关于Sontag-Type控制的注记

基于控制李雅普诺夫函数的Sontag-Type控制是仿射系统鲁棒镇定中的重要控制律.首先揭示该控制律本质上是一种变结构控制且闭环的切换面总可达,受此启发并为了相对容易地构造控制李雅普诺夫函数,运用零状态可检测概念定义弱控制李雅普诺夫函数,并证明了基于弱控制李雅普诺夫函数的Sontag-Type控制的优化镇定性.文中还证明,在温和条件下,基于弱控制李雅普诺夫函数的Sontag＿Type控制为仿射系统的输入到状态镇定控制.

Notes on Sontag-Type control

The Sontag-Type control based on the control Lyapunov function (CLF) is an important control law in robust stabilization of affine systems. Firstly, the authors pointed out that this control law is essentially a kind of variable structure control and that the switch surfaces of the resulted closed-loop are always reachable. Motivated by this and in order to comparatively easily construct CLFs, the authors defined the weak control Lyapunov function (WCLF) by using the concept of zero-state-detectability and then proved the optimal stabilization property of the Sontag-Type control based on the WCLF. Finally, the authors proved that the Sontag-Type control based on the the WCLF is an input-to-state stabilizer of the affine system under a mild condition.