抄録
An approach to the optimal allocation of sensors in a class of distributed parameter systems is considered. Since it is technically impossible to observe the system state at overall spatial domain and all real systems are subjected to stochastic disturbances, it is necessary to choose the optimal location of sensors in order to obtain the best state estimates. The measurement optimization based on the filtering theory, in which the linear system, the Gaussian noise processes, and the quadratic cost are considered, can be done a priori by solving an optimal control problem with the Riccati equation. Although the non-linearlity of the Riccati equation makes the problem analitically intractable, the necessary conditions of optimality have been derived and some simple numerical examples have been reported by various authors. The determination of optimal locations in the multi-dimensional spatial domain, however, requires much calculation time and the prior limitation of allowable measurement points. In this paper an alternative approach to allocate sensors is considered by applying the concepts of the Monte-Carlo stratified sampling method to our problem. Approximate measurement systems for the spatial continuous and the spatial averaging types of measurements are constructed by optimally allocating a give number of sensors to the prespecified strata so that the information may be preserved as much as possible. This approach cannot make the precise determination of each sensor's location, but provides an effectual method to allocate many sensors in a multi-dimensional spatial domain.
