一类输入受限非线性系统的有限时间控制

Finite-time Control for a Class of Nonlinear Systems with Input Constraints

针对一类高阶非匹配不确定非线性系统,结合有限时间Lyapunov稳定性理论,提出了系统在输入受限情况下的一种有限时间稳定控制方案。首先利用加幂积分法,设计镇定系统的有限时间稳定控制器;然后当该控制器的输出超过给定的有界上限输出时,运用Backstepping回馈思路去证明系统在控制器达到饱和后也是有限时间稳定的,从而实现了输入受限问题的分段处理。数学上严格证明了在所提方案的作用下,闭环系统是有限时间稳定的,保证了基于加幂积分法设计的控制器的输出量始终在给定的允许饱和限度内,同时被控系统是有限时间稳定的。仿真结果验证了该方法的有效性。

A finite-time control scheme under input constraints is proposed for a class of nonlinear systems with high-order mismatched uncertainties, based on finite-time Lyapunov stability theory. First of all, a finite- time controller is designed by utilizing the technique of adding a power integrator. Then, when the output of the controller exceeds the bounded upper output, the Backstepping feedback idea is used to verify that the system is stable in finite time after the controller reaches saturation, thus to realize the segmentation of the input constrained problem. It is proved mathematically that with the proposed scheme, the closed loop system is stable in finite time, which ensures that the output of the controller designed with the proposed method is always within the given allowable saturation limit, and the controlled system is stabilized in finite time. Simulation results have proved the effectiveness of the proposed method.