论文标题
通过Hölder-Coniminule实时学习，数据驱动的离散时间控制
Data-Driven Discrete-time Control with Hölder-Continuous Real-time Learning
论文作者
论文摘要
这项工作为具有未知输入输出动力学的离散时间系统的数据驱动控制提供了一个框架，并且输出可以由输入控制。该框架会导致对系统的稳定且健壮的实时控制，从而可以跟踪可行的输出轨迹。通过使用Hölder连续学习方案对未知动力学的快速实时稳定学习，这些动态被设计为离散时间稳定的干扰观察者，这是可能的。该观察者从先前的输入输出历史记录中学习，并确保模型估计错误的有限时间稳定收敛到零向量的有限邻域，如果已知系统相对于输出，输入，内部参数和状态以及时间是Lipschitz-contimunule。结合非线性稳定的控制器设计，这使得提出的框架非线性稳定且可靠，对干扰，模型不确定性和未知测量噪声。观察者和控制器设计的非线性稳定性和鲁棒性分析是使用离散的Lyapunov分析进行的。在此框架中，Hölder-连续的有限时间稳定观察者和控制器设计有助于证明这些方案的稳健性，并确保输出将输出收敛到所需的输出轨迹的界面。非线性二阶系统上的数值实验证明了该离散非线性模型控制框架的性能。
This work provides a framework for data-driven control of discrete time systems with unknown input-output dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control of the system such that a feasible output trajectory can be tracked. This is made possible by rapid real-time stable learning of the unknown dynamics using Hölder-continuous learning schemes that are designed as discrete-time stable disturbance observers. This observer learns from prior input-output history and it ensures finite-time stable convergence of model estimation errors to a bounded neighborhood of the zero vector if the system is known to be Lipschitz-continuous with respect to outputs, inputs, internal parameters and states, and time. In combination with nonlinearly stable controller designs, this makes the proposed framework nonlinearly stable and robust to disturbances, model uncertainties, and unknown measurement noise. Nonlinear stability and robustness analyses of the observer and controller designs are carried out using discrete Lyapunov analysis. Hölder-continuous Finite-time stable observer and controller designs in this framework help to prove robustness of these schemes and guaranteed convergence of outputs to a bounded neighborhood of the desired output trajectory. A numerical experiment on a nonlinear second-order system demonstrates the performance of this discrete nonlinear model-free control framework.
