Online prediction and control in nonlinear stochastic systems

In this paper conditional parametric ARX-models are suggested and studied by simulation. These non-linear models are traditional ARXmodels in which the parameters are replaced by smooth functions. The estimation method is based on the ideas of locally weighted regression. It is demonstrated that kernel estimates (local constants) are in general inferior to local quadratic estimates. For the considered application, modelling of temperatures in a district heating system, the input sequences are correlated. Simulations indicate that correlation to this extend results in unreliable kernel estimates, whereas the local quadratic estimates are quite reliable.