输入有界线性离散系统可控区域的一种有效算法  

Efficient Algorithm for Computation of Controllable Region of Linear Discrete-Time Systems with Bounded Input

作　　者：盛云龙[1] 闫治安[2] 苏宏业[1] 褚健[1] 

机构地区：[1]浙江大学先进控制研究所,杭州310027 [2]西安交通大学电气工程学院

出　　处：《西安交通大学学报》2003年第12期1255-1258,1283,共5页Journal of Xi'an Jiaotong University

基　　金：教育部优秀青年教师教学和科研奖励基金资助项目

摘　　要：针对输入有界的离散时间线性定常系统,利用凸多面体集合的几何特性,求解与有限步可控区域相联系的凸多面体集合的边界超平面法向量,进而得到有限步可控区域的精确表示.计算实践表明,与求解可控区域的传统方法相比,该方法具有更高的计算效率,且当有限步可控区域对应较多的步数时,该方法在计算效率上的优势更加显著.还结合最小时间控制问题和镇定问题,说明用该方法得到的有限步可控区域的精确描述,能够为解决约束系统的控制问题提供重要依据.Based on the geometric properties of the hyperplanes that form the boundaries of a convex polytope, an efficient algorithm is presented to determine the exact finite-step controllable state set of linear discrete-time systems with input saturation. The key point is to directly obtain the norm of each hyper-plane associated with finite-step controllable state set. The algorithm demonstrates higher computational efficiency than the traditional methods, particularly when the specified step is large enough. Moreover, minimum-time control problem and stabilization problem are also discussed to show that the exact characterization of the finite-step controllable regions via the approach can provide basis for solving control problem of constrained systems.

关 键 词：凸多面体 输入饱和约束 最小时间控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]