Parameter identification of nonlinear multirate time-delay system with uncertain output delays

The joint parameter and time-delay estimation problems for a class of nonlinear multirate time-delay system with uncertain output delays are addressed in this paper. The practical process typically has time-delay properties and the process data are often multirate, sampled with output data inevitably corrupted by uncertain delays. The linear parameter varying (LPV) finite impulse response (FIR) multirate time-delay model is initially built to describe the considered system. The problems of over-parameterization and the existence of both continuous model parameters and discrete time-delays have made the conventional maximum likelihood difficult to solve the considered problems. In order to handle these problems, the joint parameter and time-delay estimation for the LPV FIR multirate time-delay model are formulated in the expectation-maximization scheme, and the algorithm to estimate the model parameters and time-delays is derived, simultaneously based on multirate process data. The efficacy of the proposed method is verified through a numerical simulation and a practical chemical plant.