The Smith method has been used to control physical plants with dead time components, where plant states after the dead time is elapsed are predicted and a control input is determined based on the predicted states. We extend the method to the symbolic control and design a symbolic Smith controller to deal with a nondeterministic embedded system. Due to the nondeterministic transitions, the proposed controller computes all reachable plant states after the dead time is elapsed and determines a control input that is suitable for all of them in terms of a given control specification. The essence of the Smith method is that the effects of the dead time are suppressed by the prediction, however, which is not always guaranteed for nondeterministic systems because there may exist no control input that is suitable for all predicted states. Thus, in this paper, we discuss the existence of a deadlock-free symbolic Smith controller. If it exists, it is guaranteed that the effects of the dead time can be suppressed and that the controller can always issue the control input for any reachable state of the plant. If it does not exist, it is proved that the deviation from the control specification is essentially inevitable.

In this paper, we consider a networked control system where bounded network delays and packet dropouts exist in the network. The physical plant is abstracted by a transition system whose states are quantized states of the plant measured by a sensor, and a control specification for the abstracted plant is given by a transition system when no network disturbance occurs. Then, we design a prediction-based controller that determines a control input by predicting a set of all feasible abstracted states at time when the actuator receives the delayed input. It is proved that the prediction-based controller suppresses effects of network delays and packet dropouts and that the controlled plant still achieves the specification in spite of the existence of network delays and packet dropouts.