Dependent initialization of the scenario optimal control problem

[rlefringhausen]

In the current implementation, a single set of scenarios is drawn and used both

1. to compute an initialization for the scenario optimal control problem (to reduce runtimes), and
2. to solve the scenario optimal control problem and derive probabilistic robustness by removing scenarios to determine the cardinality of a support subset.

It has come to our attention that this dual use of the same scenario set conflicts with the assumptions of scenario theory. In particular, the scenarios used to compute an initial guess must be independent of those used to formulate the scenario OCP.

This issue can be resolved by drawing an independent scenario set for the initialization.

As the initialization procedure is not described in the paper, the theoretical results remain unaffected. However, the numerical experiments presented in the paper are impacted. We plan to address this issue in the future and rerun the experiments. This will likely lead to increased sampler runtimes due to the need for additional scenarios. We do not expect significant changes in the reported robustness levels.