This paper presents an approach for trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach allows for the use of a broad class of model learning tools including deep neural networks to learn uncertain dynamics while still providing guarantees of transient tracking performance throughout the learning phase, including the special case of no learning. Within the proposed approach, a disturbance estimation law is proposed 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 in 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计量法和受不确定性匹配的非线性系统扰动估计的以轨迹为中心的学习控制方法,该方法允许使用一系列广泛的示范学习工具,包括深神经网络,以学习不确定的动态,同时仍然提供在整个学习阶段跟踪性能的保证,包括不学习的特殊情况。在拟议方法中,提出了扰动估计法,以估计不确定性的点值,并附有可计算前估计误差的界限(EEEBs)。随后,将所学动态、估计的扰动和EEEBs纳入一个强大的里曼能源条件,以计算控制法,保证在整个学习阶段,即使在学习模式不完善的情况下,实际轨迹与所期望的轨迹成指数一致。另一方面,随着准确性提高,可将所学模型纳入高级规划者,以规划更好的轨迹,例如,降低能源消耗和缩短旅行时间。拟议的框架在规划的二次轨道导航中得到了验证。