一类受限系统非光滑反馈控制

Nonsmooth Feedback Control of a Class of Limited Systems

为解决一类状态受限三阶动态系统控制问题,本文基于二阶输入受限系统,采用Lyapunov函数法研究了线性反馈作用下系统的稳定性,并以二阶输入受限系统线性反馈为基础,给出了三阶状态受限系统非光滑反馈控制律设计方法,讨论了系统终值与初始条件的关系,并通过数值仿真进行验证,仿真结果表明,在已知状态初始条件的基础上给出非光滑反馈控制率,并保证闭环系统状态稳定,该设计方法是有效的。

In order to solve the control design problem for a class of third-order limited systems, the linear feedback design is first shown by Lyapunov stability theory to control the second-order system with constraint input. Based on the linear feedback design, the nonsmooth feedback design method is proposed for a class of the third-order limited systems. Moreover, the relation between the final value of the closed-loop system and the initial condition is presented. Finally, the nonsmooth feedback controllers are designed with known initial conditions of the systems in numerical simulations in order to verify the proposed nonsmooth feedback design method. The simulation results show that the closed-loop systems are stable and the proposed design method is correct.