关于统一非对称障碍李雅普诺夫函数
On unified asymmetric barrier Lyapunov functions
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中文总结 AI 辅助
本文提出一种统一非对称障碍李雅普诺夫函数，无需不连续切换函数，为输出约束非线性系统设计指数跟踪控制律，并统一对称与非对称约束的控制设计，数值实验验证其性能优于现有对数BLFs。
中文摘要 AI 辅助
障碍李雅普诺夫函数（BLFs）在处理约束控制问题时一直是一种流行的选择。在本文中，我们提出了一种统一的非对称障碍李雅普诺夫函数，它推广了现有的对数对称李雅普诺夫函数。我们证明了所提出的函数是光滑的，并且不需要文献中现有的非对称障碍李雅普诺夫函数中普遍存在的不连续切换函数。基于所提出的障碍李雅普诺夫函数，针对一类具有输出约束的单输入单输出非线性系统，设计了一种保证指数快速输出跟踪的控制律。我们证明了所提出的控制律统一了具有对称或非对称输出约束的系统的控制设计和结构。此外，我们构造性地证明了所提出的函数可以被对称类$\mathcal{K}$函数从上方和下方界定，这有助于连同所提出的控制律一起建立局部指数收敛性。最后，我们提供了数值示例来说明所提出控制的性能，并将结果与现有的对数BLFs进行比较。
英文摘要
Barrier Lyapunov functions (BLFs) have been a popular choice when dealing with constrained control problems. In the current article, we present a unified asymmetric barrier Lyapunov function that generalizes the existing logarithmic symmetric Lyapunov function. We show that the proposed function is smooth and does not require the discontinuous switching function that is ubiquitous in the asymmetric barrier Lyapunov functions existing in the literature. Based on the proposed barrier Lyapunov function, a control law, guaranteeing exponentially fast output tracking, is designed for a class of single-input single-output nonlinear systems with output constraints. We show that the proposed control law unifies the control design and structure for a system with either symmetric or asymmetric output constraints. Furthermore, we constructively show that the proposed function can be bounded from above and below by symmetric class $\mathcal{K}$ functions which help in establishing local exponential convergence together with the proposed control law. Lastly, we provide numerical examples to illustrate the performance of the proposed control and compare the results with the existing logarithmic BLFs.
发表机构
- Indian Institute of Technology Bombay（印度孟买理工学院）
机构由 AI 辅助整理，请以论文原文为准。
