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：我们针对具有潜在参数不确定性的非线性动态系统，提出了一种斯坦变分分布鲁棒控制器。该方法作为保守最坏情形模糊集优化的替代方案，采用基于任务相关不确定性分布确定性子粒子近似，使控制器能够聚焦于对闭环性能影响最显著的参数敏感度。通过将最优控制与斯坦变分推理相结合，本方法在保持计算并行性的同时，既实现了对潜在参数不确定性的鲁棒性，又避免了对不确定性模型的参数化约束假设。与可能因最坏情形设计牺牲标称性能的经典分布鲁棒优化不同，我们发现本方法通过围绕任务目标最关键的关联不确定性塑造控制律来实现鲁棒性。因此，所提出的框架将鲁棒控制与变分推理统一于单一决策理论框架中，适用于具有参数不确定性的广泛控制系统。我们在代表性控制问题上验证了该方法，实验表明其在性能-鲁棒性权衡方面优于标称、集成及经典分布鲁棒基线方法。