Deadlock-Free Symbolic Smith Controllers Based on Prediction for Nondeterministic Systems

Toshimitsu USHIO

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E104-A    No.11    pp.1593-1602
Publication Date: 2021/11/01
Publicized: 2021/05/14
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2021EAP1002
Type of Manuscript: PAPER
Category: Systems and Control
Smith predictor,  symbolic control,  dead time,  approximated alternating simulation,  deadlock,  

Full Text: FreePDF

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.