Qualitative Analysis of Distributed Physical Systems with Applications to Control Synthesis

Abstract

Many important physical phenomena, such as temper-ature distribution, air flow, and acoustic waves, are described as continuous, distributed parameter fields. Analyzing and controlling these physical processes and systems are common tasks in many scientific and en-gineering domains. However, the challenges are multi-fold: distributed fields are conceptually harder to rea-son about than lumped parameter models; computa-tional methods are prohibitively expensive for complex spatial domains; the underlying physics imposes severe constraints on observability and controllability. This paper develops an ontological abstraction and a structure-based design mechanism, in a framework collectively known as spatial aggregation (SA), for reasoning about and synthesizing distributed control schemes for physical fields. The ontological abstrac-tion models a physical field as a hierarchy of networks of spatial objects. SA applies a small number of generic operators to a field to compute concise structural de-scriptions such as iso-contours, gradient trajectories, and influence graphs. The design mechanism uses these representations to find feasible control configurations. We illustrate the mechanism using a thermal control problem from industrial heat treatment and demon-strate that the active exploitation of structural knowl-edge in physical fields yields a significant computa-tional advantage.