We provide an algorithm for the simultaneous system identification and model predictive control of nonlinear systems. The algorithm has finite-time near-optimality guarantees and asymptotically converges to the optimal (non-causal) controller. Particularly, the algorithm enjoys sublinear dynamic regret, defined herein as the suboptimality against an optimal clairvoyant controller that knows how the unknown disturbances and system dynamics will adapt to its actions. The algorithm is self-supervised and applies to control-affine systems with unknown dynamics and disturbances that can be expressed in reproducing kernel Hilbert spaces. Such spaces can model external disturbances and modeling errors that can even be adaptive to the system's state and control input. For example, they can model wind and wave disturbances to aerial and marine vehicles, or inaccurate model parameters such as inertia of mechanical systems. The algorithm first generates random Fourier features that are used to approximate the unknown dynamics or disturbances. Then, it employs model predictive control based on the current learned model of the unknown dynamics (or disturbances). The model of the unknown dynamics is updated online using least squares based on the data collected while controlling the system. We validate our algorithm in both hardware experiments and physics-based simulations. The simulations include (i) a cart-pole aiming to maintain the pole upright despite inaccurate model parameters, and (ii) a quadrotor aiming to track reference trajectories despite unmodeled aerodynamic drag effects. The hardware experiments include a quadrotor aiming to track a circular trajectory despite unmodeled aerodynamic drag effects, ground effects, and wind disturbances.

翻译：本文提出一种用于非线性系统同步系统辨识与模型预测控制的算法。该算法具备有限时间近最优性保证，并能渐近收敛至最优（非因果）控制器。特别地，该算法具有次线性动态遗憾特性，此处定义为相对于知晓未知扰动及系统动力学如何响应其动作的最优预见控制器的次优程度。该算法采用自监督机制，适用于具有未知动力学特性且扰动可在再生核希尔伯特空间中表达的控制仿射系统。此类空间可建模外部扰动及建模误差，甚至能表征其对系统状态与控制输入的自适应特性。例如，可建模航空器与船舶所受的风浪扰动，或机械系统惯性等不精确模型参数。算法首先生成随机傅里叶特征以逼近未知动力学或扰动，随后基于当前学习的未知动力学（或扰动）模型实施模型预测控制。未知动力学模型通过最小二乘法在线更新，数据来源于系统控制过程中采集的实时信息。我们在硬件实验与基于物理的仿真中验证了该算法。仿真实验包括：（i）在模型参数不精确条件下保持倒立摆直立的车杆系统；（ii）在未建模空气阻力效应条件下实现轨迹跟踪的四旋翼飞行器。硬件实验涉及在存在未建模空气阻力效应、地面效应及风扰条件下实现圆形轨迹跟踪的四旋翼飞行器。