Stein Variational Uncertainty-Adaptive Model Predictive Control

2026-04-01

AI Summary

This work addresses the challenge of robust control in nonlinear dynamical systems subject to implicit parametric uncertainty by proposing a novel integration of optimal control and Stein variational inference. Leveraging a task-oriented, particle-based nonparametric approximation of uncertainty distributions, the method adaptively concentrates computational effort on parameter regions most influential to closed-loop performance, without requiring strong prior assumptions. It uniquely embeds Stein variational gradient descent within a model predictive control framework, thereby achieving both computational parallelism and task-relevant robustness while bridging the theoretical gap between distributionally robust optimization and variational inference. Experimental results demonstrate that the approach significantly outperforms nominal control, ensemble-based methods, and classical distributionally robust baselines across representative control tasks, yielding a superior trade-off between performance and robustness.

Abstract

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.

Problem

• latent parametric uncertainty
• robust control
• model predictive control
• distributionally robust optimization
• nonlinear dynamical systems

Innovation

• Stein variational inference
• distributionally robust control
• uncertainty-adaptive MPC
• nonparametric uncertainty modeling
• performance-robustness tradeoff