Traditionally, discrete-time sampled-data systems are represented using shift-operator parametrizations. Such parametrizations are not suitable at fast sampling rates. An alternative parametrization using the so-called delta-operator is examined. It is shown how to maintain a close correspondence to continuous-time when sampling a system described in continuous-time by stochastic differential equations. Using delta-operator parametrizations makes it possible to unify discrete-time and continuous-time theory. In addition these parametrizations possess certain numerical advantages compared to shift-operator representations.
A new prediction method is developed. It is based on ideas from continuous-time but derived from discrete-time delta-operator models. It is shown to include the optimal minimum-variance predictor as a special case and to have a well-defined continuous-time limit.
By means of this new prediction method a unified framework for discrete-time and continuous-time predictive control algorithms is developed. This contains a continuous-time like discrete-time predictive controller which is insensitive to the choice of sampling period and has a well-defined limit in the continuous-time case. Also more conventional discrete-time predictive control methods may be described within the unified approach. The predictive control algorithms are extended to frequency weighted criterion functions. Also a state-space approach is described which extends straightforwardly to the multi-variable case.
Finally, aspects on the connection between system identification and control design are discussed. Several approaches to improve this interconnection have been proposed. The frequency-distribution of the estimation error with low-complexity models is treated and proves to be important for the development of control-relevant prefilters in estimation. Iterative approaches are presented, both using standard estimation methods with prefiltering and non-standard control-relevant estimation methods. New combined adaptive/iterative techniques are proposed.
