Spatial Aggregation : Modeling and controllingphysical fields
Christopher Bailey-Kellogg, Feng Zhao · 2015
Many important physical phenomena, such as temper-ature distribution, air flow, and acoustic waves, are described as continuous, distributed parameter fields. Controlling a doptimizing these physical processes and systems are common design tasks in many sci-entific and engineering domains. However, the chal-lenges are multifold: distributed fields are concep-tually harder to reason about han lumped parame-ter models; computational methods are prohibitively expensive for complex spatial domains; the underly-ing physics imposes severe constraints on observability and controllability. This paper develops anontological abstraction and an aggregation-disaggregation mechani.qm, in a f~ame-work collectively known as spatial aggregation (SA), for reasoning about and synthesizing distributed control schemes for physical fields. The ontological abstraction models physical fields as networks of spa-tial objects. The aggregation-disaggregation mecha-nism employs a set of data types and generic oper-ators to find a feasible control structure, specifying control placement and associated actions that satisfy given constraints. SA abstracts common computa-tional patterns of control design and optimization in a small number of operators to support modular pro-gramming; it builds concise and articulable structural descriptions for physical fields. We illustrate the use of the SA ontological abstraction and operators in an example of regulating a thermal field in industrial heat treatment.