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The Scenario Approach to Robust Control Design

机译：鲁棒控制设计的方案方法

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This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control problems representable by means of parameter-dependent linear matrix inequalities (LMIs). It is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem (the scenario problem) whose solution is approximately feasible for the original (usually infinite) set of constraints, i.e., the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased. We provide an explicit and efficient bound on the number of samples required to attain a-priori specified levels of probabilistic guarantee of robustness. A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense.
机译：本文针对鲁棒控制分析和综合问题提出了一种新的概率解决方案框架，该框架可以以线性目标最小化的形式表示，该线性目标受不确定性项参数化的凸约束的约束。这包括通过依赖于参数的线性矩阵不等式（LMI）可以表示的一类NP硬控制问题。本文表明，通过对约束的适当采样，可以得到标准凸优化问题（场景问题），该问题的解对于原始（通常为无限）约束集（即原始集的度量）近似可行随着样本数量的增加，方案解决方案违反的约束迅速减少到零。我们为达到先验指定水平的鲁棒性概率保证所需的样本数量提供了明确而有效的界限。因此，如果要在提出的风险调整意义上实现鲁棒性，则通常很难在确定性鲁棒性的意义上解决的一系列控制问题适合多项式时间解。

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