Book Description

The main purpose of this dissertation is to define and solve problems on optimal sensing and actuating policies in Cyber-Physical Systems (CPSs). Cyber-physical system is a term that was introduced recently to define the increasing complexity of the interactions between computational hardwares and their physical environments. The problem of designing the "cyber" part may not be trivial but can be solved from scratch. However, the "physical" part, usually a natural physical process, is inherently given and has to be identified in order to propose an appropriate "cyber" part to be adopted. Therefore, one of the first steps in designing a CPS is to identify its "physical" part. The "physical" part can belong to a large array of system classes. Among the possible candidates, we focus our interest on Distributed Parameter Systems (DPSs) whose dynamics can be modeled by Partial Differential Equations (PDE). DPSs are by nature very challenging to observe as their states are distributed throughout the spatial domain of interest. Therefore, systematic approaches have to be developed to obtain the optimal locations of sensors to optimally estimate the parameters of a given DPS. In this dissertation, we first review the recent methods from the literature as the foundations of our contributions. Then, we define new research problems within the above optimal parameter estimation framework. Two different yet important problems considered are the optimal mobile sensor trajectory planning and the accuracy effects and allocation of heterogeneous sensors. Under the remote sensing setting, we are able to determine the optimal trajectories of remote sensors. The problem of optimal robust estimation is then introduced and solved using an interlaced "online" or "real-time" scheme. Actuation policies are introduced into the framework to improve the estimation by providing the best stimulation of the DPS for optimal parameter identification, where trajectories of both sensors and actuators are optimized simultaneously. We also introduce a new methodology to solving fractional-order optimal control problems, with which we demonstrate that we can solve optimal sensing policy problems when sensors move in complex media, displaying fractional dynamics. We consider and solve the problem of optimal scale reconciliation using satellite imagery, ground measurements, and Unmanned Aerial Vehicles (UAV)-based personal remote sensing. Finally, to provide the reader with all the necessary background, the appendices contain important concepts and theorems from the literature as well as the Matlab codes used to numerically solve some of the described problems.