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.

中文翻译：

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混合系统，迭代学习控制和非最小阶段

在过去的几十年中，由于混合系统简化了对复杂的非线性系统建模的任务，因此其稳步增长。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典型示例。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组装任务以及增材制造中的材料沉积。因此，他们还将从迭代学习控制（ILC）中受益匪浅，它是一类重复系统的前馈控制器，通过从过去的过程周期的错误中学习，可以在输出参考跟踪中实现高性能。但是，文献不足以说明混合模型中的ILC合成。本文的主要目的是为确定性，离散时间混合系统（即分段定义（PWD）系统）提供一种适用于ILC的理论。总之，本文要解决的三个主要差距是：（1）现有混合建模框架与ILC综合技术之间缺乏兼容性；（2）基于牛顿法（NILC）的ILC对于不稳定逆系统的失败；以及（3）分段仿射（PWA）系统（PWD系统的子集）缺乏反演和稳定反演理论。通过（1）为PWD系统开发闭式表示形式，（2）在NILC的指导下开发新的ILC框架，并具有结合稳定模型反演技术的新功能，解决了这些问题。