  Existing methods for nonlinear robust control often use scenario-based
approaches to formulate the control problem as nonlinear optimization problems.
Increasing the number of scenarios improves robustness, while increasing the
size of the optimization problems. Mitigating the size of the problem by
reducing the number of scenarios requires knowledge about how the uncertainty
affects the system. This paper draws from local reduction methods used in
semi-infinite optimization to solve robust optimal control problems with
parametric uncertainty. We show that nonlinear robust optimal control problems
are equivalent to semi-infinite optimization problems and can be solved by
local reduction. By iteratively adding interim globally worst-case scenarios to
the problem, methods based on local reduction provide a way to manage the total
number of scenarios. In particular, we show that local reduction methods find
worst case scenarios that are not on the boundary of the uncertainty set. The
proposed approach is illustrated with a case study with both parametric and
additive time-varying uncertainty. The number of scenarios obtained from local
reduction is 101, smaller than in the case when all $2^{14+3\times192}$
boundary scenarios are considered. A validation with randomly drawn scenarios
shows that our proposed approach reduces the number of scenarios and ensures
robustness even if local solvers are used.
