被动非线性系统实际稳定的最近邻控制
Nearest Neighbor Control For Practical Stabilization of Passive Nonlinear Systems
AI总结：
本文研究连续时间被动非线性系统在离散控制动作下的静态输出反馈实际稳定化，提出基于最近邻的反馈映射，证明仅需 $m+1$ 个离散输入点即可实现稳定，并给出构造性设计算法。
摘要：
本文研究连续时间（增量）被动非线性系统的静态输出反馈稳定化，其中控制动作只能从离散（且可能有限）的点集中选择。为此，我们在系统满足大时间范数可观测，且可实现控制动作的凸包在其内部包含目标常值输入（对应于平衡点）的假设下进行研究。我们提出了一种基于最近邻的静态反馈映射，从输出空间映射到有限控制动作集，能够实际稳定闭环系统。因此，我们证明对于这类具有 $m$ 维输入空间的系统，只需 $m+1$ 个离散输入点（对于一般被动系统除零外，或对于增量被动系统除目标常值输入外）即可满足要求。此外，我们提出了一种构造性算法，利用所提最近邻控制设计满足实际稳定条件的 $m+1$ 个非零输入点。
英文摘要：
This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with $m$-dimensional input space, it is sufficient to have $m+1$ discrete input points (other than zero for general passive systems or the target constant input for incrementally passive systems). Furthermore, we present a constructive algorithm to design such $m+1$ nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control.
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。
