We propose a Stein variational distributionally robust controller for nonlinear dynamical systems with latent parametric uncertainty. The method is an alternative to conservative worst-case ambiguity-set optimization with a deterministic particle-based approximation of a task-dependent uncertainty distribution, enabling the controller to concentrate on parameter sensitivities that most strongly affect closed-loop performance. Our method yields a controller that is robust to latent parameter uncertainty by coupling optimal control with Stein variational inference, and avoiding restrictive parametric assumptions on the uncertainty model while preserving computational parallelism. In contrast to classical DRO, which can sacrifice nominal performance through worst-case design, we find our approach achieves robustness by shaping the control law around relevant uncertainty that are most critical to the task objective. The proposed framework therefore reconciles robust control and variational inference in a single decision-theoretic formulation for broad classes of control systems with parameter uncertainty. We demonstrate our approach on representative control problems that empirically illustrate improved performance-robustness tradeoffs over nominal, ensemble, and classical distributionally robust baselines.

翻译：我们提出了一种针对具有潜在参数不确定性的非线性动力系统的斯坦因变分分布鲁棒控制器。该方法是一种替代保守最坏情况模糊集优化的方案，采用任务相关不确定性分布的确定性粒子近似，使控制器能够聚焦于对闭环性能影响最大的参数敏感性。通过将最优控制与斯坦因变分推断相结合，该方法在保持计算并行性的同时，避免了不确定性模型的参数化限制性假设，从而获得对潜在参数不确定性具有鲁棒性的控制器。与通过最坏情况设计可能牺牲标称性能的经典分布鲁棒优化方法不同，我们发现所提方法通过围绕对任务目标最关键的关联不确定性来塑造控制律，从而实现鲁棒性。因此，该框架在单一决策论公式中调和了鲁棒控制与变分推断，适用于具有参数不确定性的广泛控制系统类别。我们在代表性控制问题上展示了该方法，实验结果证实其相对于标称方法、集成方法和经典分布鲁棒基线方法，在性能-鲁棒性权衡方面取得了更优表现。