论文标题
自动场景生成可靠的最佳控制问题
Automatic Scenario Generation for Robust Optimal Control Problems
论文作者
论文摘要
非线性鲁棒控制的现有方法通常使用基于方案的方法将控制问题作为非线性优化问题。增加场景的数量可以提高鲁棒性，同时增加优化问题的大小。通过减少方案数量来减轻问题的大小，需要了解不确定性如何影响系统的知识。本文摘自半无限优化的局部还原方法，以解决与参数不确定性的强大最佳控制问题。我们表明，非线性鲁棒的最佳控制问题等效于半无限优化问题，可以通过局部减少来解决。通过迭代将临时全球最差的场景添加到该问题中，基于本地减少的方法提供了一种管理场景总数的方法。特别是，我们表明局部还原方法发现不在不确定性集界限的最坏情况。用参数和添加剂时变不确定性的案例研究来说明所提出的方法。从本地还原获得的方案数量为101，比考虑所有$ 2^{14+3 \ times192} $边界方案的情况小。使用随机绘制的方案的验证表明，即使使用了本地求解器，我们提出的方法也会减少方案的数量并确保鲁棒性。
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.
