Asynchronous, distributed, decision-making systems with semi-autonomous entities: a mathematical framework

For many military and civilian large-scale, real-world systems of interest, data are first acquired asynchronously, i.e., at irregular intervals of time, at geographically-dispersed sites, processed utilizing decision-making algorithms, and the processed data then disseminated to other appropriate sites. The term real-world refers to systems under computer control that relate to everyday life and are beneficial to the society in the large. The traditional approach to such problems consists of designing a central entity which collects all data, executes a decision-making algorithm sequentially to yield the decisions, and propagates the decisions to the respective sites. Centralized decision-making algorithms are slow and highly vulnerable to natural and artificial catastrophes. Recent literature includes successful asynchronous, distributed, decision-making algorithm designs wherein the local decision making at every site replaces the centralized decision making to achieve faster response, higher reliability, and greater accuracy of the decisions. Two key issues include (1) the lack of an approach to synthesize asynchronous, distributed, decision-making algorithms, for any given problem, and (2) the absence of a comparative analysis of the quality of their decisions. This paper proposes MFAD, a Mathematical Framework for Asynchronous, Distributed Systems, that permits the description of centralized decision-making algorithms and facilities the synthesis of distributed decision-making algorithms. MFAD is based on the Kohn-Nerode distributed hybrid control paradigm