凸规划与离散系统H∞输出控制

H∞ Output Control of Discrete-Time Systems Via Convex Optimization

中文关键词  H∞控制  输出反馈  凸优化  控制系统设计  离散系统

英文关键词  H∞ control  output feedback  convex optimization  discrete-time systems

中文摘要

      本文提出了一种求解离散系统最优Ｈ∞输出控制器的凸优化方法．利用非线性矩阵映射，文中表明Ｈ∞输出控制问题可以转化为在n（n+1）+1维空间内凸集上的线性目标函数优化问题，这里ｎ为系统阶次．在可镇定、可检测的条件下，该凸集为有界的．由本文给出设计方法得到的输出Ｈ∞控制器可以使得闭环Ｈ∞范数任意接近最优．本文提出方法可以处理具有凸约束的Ｈ∞输出控制问题．

英文摘要

      This paper presents a convex optimization approach to（nearly）optimal H∞ output control problem of discrete-time systems.By using nonlinear matrix valued mapping，it is shown that the H∞ output problem can be formulated as minimization of a linear objective function over a convex set in n（n+1）+1 dimensional space where n is the system dimension.Under the detectability and stabilizability conditions，the set is bounded.The H∞ norm of the closed loop system yielded by this method can come arbitrarily close to the minimum H∞ norm.The method proposed can handle the additional convex constraints.