C. Bailey-Kellogg, "The spatial aggregation language for modeling and controlling distributed physical systems", PhD thesis, Ohio State University, 1999. [preprint]

Many important science and engineering applications, such as predicting weather patterns, controlling the temperature distribution over a semiconductor wafer, and controlling the noise of a photocopy machine, require interpreting data and designing decentralized controllers for spatially distributed systems. This thesis describes the Spatial Aggregation Language (SAL), a novel programming language and environment supporting data interpretation and control tasks for distributed physical systems. SAL provides a set of powerful, high-level components that make explicit use of domain-specific physical knowledge, such as metrics, adjacency relations, and equivalence predicates, in order to uncover and exploit structures in distributed physical data at multiple levels of abstraction. The language data types and operators manipulate structured representations of spatial objects in distributed physical systems at multiple levels of abstraction. The programming environment supports rapid prototyping of application programs and interactive manipulation of the resulting structures. In comparison with existing tools, the Spatial Aggregation Language offers high level programming abstractions explicitly encoding physical knowledge; this approach supports a variety of inference, explanation, tutoring, and design tasks.

This thesis presents as a case study novel approaches to decentralized control design, in the context of thermal regulation. This case study develops novel algorithms for control placement and parameter design for 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. This case study demonstrates the utility of the Spatial Aggregation Language operators in supporting the programming of these computations in a vocabulary natural for the domain.