发表机构
Institute for Computational and Mathematical Engineering; Stanford University（计算与数学工程研究所; 斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对扰动分布随时间漂移的有限时域LQR问题，提出事前分布鲁棒遗憾优化方法，通过时间耦合矩模糊集和仿射扰动反馈合成，将问题转化为半定规划，实验验证其能显著降低最坏情况遗憾。
AI 中文摘要
我们研究了有限时域LQR问题，其中独立扰动的分布可能随时间漂移。我们通过事前分布鲁棒遗憾优化（DRRO）来处理这种演化中的不确定性，该方法最小化相对于已知分布序列的最优因果控制器的最大超额期望成本。为了指定可接受的分布序列，我们引入了一个时间耦合的矩模糊集，该模糊集具有Gelbrich动能预算和第二个预算，用于限制与参考矩的偏离以及持续的累积失配。尽管矩在时间上耦合，仿射扰动反馈合成恰好简化为半定规划。最优策略利用过去的扰动来预测由当前和未来扰动均值确定的标称LQR修正。SDP解还产生最坏情况矩路径和相应的分布。对于标准分布鲁棒优化（DRO），类似的SDP松弛可能存在对偶间隙。投资组合清算实验表明，在漂移模糊集上，最坏情况遗憾显著低于常见定律的DRRO和标称控制。
英文摘要
We study finite-horizon LQR with independent disturbances whose laws may drift over time. We address uncertainty in this evolution through ex-ante distributionally robust regret optimization (DRRO), which minimizes worst-case excess expected cost relative to the optimal causal controller that knows the law sequence. To specify the admissible law sequences, we introduce a temporally coupled moment ambiguity set with a Gelbrich kinetic-energy budget and a second budget limiting departures from reference moments and persistent cumulative mismatch. Despite the coupling of moments across time, affine disturbance-feedback synthesis reduces exactly to a semidefinite program. An optimal policy uses past disturbances to predict the correction to nominal LQR determined by current and future disturbance means. The SDP solution also yields worst-case moment paths and corresponding laws. For standard distributionally robust optimization (DRO), the analogous SDP relaxation can have a duality gap. Portfolio liquidation experiments show substantially lower worst-case regret over the drifting ambiguity set than common-law DRRO and nominal control.
Comments16 pages, 2 figures, 1 table. Submitted to the 2027 American Control Conference (ACC); under review
