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

For many military and civilian large-scale, realworld 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 the lack of an approach to synthesize asynchronous, distributed, decision making algorithms, for any given problem, and 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. It has been a belief that since the centralized control gathers every necessary data from all entities in the system and utilizes them to compute the decisions, the decisions may be “globally” optimal. In truth, however, as the frequency of the sensor data increases and the environment gets larger, dynamic, and more complex, the decisions are called into question. In the distributed decisionmaking system, the centralized decision-making is replaced by those of the constituent entities that aim at minimizing a Lagrangian, i.e. a local, non-negative cost criterion, subject to the constraints imposed by the global goal. Thus, computations are carried out locally, utilizing locally obtained dataand appropriate information that is propagated from other sites. It is hypothesized that with each entity engaged in optimizing its individual behavior, asynchronously, concurrently, and independent of other