Manyimportant physical phenomena,such as temperature distribution, air flow, and acoustic waves,are describedas continuous,distributed parameterfields. Analyzingandcontrolling these physical processesand systemsare commontasks in manyscientific and engineering domains.However,the challenges are multifold: distributed fields are conceptuallyharderto reason about than lumpedparameter models; computational methodsare prohibitively expensivefor complex spatial domains;the underlyingphysicsimposessevere constraints onobservabilityandcontrollability. er develops an ontological abstraction and a structure-based design mechanism,in a framework collectively knownas spatial aggregation (SA), for reasoning about and synthesizing distributed control schemesfor physical fields. Theontological abstraction modelsa physical field as a hierarchyof networks of spatial objects. SAapplies a smallnumberof generic operators to a field to computeconcise structural descriptions suchas iso-contours, gradientt...