输入时延下约束不确定系统的有限时间控制

Finite Time Control of Constrained Uncertain Systems with Input Delay

针对一类具有非对称时变输出约束和输入时延的不确定非线性系统,提出有限时间反步控制策略.首先,设计新型非线性变换函数将约束系统转化为无约束系统,解决非对称时变输出约束问题;其次,为了处理反步控制的“计算爆炸”问题,构造新型的有限时间滤波器,且通过误差补偿机制消除滤波误差,采用Pade近似法和中间变量补偿输入时延对控制系统的影响;再次,根据Lyapunov理论证明闭环系统的实际有限时间稳定性,且输出不会违反约束;最后,通过滤波器的对比仿真和机械臂系统的仿真验证新型滤波器和有限时间控制策略的有效性.

A finite time backstepping control strategy is proposed for a class of uncertain nonlinear systems with asymmetric time-varying output constraints and input delay.Firstly,a new nonlinear transformation function that transforms the constrained system into an unconstrained system is proposed to solve the asymmetric time-varying output constraint.Secondly,To deal with the “explosion of complexity” problem of backstepping control,a new finitetime filter is constructed,where the filter error is eliminated by an error compensation mechanism.Then the Pade approximation method and intermediate variable are applied to compensate for the influence of input delay on the control system.According to the Lyapunov theory,the finite-time stability of the closed-loop system is proved,and the output does not violate the constraint.Finally,the effectiveness of the new filter and finite-time control strategy is verified by the comparative simulation of the filter and the simulation of a manipulator system.