Ufuk Topcu - Ph.D. Dissertation
Here is my Ph.D. disseration "Quantitative Local Analysis of Nonlinear Systems" filed on July 11, 2008 at UC Berkeley.
I keep an errata sheet for the dissertation (last updated November 1, 2008). Please e-mail me, if you find any errors.
This is work in progress and eventually - hopefully - general purpose software for quantitative local analysis of nonlinear systems of reasonable dimension will be provided.
A list of papers related to the work reported in the dissertation is below. For more information on this work see Development of Analysis Tools for Certification of Flight Control Laws.
U. Topcu, A. Packard, and P. Seiler, "Local stability analysis using simulations and sum-of-squares programming," To appear in Automatica.
U. Topcu and A. Packard, "Stability region analysis for uncertain nonlinear systems," To appear in
the IEEE Transactions on Automatic Control, 2007.
U. Topcu, A. Packard, P. Seiler, and G. Balas, "Robust region-of-attraction estimation," Submitted to the IEEE Transactions on Automatic Control, 2008.
W. Tan, U. Topcu, P. Seiler, and G. Balas, and A. Packard "Simulation-aided reachability and local gain analysis for nonlinear dynamical systems," To appear in the proceedings of the Conference on Decision and Control, pp. 3428-3433, 2008.
U. Topcu and A. Packard, "Stability region analysis for uncertain nonlinear systems," In the proceedings of the Conference on Decision and Control, pp. 1693-1698, 2007.
U. Topcu, A. Packard, P. Seiler, and T. Wheeler, "Stability region analysis using simulations and sum-of-squares programming," In the proceedings of the American Control Conference, pp. 6009-6014, 2007.
U. Topcu, A. Packard, P. Seiler, and G. Balas, "Local stability analysis for uncertain nonlinear systems using a branch-and-bound algorithm," In the proceedings of the American Control Conference, pp. 3428--3433, 2008.
Data and Results
(updated July 19, 2008)
In the examples throughout the disseration, I occasionally did not provide exact numerical
values used for computations. I either stated the form or an approximation of the
specific expression. Similarly, I did not provide certifying Lyapunov functions and
multipliers. All missing data and results for all examples in this thesis are (or will soon be) below.
Necessary Software: Matlab, and the @polynomial class which
is included in the
SOSTOOLS release. The software packages
SOSTOOLS,
Sedumi, and
Yalmip were used to compute the certificates in the files
below, but are not required to manipulate the data.
Section 3.3.1 - Van der Pol dynamics
Section 3.3.2 - Examples from the literature
Example E1
Example E2
Example E3
Example E4
Example E5
Example E6
Example E7
Section 3.3.3 - Controlled short period aircraft dynamics
Section 3.3.4 - Pendubot dynamics
Section 3.3.5 - Closed-loop dynamics with nonlinear observer based controller
Section 4.5.1 - Examples from the literature
Example (1)
Example (2)
Example (3)
Section 4.5.2 - Controlled short period aircraft dynamics
Section 5.4.1 - An example from the literature
Section 5.4.2 - Controlled short period aircraft dynamics
Section 5.4.3 - Controlled Short Period Aircraft Dynamics with Unmodeled Dynamics
Case (i)
Case (ii) - please email me for more detailed results of this section.
Section 6.3 - Examples
Example (1) - Reachability analysis for a system from the literature
Example (2) - Reachability analysis for pendubot dynamics
Example (3) - L2-to-L2 gain analysis for a system with adaptive controller
Section 6.5.1 - Controlled short period aircraft dynamics
Case (i) (without parametric uncertainty)
Case (ii) (with parametric uncertainty)