Iterative convex methods for control
Abstract/Contents
- Abstract
- This thesis examines ways to leverage the techniques of convex optimization for control problems (and other problems) that are not necessarily convex by using iterative procedures. Often we can find very good solutions to hard problems by solving a series of simpler problems. As the techniques for convex optimization have improved over the past couple decades, the qualifications for simple problems have expanded dramatically allowing for these simple steps to be remarkably complicated. By leveraging this increased complexity we develop algorithms that are more efficient and capable of handling more complex models. In the first chapter of this thesis we examine the problem of trajectory optimization, in particular the minimum-time traversal of a fixed path. This is a problem that arises in machining, automated racing, surveillance, and other applications. We explore a change of variables that makes the problem convex. We exploit the structure of the problem to efficiently find solutions. This speed allows the algorithm to be used in online settings as part of model predictive control (MPC) loops. The algorithm can also be used to rapidly evaluate different trajectories to identify the fastest one. This evaluation splits the minimum time trajectory problem into a series of fast trajectory evaluations. In the second section of the thesis we examine a technique called the convex-concave procedure (CCP) which addresses difference of convex (DC) problems. This iterative procedure finds local minima of DC problems by solving a sequence of convex problems. We present a number of extensions to this algorithm to allow a much wider range of problem classes to be considered, including a vector form of the problem and extensions to address large scale problems. We then present a series of examples to highlight various aspects of these algorithms. In the last section of the thesis we leverage CCP to address the antagonistic control problem. Whereas a typical control problem attempts to minimize an objective, the antagonistic control problem maximizes an objective. This simulates an aggressor taking control of a system to do it harm. Having knowledge of how and when harm can be done to a system, allows for better defense of the system. We also demonstrate how the S-procedure can be used to get an upper bound on the negative behavior to pair with the lower bound provided by CCP.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lipp, Thomas |
|---|---|
| Associated with | Stanford University, Department of Mechanical Engineering. |
| Primary advisor | Boyd, Stephen P |
| Primary advisor | Gerdes, J. Christian |
| Thesis advisor | Boyd, Stephen P |
| Thesis advisor | Gerdes, J. Christian |
| Thesis advisor | Lall, Sanjay |
| Advisor | Lall, Sanjay |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Thomas Lipp. |
|---|---|
| Note | Submitted to the Department of Mechanical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Thomas William Lipp
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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