多Euler-Lagrange系统抑制抖振分布式有限时间包含控制

Distributed chattering reduction finite-time containment control for multiple Euler-Lagrange systems

为了抑制多Euler-Lagrange系统分布式包含控制时控制输出的抖振现象,且实现系统的有限时间收敛,对多EulerLagrange系统的抑制抖振分布式有限时间包含控制方法进行了研究.在系统存在模型不确定性与外界干扰的情形下,采用有限时间滑模控制方法,结合系统的模型特点,提出了分布式有限时间包含控制算法.首先,通过定义包含控制误差变量和选取合适的高阶有限时间滑模变量,设计了一种分布式有限时间包含控制律.为了实现控制器输出的抑制抖振特性,将符号函数项包含在控制律的导数中,经过积分后,可以得到连续的控制输出.针对系统存在的模型不确定性和外界干扰,设计了自适应估计律对其上界进行估计和补偿.基于图论和矩阵理论,利用Lyapunov方法证明了系统能够在有限时间内稳定,且模型不确定性和外界干扰的估计是有效的.最后,选取多机械臂系统作为模型进行了仿真验证.结果表明,所提控制算法对滑模控制中因不连续的切换项产生的抖振现象有很好的抑制作用,且系统可以在有限时间内实现收敛.

This study is carried out to investigate the distributed chattering reduction finite-time containment control for multiple Euler-Lagrange systems with systems model uncertainties and external disturbances.Firstly,by defining containment control error variables and choosing an appropriate high-order finite-time sliding variable,a distributed finite-time containment control algorithm was designed.To reduce chattering,the sign function term was included in the derivative of the control law and the continuous control output was obtained by definite integral.Besides,adaptive estimation laws were proposed to approximate the upper bound of the model uncertainties and external disturbances.Based on the graph theory and matrix theory,it is demonstrated that the systems are stable in finite time and the estimation to model uncertainties and external disturbances is effective by Lyapunov method.Finally,simulation results show the effectiveness of the control law.