Abstract
Timed Event Graphs (TEGs) are a graphical model for decision free and time-invariant Discrete Event Systems (DESs). To express systems with time-variant behaviors, a new form of synchronization, called partial synchronization (PS), has been introduced for TEGs. Unlike exact synchronization, where two transitions t1,t2 can only fire if both transitions are simultaneously enabled, PS of transition t1 by transition t2 means that t1 can fire only when transition t2 fires, but t1 does not influence the firing of t2. This, for example can describe the synchronization between a local train and a long distance train. Of course it is reasonable to synchronize the departure of a local train by the arrival of long distance train in order to guarantee a smooth connection for passengers. In contrast, the long distance train should not be delayed due to the late arrival of a local train. Under the assumption that PS is periodic, we can show that the dynamic behavior of a TEG under PS can be decomposed into a time-variant and a time-invariant part. It is shown that the time-variant part is invertible and that the time-invariant part can be modeled by a matrix with entries in the dioid {mathcal{M}}_{in}^{ax}left [!left [gamma ,delta right ]!right ], i.e. the time-invariant part can be interpreted as a standard TEG. Therefore, the tools introduced for standard TEGs can be used to analyze and to control the overall system. In particular, in this paper output reference control for TEGs under PS is addressed. This control strategy determines the optimal input for a predefined reference output. In this case optimality is in the sense of the ”just-in-time” criterion, i.e., the input events are chosen as late as possible under the constraint that the output events do not occur later than required by the reference output.
Highlights
Introduction and motivationTimed Event Graphs (TEGs) are a subclass of timed Petri nets where each place has exactly one input and one output transition and all arcs have weight 1
It is shown that the time-variant part is invertible and that the time-invariant part can be modeled by a matrix with entries in the dioid Mainx [[γ, δ]], i.e. the time-invariant part can be interpreted as a standard TEG
In David-Henriet et al (2014, 2015, 2016), dioid theory has been applied to Timed Event Graphs under Partial Synchronization (TEGsPS) and first results have been obtained for performance evaluation and controller synthesis for TEGsPS
Summary
TEGs are a subclass of timed Petri nets where each place has exactly one input and one output transition and all arcs have weight 1. In Hamaci et al (2006) and Trunk et al (2017b) output reference control was studied for TEGs with positive integer weights on the arcs These TEGs exhibit event-variant behavior and can be seen as the counter-part to TEGsPS. Similar to transfer functions for standard TEGs in the dioid Mainx [[γ , δ]], the transfer behavior of TEGsPS is described by cyclic series in the dioid Tper [[γ ]]. These transfer functions are useful, for instance, for computing the output for a given input of a system, for system composition and for control synthesis. Results on the residuation of the product in the dioid Tper [[γ ]] are obtained
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
