivariable discrete-time process that includes a state-dependent (nonlinear and possibly unstable) model that links the output and any unstructured nonlinear input subsystem. The input subsystem can involve an operator of very general nonlinear form, but this has to be assumed to be stable. This is the first NGMV control solution that is suitable for systems containing an unstable nonlinear sub-system contained in a state-dependent model.