Quantitative Local Analysis of Nonlinear Systems - University of ...
Quantitative Local Analysis of Nonlinear Systems - University of ...
Quantitative Local Analysis of Nonlinear Systems - University of ...
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Abstract<br />
<strong>Quantitative</strong> <strong>Local</strong> <strong>Analysis</strong> <strong>of</strong> <strong>Nonlinear</strong> <strong>Systems</strong><br />
by<br />
Ufuk Topcu<br />
Doctor <strong>of</strong> Philosophy in Engineering - Mechanical Engineering<br />
<strong>University</strong> <strong>of</strong> California, Berkeley<br />
Pr<strong>of</strong>essor Andrew K. Packard, Chair<br />
This thesis investigates quantitative methods for local robustness and performance<br />
analysis <strong>of</strong> nonlinear dynamical systems with polynomial vector fields. We propose measures<br />
to quantify systems’ robustness against uncertainties in initial conditions (regions-<strong>of</strong>attraction)<br />
and external disturbances (local reachability/gain analysis). S-procedure and<br />
sum-<strong>of</strong>-squares relaxations are used to translate Lyapunov-type characterizations to sum<strong>of</strong>-squares<br />
optimization problems. These problems are typically bilinear/nonconvex (due to<br />
local analysis rather than global) and their size grows rapidly with state/uncertainty space<br />
dimension.<br />
Our approach is based on exploiting system theoretic interpretations <strong>of</strong> these optimization<br />
problems to reduce their complexity. We propose a methodology incorporating simulation<br />
data in formal pro<strong>of</strong> construction enabling more reliable and efficient search for robustness<br />
and performance certificates compared to the direct use <strong>of</strong> general purpose solvers. This<br />
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