A Distributed Parameter Approach to Design and
Optimal Control of Dynamic Sensor Networks

John A. Burns, PhD

Interdisciplinary Center for Applied Mathematics
Virginia Tech
Blacksburg, VA  24061

Abstract

In this paper we discuss a class of sensor/actuator location problems for optimal zonal estimation and control of systems governed by partial differential equations (PDEs). We show that these problems are naturally formulated as infinite dimensional optimal control problems with operator Riccati equations as constraints and discuss theoretical and computational issues associated with these problems. We formulate the problems as hybrid systems on infinite dimensional spaces (coupled systems of partial, ordinary and delay differential equations) and use infinite dimensional theory to develop computational algorithms for the problems. We present numerical results to illustrate the ideas and suggest areas for future research.