输入受限不确定线性系统混合镇定

Mixed Stabilization of Uncertain Linear Systems with Input Constrains

针对输入受限不确定线性系统,同时考虑其暂态性能和稳态性能,提出了混合稳定的概念和控制策略.使得闭环系统在满足给定的输入约束条件下,在给定的时间区间内有限时间稳定,在无穷时间区间上渐近稳定.分别将有限时间控制问题和无穷时间控制问题转化为线性矩阵不等式(LMI)约束的可行解问题.本质上混合稳定控制器是关于时间的分段函数.为了减缓前后两个控制器在切换时刻的不连续性所带来的潜在的抖振,本文通过引入一个时间缓冲得到改进的混合稳定控制器,并通过某高超声速飞行器再入数学模型仿真,验证了控制器设计方法的有效性.

In view of the transient and steady performance,we propose a mixed-stability-control scheme for the uncertain linear systems with input constraints.This scheme guarantees both the finite-time stability and the asymptotic stability in the sense of Lyapunov for the closed-loop system.The control problem is expressed as a feasibility counterpart of linear-matrix-inequality（LMI）constraints.The mixed controller is a piecewise function of time,and thus potentially causes the transient jump due to the discontinuity of the controller at the switching time.For the purpose ofretarding the vibration,this paper introduces a time-interval buffer to modify the mixed controller.Finally,the numerical simulation applied to the mathematical model of a reentry hypersonic vehicle shows the validity of the proposed approach.