We propose a method to overbound reachable sets on finite time horizons for continuous-time nonlinear systems with polynomial dynamics. The analysis considers uncertain initial conditions, parameters, L2 disturbances, and perturbations characterized by time-domain, integral quadratic constraints (IQCs). This method makes use of time-dependent polynomial storage functions that satisfy certain dissipation inequalities on local regions of the state space, intervals of time and bounded sets of uncertain parameters. The S-procedure and sum-of-square techniques are used to derive the computation algorithms, and an objective function is introduced to find an over-approximation with a desired shape. Both pedagogical and practically motivated examples are presented, including a 7-state F-18 aircraft model.
from cs updates on arXiv.org https://ift.tt/2KDkQka
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