右端非光滑的时滞非线性系统的适应L_2控制

Adaptive L_2-gain Control for Systems of Time-delay Differential Equations with Nonsmooth Right-hand Sides

基于Filippov集值映射和非光滑控制理论,本文给出了右端非光滑的时滞非线性系统的适应L_2控制设计方法.通过扩展链法则到Lyapunov-Krasovkii泛函和扩展适应L_2增益和系统稳定性之间的关系到非光滑系统,适应L_2控制器的设计被引入.在Filippov解的意义下,适应L_2控制器保证非光滑闭环时滞系统扰动衰减且内稳定.

Motivated by Filippov set-valued mapping and theory of nonsmooth analysis, adaptive L2-gain controller design approach is proposed for systems of time-delay differential equations with nonsmooth right-hand sides. By chain rule for Lyapunov-Krasovkii functional and a result about the relation between L2-gain and stability, an adaptive L2-gain controller is derived. Under certain conditions, it is proven that the nonsmooth system is controllable and the control law guarantees the close-loop system disturbance attenuation with internal stability in the sense of Filippov solutions.