控制输入受限的准全控制利用率有限时间稳定控制

Quasi-complete control utilization finite time stable control with input constraint

针对控制输入受限的非线性系统,分6种情况证明有限时间稳定控制器(finite time stable controller,FTSC)作用下的系统状态收敛速度在论域空间中每一点必快于非有限时间稳定控制器(non-FTSC,NFTSC)作用下的系统状态收敛速度,并给出每一类情况下设计参数应满足的充分性约束条件,同时证明这些条件的存在性.在此基础上,提出全控制利用率控制器(CCUC)的定义,证明CCUC必然引起抖振,进而提出准全控制利用率控制器(QCCUC)设计的思想,并证明控制输入受限条件下,FTSC的控制利用率必优于任意快速FTSC(FFTSC),即具有更优的控制性能,从而得到一系列关于参数优化的结论.理论证明的结论通过图表、数例和仿真得到了验证.所得结论对终端滑模控制、加幂积分控制、有限时间稳定backstepping控制等多种FTSC均广泛适用.

For nonlinear systems with input constraint,it is proved that the convergence speed of state under the action of a finite time stable controller(FTSC)is faster than that under the action of a non-FTSC at any point in state space.Sufficient conditions in six cases are summarized to guarantee the conclusion and it is proved that these conditions are attainable with appropriate parameter selection.Then,the definition of a complete control utilization controller(CCUC)is proposed,and it is proved that the convergence speed under the action of the FTSC is faster than that under the action of fast FTSC with input constraint.A series of conclusions concerning the parameter optimization are proposed to improve the control performance.Numerical examples,simulations,figures and tables are used to illustrate the proposed theory and make the conclusions more understandable.The proposed conclusions are fit for the improvement of nearly all kinds of FTSC methods,such as terminal sliding mode control,adding one power integrator control and finite time stable backstepping control.