A Mathematical Framework for Asynchronous, Decentralized, Decision-Making Algorithm with Semi-Autonomous Entities: Synthesis, Simulation, and Evaluation

For many military and civilian large-scale, real-world problems of interest, data is 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. Examples include the battlefield where intelligence data is gathered from different sources and processed to yield decisions and the proposed intelligent vehicle highway system where incident-related data is acquired along the highways to determine the best routes for traffic. The traditional approach to such problems consists of designing a central entity which collects all data and executes a decision making algorithm sequentially to yield the decisions. Centralized decision making algorithms are slow and highly vulnerable to natural and artificial catastrophes. Recent literature contains proposals for asynchronous, distributed, decision making algorithms wherein 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 with asynchronous, distributed, decision making algorithms include the lack of a suitable mechanism to synthesize them for any given problem and a comparative analysis of the quality of their decisions. This paper proposes a mathematical framework, MFAD, based on the Kohn-Nerode distributed hybrid control paradigm, to describe a centralized decision-making algorithm and to synthesize from it a distributed decision-making algorithm. Ideally, the centralized control gathers all