Title: Adaptive Robust Model Predictive Control via Uncertainty Cancellation Show Chinese title

Title: 基于不确定性消除的自适应鲁棒模型预测控制

Abstract: We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. We apply contemporary statistical estimation techniques to certify the system's safety through persistent constraint satisfaction with high probability. Moreover, we propose using Bayesian meta-learning algorithms that learn calibrated model priors to help satisfy the assumptions of the control design in challenging settings. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods and that the use of Bayesian meta-learning allows us to adapt to the test environments more rapidly. Show Chinese abstract

Abstract: 我们提出了一种基于学习的鲁棒预测控制算法，该算法能够补偿一类离散时间系统中动力学的显著不确定性，这些系统本质上是线性的，并具有一个加性非线性分量。 这类系统通常用于建模未知环境对名义系统产生的非线性效应。 我们优化了一类由确定性等价“估计并消除”控制律启发的非线性反馈策略，以在存在大范围不确定性的情况下实现显著的性能提升，在这种情况下，现有的基于学习的预测控制算法往往难以保证安全性。 与鲁棒自适应MPC之前的研究所不同，我们的方法使我们能够利用通过在线函数逼近学习到的先验未知动力学中的结构（即数值预测）。 我们的方法还将典型的非线性自适应控制方法扩展到具有状态和输入约束的系统，即使我们不能直接从动力学中消除加性不确定函数。 我们应用当代统计估计技术，通过高概率下的持续约束满足来认证系统的安全性。 此外，我们提出了使用贝叶斯元学习算法来学习校准的模型先验，以帮助在具有挑战性的设置中满足控制设计的假设。 最后，我们在仿真中展示了我们的方法可以容纳比现有方法更显著的未知动力学项，并且使用贝叶斯元学习可以使我们更快地适应测试环境。