On (the existence of) Control Lyapunov Barrier Functions
On (the existence of) Control Lyapunov Barrier Functions
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关于控制李亚普诺夫势垒函数（的存在）
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Christopher M. Kellett
中科院分区：
文献类型：
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作者：
P. Braun;Christopher M. Kellett
最近，文献[17]提出了用于状态约束非线性动力系统镇定的控制Lyapunov障碍函数(CLBF)。在光滑CLBF存在的假设下，利用Sontag的普适公式定义了保证约束满足的连续反馈。然而，正如我们在本文中所证明的那样，上述方法忽略了在状态约束的情况下不连续控制器的必要性。此外，我们还证明了光滑CLBF的假设将状态约束限制在由无界集合定义的约束。因此，我们引入了非光滑完全控制Lyapunov函数(CCLF)的概念，并指出了在存在状态约束的情况下如何将其用于镇定。
Recently, [17] proposed control Lyapunov barrier functions (CLBFs) for the stabilization of nonlinear dynamical systems with state constraints. Under the assumption of the existence of a smooth CLBF, Sontag’s universal formula was used to define a continuous feedback ensuring that the constraints are satisfied. However, as we demonstrate in this paper, the above approach neglects the necessity of discontinuous controllers in the case of state constraints. Additionally, we show that the assumption of a smooth CLBF limits the state constraints to those defined by unbounded sets. Consequently, we introduce the notion of nonsmooth complete control Lyapunov functions (CCLFs) and indicate how they may be used for stabilization in the presence of state constraints.