Spatial Aggregation : Modeling and controllingphysical fields

Many important physical phenomena, such as temperature distribution,air flow, and acoustic waves, are described as continuous, distributed parameter fields. Controlling and optimizing these physical processes and systems are com- mon design tasks in many scientificand engineer- ing domains . However, the challenges are multi- fold: distributed fieldsare conceptually harder to reason about than lumped parameter models ; computational methods are prohibitivelyexpen- sivefor complex spatialdomains ;the underlying physics imposes severe constraintson observabil- ity and controllability . This paper develops an ontological abstraction and an aggregation-disaggregation mechanism .in a framework collectivelyknown as spatial ag- gregation (SA), for reasoning about and syn- thesizing distributed control schemes for phys- ical fields. The ontological abstraction mod- els physical fieldsas networks of spatialobjects. The aggregation-disaggregation mechanism em- ploys a setof data types and genericoperators to find a feasiblecontrol structure, specifying con- trol placement and associated actions that sat- isfy given constraints. SA abstracts common computational patterns of controldesign and op- timization in a small number of operators to support modular programming ;itbuilds concise and articulablestructural descriptions forphysi- cal fields. We illustratethe use of the SA onto- logicalabstraction and operators in an example of regulating a thermal fieldin industrialheat treatment .