A method is developed to estimate the projection of a higher dimensional (three or more) controllable set onto a lower dimensional (usually one or two) space. This method requires that an n-dimensional dynamical system subject to a scalar control be transformed into two lower dimensional subsystems by choosing a proper transformation matrix. It is shown that such a transformation can always be determined for an n-dimensional linear I/O system. For some nonlinear dynamical system problems such as an aircraft missile avoidance problem, a proper transformation matrix still can be determined. From the transformed system, both an overestimate and an underestimate for an actual projected controllable set in the state space of interest can be provided by using the method presented in this dissertation. With these information, the actual projected controllable set can be estimated. Two linear I/O systems subject to a scalar control and an aircraft missile avoidance problem are used to illustrate the method.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/184443 |
| Date | January 1988 |
| Creators | Wu, Zong Yeng. |
| Contributors | Vincent, Thomas L., Schultz, Donald G., Joshi, Shiv P., Cellier, Francois E. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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