在噪声分布不确定时，设计鲁棒最优控制策略以最小化最坏情况下的后悔值。
Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets
- 基于均值与协方差的不确定性集，构造因果线性控制策略。
- 将最坏情况后悔优化转化为可解的凸规划问题，具正则化特性。
- 适用于对鲁棒性要求高的控制系统设计，如工业自动化、机器人控制。
我们研究一类有限时域的线性二次随机控制问题，其中噪声过程的概率分布未知，但假设其属于一个模糊集，该模糊集包含所有均值和协方差位于给定名义值为中心的范数球内的分布。为应对这种不确定性，我们设计因果仿射控制策略，以最小化在模糊集内所有分布下的最坏情况期望后悔值。所得到的极小极大最优控制问题被证明等价于一个可处理的凸规划问题，可解释为名义线性二次随机控制问题的正则化版本。基于该凸重构的对偶形式，我们提出一种可扩展的投影子梯度方法，以任意精度计算最优控制器。数值实验表明，该方法在性能上优于现有主流数据驱动控制设计方法。
原文摘要 · Abstract (English)
We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set. The resulting minimax optimal control problem is shown to admit an equivalent reformulation as a tractable convex program, which can be interpreted as a regularized version of the nominal linear-quadratic stochastic control problem. Based on the dual of this convex reformulation, we develop a scalable projected subgradient method for computing optimal controllers to arbitrary accuracy. Numerical experiments are provided to compare the proposed method with state-of-the-art data-driven control design methods.
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