Polynomial approach to nonlinear predictive generalized minimum variance control

M.J. Grimble, P.M. Majecki

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A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes.
Original languageEnglish
Pages (from-to)411-424
Number of pages14
JournalIET Control Theory and Applications
Issue number3
Publication statusPublished - 1 Mar 2010


  • polynomial systems
  • optimal
  • predictive
  • nonlinear
  • minimum variance
  • transport delays

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