Generalized Predictive Control for Non-Stationary Systems

This paper shows how the generalized predictive control (GPC) can be extended to non-stationary (time-varying) systems. If the time-variation is slow, then the classical GPC can be used in context with an adaptive estimation procedure of a time-invariant ARIMAX model. However, in this paper prior knowledge concerning the nature of the parameter variations is assumed available. The GPC is based on the assumption that the prediction of the system output can be expressed as a linear combination of present and future controls. Since the Diophantine equation cannot be used due to the time-variation of the parameters, the optimal prediction is found as the general conditional expectation of the system output. The underlying model is of an ARMAX-type instead of an ARIMAX-type as in the original version of the GPC (Clarke, D. W., C. Mohtadi and P. S. Tuffs (1987). Automatica, 23, 137-148) and almost all later references. This implies some further modifications of the classical GPC.