Influence-based model decomposition for reasoning about spatially distributed physical systems Original Research Article

Many important science and engineering applications, such as regulating the temperature distribution over a semiconductor wafer and controlling the noise from a photocopy machine, require interpreting distributed data and designing decentralized controllers for spatially distributed systems. Developing effective computational techniques for representing and reasoning about these systems, which are usually modeled with partial differential equations (PDEs), is one of the major challenge problems for qualitative and spatial reasoning research. This paper introduces a novel approach to decentralized control design, influence-based model decomposition, and applies it in the context of thermal regulation. Influence-based model decomposition uses a decentralized model, called an influence graph, as a key data abstraction representing influences of controls on distributed physical fields. It serves as the basis for novel algorithms for control placement and parameter design for distributed systems with large numbers of coupled variables. These algorithms exploit physical knowledge of locality, linear superposability, and continuity, encapsulated in influence graphs representing dependencies of field nodes on control nodes. The control placement design algorithms utilize influence graphs to decompose a problem domain so as to decouple the resulting regions. The decentralized control parameter optimization algorithms utilize influence graphs to efficiently evaluate thermal fields and to explicitly trade off computation, communication, and control quality. By leveraging the physical knowledge encapsulated in influence graphs, these control design algorithms are more efficient than standard techniques, and produce designs explainable in terms of problem structures.