Optimal scanning measurement problem for a stochastic distributed-parameter system

Abstract

This paper deals with the problem of determining the optimal measurement scheduling for a stochastic distributed-parameter system (DPS) based on spatially continuous and discrete-scanning observations. These two types of measurement are realized by the optimal motion of spatially-movable sensors and the optimal selection of measurement data from spatially-fixed sensors, respectively. For the continuous scanning case, the existence of optimal solutions for the problem is proved and the N-modal approximation problem is established. For the discrete case, however, it is impossible to derive the existence conditions. Therefore, it is shown that there exist optimal relaxed solutions by introducing the relaxed control theory. A practical method for constructing an approximate solution for the relaxed problem is proposed. Necessary conditions for approximate-optimality are represented in the form of a matrix minimum principle, and a feasible algorithm is developed to determine the approximate solution. A numerical example is considered and the present two types of optimal measurement trajectory are compared.