Contents I. Introduction
In many engineering applications a process to be controlled, or simply monitored, is located far from the computing unit and the measured data are transmitted through a low-rate communication system (e.g., in aerospace applications). In the above cases the measured outputs are available for computations after a non negligible time delay. In some applications (e.g., in biochemical reactors) the measurement process intrinsically provides an out-of-date output. In both cases the reconstruction of the present system state using past measurements may be significant. This is a classical state prediction problem. An important engineering application of state prediction occurs when the control variable can be applied to the system with a non negligible delay after its computation. In this case it is clear that a state feedback control law can be used only if computed on the predicted state. In the case of linear systems, such a control problem is solved by the so-called Smith Predictor [18], which is not exactly a predictor: it is a predictive model-based control scheme requiring state-prediction. Many other algorithms for predictive control of systems with input delay have been proposed in the literature (see e.g., [3], [5], [17], and [19]), and all of them include a state predictor. However, in such schemes little attention is devoted to the predictor implementation, often realized in open-loop, under the assumption of stability of the process. In [7], different implementations of the state predictor inside a Smith controller have been discussed and a closed-loop implementation is proposed. In [14], [16]the Smith approach is extended for closed-loop control of nonlinear systems with delayed input. As in the case of linear systems the state prediction is obtained by an open-loop algorithm, so that the accuracy of the predicted state is not guaranteed for unstable systems.
