Speaker
Description
Robust controllers that stabilize dynamical systems even under disturbances and
noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While
methods such as gradient sampling can handle the nonconvexity and nonsmoothness, the costs of
evaluating the objective function may be substantial, making robust control challenging for dynamical systems with high-dimensional state spaces. In this work, we introduce multifidelity variants
of gradient sampling that leverage low-cost, low-fidelity models with low-dimensional state spaces
for speeding up the optimization process while nonetheless providing convergence guarantees for a
high-fidelity model of the system of interest, which is primarily accessed in the last phase of the
optimization process. Our first multifidelity method initiates gradient sampling on higher-fidelity
models with starting points obtained from cheaper, lower-fidelity models. Our second multifidelity
method relies on ensembles of gradients that are computed from low- and high-fidelity models. Numerical experiments with controlling the cooling of a steel rail profile and laminar flow in a cylinder
wake demonstrate that our new multifidelity gradient sampling methods achieve up to two orders
of magnitude speedup compared to the single-fidelity gradient sampling method that relies on the
high-fidelity model alone.
