混杂系统、迭代学习控制和非最小相位
Hybrid Systems, Iterative Learning Control, and Non-minimum Phase
摘要：
混杂系统在过去的几十年中已经稳步增长的普及，因为他们简化了建模复杂的非线性系统的任务。腿部运动、机器人操纵和增材制造是受益于混合建模的系统的代表性示例。它们也是重复过程的主要例子;步行中的步态周期，机器人操作中的产品装配任务，以及增材制造中的材料沉积。因此，他们也将大大受益于迭代学习控制（ILC），一类前馈控制器的重复系统，实现高性能的输出参考跟踪从过去的过程周期的错误学习。然而，文献是缺乏ILC合成的混合模型。本论文的主要目的是为确定性离散混杂系统，即分段定义（PWD）系统，提供一种广泛适用的迭代学习控制理论。总之，本论文解决的三个主要差距是：（1）现有的混合建模框架和迭代学习控制合成技术之间缺乏兼容性，（2）基于牛顿法的迭代学习控制（NILC）在具有不稳定逆的系统中失败，以及（3）缺乏分段仿射（PWA）系统（PWD系统的子集）的逆和稳定逆理论。这些问题的解决（1）开发一个封闭形式的PWD系统的表示，（2）开发一个新的ILC框架通知NILC，但新的能力，将稳定模型反演技术，和（3）推导出传统的和稳定的模型反演理论PWA系统。
英文摘要：
Hybrid systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. Legged locomotion, robotic manipulation, and additive manufacturing are representative examples of systems benefiting from hybrid modeling. They are also prime examples of repetitive processes; gait cycles in walking, product assembly tasks in robotic manipulation, and material deposition in additive manufacturing. Thus, they would also benefit substantially from Iterative Learning Control (ILC), a class of feedforward controllers for repetitive systems that achieve high performance in output reference tracking by learning from the errors of past process cycles. However, the literature is bereft of ILC syntheses from hybrid models. The main thrust of this dissertation is to provide a boradly applicable theory of ILC for deterministic, discrete-time hybrid systems, i.e. piecewise defined (PWD) systems. In summary, the three main gaps addressed by this dissertation are (1) the lack of compatibility between existing hybrid modeling frameworks and ILC synthesis techniques, (2) the failure of ILC based on Newton's method (NILC) for systems with unstable inverses, and (3) the lack of inversion and stable inversion theory for piecewise affine (PWA) systems (a subset of PWD systems). These issues are addressed by (1) developing a closed-form representation for PWD systems, (2) developing a new ILC framework informed by NILC but with the new ability to incorporate stabilizing model inversion techniques, and (3) deriving conventional and stable model inversion theories for PWA systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
