Adaptive control via embedding in reproducing kernel Hilbert spaces
Adaptive control via embedding in reproducing kernel Hilbert spaces
复制标题
通过嵌入再生内核希尔伯特空间的自适应控制
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Yun
中科院分区：
文献类型：
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作者：
A. Kurdila;Yun
本文通过将原L1自适应控制问题嵌入再生核Hilbert空间（RKHS）中，导出了具有不确定非线性动态系统的自适应跟踪控制问题的一种形式。本文证明了RKHS中闭环演化律的适定性，并给出了稳定性和跟踪收敛的充分条件。当动态中的不确定性表示在RKHS，满足一定的基本平滑性能，自适应控制器产生一个闭环系统，其稳定性和收敛性类似于传统的模型参考和L1控制系统的常微分方程。
This paper derives a formulation of an adaptive tracking control problem for systems having uncertain nonlinear dynamics by embedding an original L1 adaptive control problem in a reproducing kernel Hilbert space (RKHS). This paper proves the well-posedness of the closed loop evolution laws in the RKHS and derives sufficient conditions for stability and tracking convergence. When the uncertainty in the dynamics is represented in a RKHS that satisfies certain fundamental smoothness properties, the adaptive controller yields a closed loop system whose stability and convergence properties are analogous to that obtained for conventional model reference and L1 control for systems of ordinary differential equations.