非匹配条件下非线性系统的指定时间二阶滑模控制

Prescribed-time SOSM control of nonlinear systems subject to mismatched terms

针对不确定非线性系统设计一种新型指定时间二阶滑模(SOSM)控制器.首先,通过选取新的滑模变量,将标准的二阶滑模积分链系统推广至带有非匹配项的新二阶滑模动态系统,新滑模动态系统的使用可以有效减少传统滑模系统控制通道中的不确定性;其次,通过使用时变放缩函数的概念,在非匹配项的增益函数上界未知的情况下,针对新的滑模动态系统提出一种基于切换策略的指定时间SOSM控制算法.所提出的控制器从一个有限时间域的SOSM控制器切换到传统的有限时间SOSM控制器,前者可以保证滑模变量在有限时间域内实现指定时间收敛到零,且收敛时间不依赖于系统的初始条件;后者可以保证滑模变量此后始终保持在零.最后,对闭环系统的指定时间稳定性进行了分析,通过仿真对比验证了理论结果的有效性.

A novel prescribed-time second-order sliding mode(SOSM)controller is proposed for uncertain nonlinear systems.Firstly,by selecting the new sliding mode variable,the standard SOSM integral chain system is extended to a new SOSM dynamic system with mismatched terms,and the use of the new sliding mode system can effectively reduce the uncertainties in input channel.Secondly,by using the concept of time-varying scaling function,a prescribed-time SOSM control algorithm based on switching strategy is proposed for the new sliding mode system when the upper limit of the gain function of the mismatched item is unknown.The proposed controller switches from a finite time domain SOSM controller to the traditional finite time SOSM controller,the former can ensure that the sliding mode variable converges to zero at a prescribed time in the finite time domain,and the convergence time does not depend on the initial conditions of the system,and the latter can ensure that the sliding mode variable remains at zero thereafter.Finally,the prescribed time stability of the closed-loop system is analyzed.The theoretical results are verified by simulation comparison.