输入受限约束下的无抖振有限时间稳定趋近律设计

Finite time stable chattering-free reaching law design with bounded input

首先,证明最新的fal函数趋近律第2项慢于普通幂次项,整体性能弱于普通幂次趋近律,而多幂次项趋近律存在抖振,且在输入受限约束下,不论如何选择初始状态和参数,趋近速度总是慢于单幂次项趋近律;然后,提出输入受限约束下的变指数幂次趋近律,满足无抖振、有限时间趋近到滑模面、提高收敛速度3项指标要求;最后,推导其收敛时间的上界解析式,证明其收敛速度快于现有5种趋近律,并给出参数选择所需的充分条件.仿真结果表明了改进方案的优越性.

Some drawbacks of the latest reaching laws are proposed as follows： the second term of the fal function reaching law is slower and unnecessary compared with the first term; the multi-power terms reaching law is chattering and slower than the sole power term reaching law under bounded input restriction, no matter how parameters are selected, nor how the initial conditions are given. Then, a variable power reaching law is proposed aiming at three goals： chattering free, reaching at sliding mode in finite time, and speeding up convergence. The analytical expression of convergence time and its upper bound are derived, and the sufficient conditions are given. Simulation results show the superiority of the proposed reaching law.