The goal of an optimal control algorithm is to improve the performance of a system. For a stochastic system, a typical optimal control method minimizes the mean (first cumulant) of the cost function. However, there are other statistical properties of the cost function, such as variance (second cumulant) and skewness (third cumulant), which will affect the system performance. In this dissertation, the work on the statistical optimal control are presented, which extends the traditional optimal control method using cost cumulants to shape the system performance. Statistical optimal control will allow more design freedom to achieve better performance. The solutions of statistical control involve solving partial differential equations known as Hamilton-Jacobi-Bellman equation. A numerical method based on neural networks is employed to find the solutions of the Hamilton-Jacobi-Bellman partial differential equation. Furthermore, a complex problem such as multiple satellite control, has both continuous and discrete dynamics. Thus, a hierarchical hybrid architecture is developed in this dissertation where the discrete event system is applied to discrete dynamics, and the statistical control is applied to continuous dynamics. Then, the application of a multiple satellite navigation system is analyzed using the hierarchical hybrid architecture. Through this dissertation, it is shown that statistical control theory is a flexible optimal control method which improves the performance; and hierarchical hybrid architecture allows control and navigation of a complex system which contains continuous and discrete dynamics. / Electrical and Computer Engineering
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/1570 |
| Date | January 2011 |
| Creators | Kang, Bei |
| Contributors | Won, Chang-Hee, 1967-, Butz, Brian P., Vainchtein, Dmitri, Biswas, Saroj K., Nersesov, Sergey G., 1976- |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 203 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/1552, Theses and Dissertations |
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