发表机构
Institute for Advanced Study, Shenzhen University（深圳大学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对可逆非线性MIMO系统，证明在全局正则修正逆条件下，固定齐次线性输出分配产生满射输出导数映射，并据此构造光滑动态控制器，实现任意初始状态下的精确跟踪。
AI 中文摘要
非线性多变量系统的全局逆问题提出了一个疑问：所选输出导数的每个目标值是否都能由系统状态实现。我们证明，在具有固定行选择和有限终止于满输入秩的全局正则修正逆条件下，每个固定的齐次线性输出分配都会产生一个具有光滑全局截面的满射输出导数映射。该结果要求每个有限区间上的状态界以初始状态和有限个输出导数来表示，且对输入一致成立。这个条件严格弱于弱一致零状态可检测性，使得在全局逆方法中用于稳定的独立满射性要求成为在所陈述的逆假设下可检测性的一个推论。该截面为每个导数目标光滑地选择一个实现状态，包括在存在内部动力学的情况下，并通过完全提升兼容的光滑参考来构造。对于已知系统，相同的提升方法利用全状态反馈和当前参考导数产生一个光滑的动态控制器，并以系统状态进行初始化。从任何初始状态出发，它都能在任意给定的正时间后精确跟踪任何光滑期望输出。
英文摘要
Global inversion of nonlinear multivariable systems raises the question of whether every target value of the selected output derivatives can be realized by a plant state. We prove that, under globally regular modified inversion with fixed row selection and finite termination at full input rank, every fixed homogeneous linear output assignment yields a surjective output-derivative map with a smooth global section. The result requires a state bound on each finite interval in terms of the initial state and finitely many output derivatives, uniformly over inputs. This condition is strictly weaker than weak uniform zero-state detectability, making the separate surjectivity requirement in a global inversion approach to stabilization a consequence of detectability under the stated inversion hypotheses. The section selects a realizing state smoothly for every derivative target, including in the presence of internal dynamics, and is constructed through complete lifting of compatible smooth references. For known plants, the same lifting method yields a smooth dynamic controller using full state feedback and current reference derivatives, with initialization from the plant state. From any initial state, it achieves exact tracking of any smooth desired output after any prescribed positive time.
Comments15 pages
