Discrete-scanning observation problem for stochastic non-linear discrete-time distributed parameter systems

Abstract

The problem of determining the suboptimal measurement scheduling for a stochastic discrete-time distributed parameter systems described by non-linear partial differential equations is discussed. The discrete-scanning observations are realized by the suboptimal selection of measurement data from spatially fixed sensors. The problem statement is in such a form that the stochastic matrix principle of Pontryagin can be applied to obtain the necessary conditions for optimally. Based on successive approximation of the suboptimal filtering equations, a computationally advantageous approach is developed to obtain the algorithm without solving the non-linear two-point boundary value problem. Numerical example is presented to illustrate the application of our approach to solve the problem of location of monitoring stations for an air pollutant process.