不确定线性系统的可达集估计

本文针对线性不确定系统,研究了系统状态可达集估计问题.在已知参考输入,未知扰动有界的条件下,提出了一种新的可达集估计方法,并把所提方法推广到系统不稳定的情况,分别估计出不稳定系统的闭环可达集和开环可达集.通过分析动态系统的李雅普诺夫函数,将求取系统可达集的问题转化为线性矩阵不等式优化问题,并将可达集范围用椭球集形式表述.最后分别通过数值仿真分析,验证了所提出方法对线性系统可达集估计的有效性.

Reachable set estimation for uncertain linear systems

This paper studies the problem of state reachable set estimation for uncertain linear systems. A new reachable set estimation method for discrete systems is proposed under the condition of known input and unknown bounded disturbance. And this method is extended to the unstable systems. In this extension, the reachable sets of the closed-loop and open-loop of the unstable systems are estimated respectively. By analyzing Lyapunov function of dynamic system, the problem of reachable set estimation of system is transformed into the optimization problem of linear matrix inequality. On the basis of these conditions, a series of ellipsoid containing the reachable set of the considered system is obtained. Finally, the effectiveness of the proposed method for the estimation of the reachability set of linear systems is verified by the simulation analysis of numerical examples.