Synchronization, linearity, and beyond
Year: 2025
Type: dissertation
Abstract: This thesis is dedicated to the study of discrete-event systems (DES) exhibiting resource-sharing and partial-synchronization phenomena, the latter consisting in the presence of external signals restricting the occurrence of certain events. The results are developed within a well-established framework for the modeling and control of discrete-event systems based on tropical algebra, where the basic modeling structures form a subclass of timed Petri nets called timed event graphs (TEGs). A notable advantage of using TEGs is the fact that their evolution can be described by linear equations in a tropical-algebraic setting such as the max-plus or the min-plus algebra. This has given rise to a solid control theory for the class of systems that can be modeled as TEGs, including methods for feedforward, feedback, and observer-based control design. Nonetheless, this system class is not suitable for modeling practically-relevant phenomena involving concurrency. The main contribution of this thesis is to further enrich the existing TEG-based control framework by encompassing the phenomena of resource-sharing and partial synchronization, neither of which can be modeled by TEGs alone. Both these phenomena bring additional restrictions (internal in the former case, external in the latter) to the occurrence of certain events in the system. In both cases, we show that these restrictions can be expressed as inequalities in the semiring of counters by making use of an operation called Hadamard product. We then proceed to propose a formal and systematic method for optimal output-reference control of systems exhibiting either of these phenomena, where optimality is interpreted in a just-in-time sense: control inputs are provided as late as possible while guaranteeing that the resulting system outputs do not occur later than dictated by the reference signal. The method also extends to the cases in which the output-reference signals (in the case of resource-sharing) or the external restrictions (in the case of partial synchronization) may change unexpectedly during the operation of the system. Finally, a unified method is presented which allows to systematically obtain optimal control inputs for systems in which both treated phenomena are simultaneously present.
Author: Schafaschek, Germano
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6885987160
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