论文标题
在有限的干扰下对分段仿射系统的层次控制的强大近似模拟
Robust Approximate Simulation for Hierarchical Control of Piecewise Affine Systems under Bounded Disturbances
论文作者
论文摘要
分段仿射（PWA）系统在许多实际情况下广泛应用，例如对非线性系统和混合动力学的控制。但是，大多数现有的PWA控制方法相对于模式和系统尺寸的数量具有较差的可伸缩性，并且对性能的干扰可能不强。在本文中，我们提出了一种强大的基于近似模拟的控制方法，用于在有限的外部干扰下针对PWA系统。首先，设计较低维线性系统（抽象）和相关的接口旨在启用PWA系统（混凝土系统）的输出以跟踪抽象的输出。然后，设计了类似Lyapunov的仿真函数，以显示两个系统之间输出误差的界限。此外，线性抽象获得的结果扩展到更简单的PWA系统是抽象的情况。为了说明所提出方法的有效性，为两个设计示例提供了仿真结果。
Piecewise affine (PWA) systems are widely applied in many practical cases such as the control of nonlinear systems and hybrid dynamics. However, most of the existing PWA control methods have poor scalability with respect to the number of modes and system dimensions and may not be robust to the disturbances in performance. In this paper, we present a robust approximate simulation based control method for PWA systems under bounded external disturbances. First, a lower-dimensional linear system (abstraction) and an associated interface are designed to enable the output of the PWA system (concrete system) to track the output of the abstraction. Then, a Lyapunov-like simulation function is designed to show the boundedness of the output errors between the two systems. Furthermore, the results obtained for linear abstraction are extended to the case that a simpler PWA system is the abstraction. To illustrate the effectiveness of the proposed approach, simulation results are provided for two design examples.
