This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The proposed approach allows for the use of deep neural networks to learn uncertain dynamics while still providing guarantees of transient tracking performance throughout the learning phase. Within the proposed approach, a disturbance estimation law is adopted to estimate the pointwise value of the uncertainty, with pre-computable estimation error bounds (EEBs). The learned dynamics, the estimated disturbances, and the EEBs are then incorporated in a robust Riemannian energy condition to compute the control law that guarantees exponential convergence of actual trajectories to desired ones throughout the learning phase, even when the learned model is poor. On the other hand, with improved accuracy, the learned model can be incorporated into a high-level planner to plan better trajectories with improved performance, e.g., lower energy consumption and shorter travel time. The proposed framework is validated on a planar quadrotor navigation example.

翻译：本文介绍了一种基于收缩指标的以轨迹为中心的学习控制办法和对受不确定性匹配的非线性系统进行扰动估计的办法; 提议的办法允许利用深神经网络学习不确定的动态,同时仍然为整个学习阶段的瞬时跟踪提供保证; 在拟议的办法中,采用扰动估计法来估计不确定性的点值,加上可计算前的估计误差界限(EEEBs); 然后,将所学的动态、估计的扰动和EEEB纳入一个强大的里伊曼尼能源条件,以计算出控制法,保证在整个学习阶段,即使在所学的模型贫乏时,实际轨迹与所希望的轨迹成指数趋同。 另一方面,随着准确性提高,可将所学的模型纳入一个高级规划者之中,以更好的性能规划,例如,降低能源消耗和缩短旅行时间。提议的框架将在一个平面二次轨导航中验证。