Abstract

The problem of determining optimal observation strategies for identification of unknown parameters in distributed-parameter system is discussed. Particularly, a setting where the measurement process is performed by collecting spatial data from mobile nodes with sensing capacity forming an organized network is considered. The framework is based on the use of a criterion defined on the Fisher information matrix associated with the estimated parameters as a measure of the information content in the measurements. Motivations stem from engineering practice, where the clusterization of measurements at some spatial positions and at a given time moment often leads to a decrease in the robustness of the observational system to the model misspecification. Furthermore, there are some technical limitations imposed on the sensor paths in order to avoid collisions, satisfy energy constraints and/or provide a proper deployment of mobile sensor nodes. The approach is to convert the problem to a canonical optimal control one in which the control forces of the sensors may be optimized. Then, through an adaptation of some pairwise communication algorithms, a numerical scheme is developed, which decomposes the resulting problem and distributes the computational burden between network nodes. Numerical solutions are then obtained using widespread powerful numerical packages which handle various constraints imposed on the node motions. As a result, an adaptive scheme is outlined to determine guidance policies for network nodes in a decentralized fashion.