广义状态表示下最小欠驱动构型平坦拉格朗日系统的精确线性化研究
On the Exact Linearization of Minimally Underactuated Configuration Flat Lagrangian Systems in Generalized State Representation
AI总结：
本文针对最小欠驱动构型平坦拉格朗日控制系统，研究广义状态准静态反馈下的精确线性化问题，引入广义拉格朗日控制系统，给出可实现静-静过渡的积分器链所有可能长度，并证明无需Brnovský状态即可系统推导对应反馈律。
摘要：
本文研究具有p个自由度、p-1个控制输入的构型平坦拉格朗日控制系统，在广义状态表示下通过其广义状态的准静态反馈实现精确线性化的问题。我们正式引入广义拉格朗日控制系统，这类系统是将构型变量而非力视为输入时得到的。本工作给出了通过可实现静-静过渡的广义状态准静态反馈律进行精确线性化时，所能得到的积分器链的所有可能长度。我们证明这类反馈律无需使用Brnovský状态即可系统推导得到。
英文摘要：
In this paper, we examine the exact linearization of configuration flat Lagrangian control systems in generalized state representation with p degrees of freedom and p-1 control inputs by quasi-static feedback of its generalized state. We formally introduce generalized Lagrangian control systems, which are obtained when configuration variables are considered as inputs instead of forces. This work presents all possible lengths of integrator chains achieved by an exact linearization with a quasi-static feedback law of the generalized state that allows for rest-to-rest transitions. We show that such feedback laws can be systematically derived without using Brunovský states.
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