Automatic Scenario Generation for Robust Optimal Control Problems

TL;DR

This paper introduces a local reduction method for robust optimal control that efficiently manages scenario numbers by identifying worst-case uncertainties, improving robustness without excessive computational complexity.

Contribution

It presents a novel local reduction approach that finds non-boundary worst-case scenarios, reducing scenario count in robust control problems compared to traditional boundary-based methods.

Findings

Scenario count reduced to 101 from over 2 million.

Method finds worst-case scenarios outside the boundary of uncertainty.

Approach maintains robustness with fewer scenarios.

Abstract

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.