关于最大能量可塑性的IDA-PBC
On IDA-PBC with Maximum Energy Shapeability
AI总结：
本文提出最大能量可塑性概念，通过转换匹配方程简化IDA-PBC设计，以磁悬浮系统为例展示了其应用。
摘要：
互连与阻尼分配被动控制（IDA-PBC）是用于仿射非线性系统的一种已确立的稳定化技术。然而，其应用通常受到求解一组偏微分方程（PDEs）的限制，即所谓的匹配方程。本文引入了“最大能量可塑性”的概念，描述了匹配方程的齐次部分允许m个独立解，其中m是控制输入的维度。我们证明，最大能量可塑性通过将匹配方程转换为更容易求解的PDE集，使IDA-PBC设计能够系统化。还提供了最大能量可塑性的充分条件。证明了一些现有的构造性IDA-PBC设计实际上隐式地利用了最大能量可塑性。所提出的IDA-PBC设计程序通过磁悬浮系统进行了说明。
英文摘要：
Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a well-established stabilization technique for affine nonlinear systems. However, its application is generally hindered by the requirement of solving a set of partial differential equations (PDEs), i.e., the so-called matching equation. This paper explores the notion of maximum energy shapeability which describes the scenario that the homogeneous part of the matching equation admits $m$ independent solutions with $m$ the dimension of the control input. We show that the maximum energy shapeability enables a systematic procedure for the IDA-PBC design by transforming the matching equation into a set of new PDEs. Specifically, the transformed matching equation admits an explicit solution in the single input case. Sufficient conditions for maximum energy shapeability are also provided. It is shown that some existing constructive IDA-PBC designs actually implicitly exploit the maximum energy shapeability. The proposed procedure for the IDA-PBC design is demonstrated with two practical examples.
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