Analytical investigations of real-world, hybrid dynamical
systems are technically challenging. Consequently, simulation plays
a vital role in their analysis. Simulation typically addresses
forward problems though, offering limited insights into parametric
influences. The talk will address this issue, presenting
computationally efficient algorithms that extend the capabilities of
simulation. The starting point is a model that captures the
intricacies of hybrid systems, yet is suited to numerical
integration. It will be shown that trajectory sensitivities are well
defined for hybrid systems, and can be computed efficiently. These
sensitivities allow the mapping of parameter uncertainty into
approximate error bounds on nominal (piecewise smooth) trajectories.
Furthermore, they provide gradient information that facilitates the
solution of inverse problems. A range of algorithms will be
presented, including shooting methods for locating (possibly
non-smooth) limit cycles and grazing phenomena, and optimization
algorithms for parameter estimation and controller tuning.
Illustrations will be drawn from various application areas.
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