We continue to investigate the impacts of communication delays on networked control of discrete event systems (DES). Our previous results show that nondeterministic communication delays result in nondeterminism in the languages generated by the controlled system, which makes the networked control problems more complex. In this paper we investigate the language nondeterminism. We define delay observability and delay controllability. If the language to be synthesized is delay observable and delay controllable, we can synthesize a networked supervisor to control the DES such that the language generated by the controlled system is deterministic, that is, we can synthesize a “deterministic” state-estimate-based networked supervisor. We derive algorithms to check delay controllability and delay observability. If the language to be synthesized is not delay observable and/or delay controllable, we can find its infimal delay controllable and delay observable superlanguage and maximal delay controllable and delay observable sublanguages. We develop algorithms to find these superlanguages and sublanguages. All the algorithms proposed in the paper are of polynomial computational complexity.
['Shaolong Shu', 'Feng Lin']
Deterministic Networked Control of Discrete Event Systems With Nondeterministic Communication Delays