Nonlinear control design for linear differential inclusions via convex hull of quadratics
Nonlinear control design for linear differential inclusions via convex hull of quadratics
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DOI：
10.1016/j.automatica.2006.10.015
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发表时间：
2007-04
期刊：
影响因子：
--
通讯作者：
T. Hu
中科院分区：
文献类型：
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作者：
T. Hu
提出了一种线性微分夹杂体鲁棒稳定和鲁棒性能的非线性控制设计方法。一个最近引入的非二次Lyapunov函数，二次函数的凸包，将用于构造非线性状态反馈律。设计目标包括最大收敛速率的稳定性、最小可达集的抗干扰性和最小增益。从双线性矩阵不等式（bmi）的角度推导了稳定和性能的条件，并将现有的线性矩阵不等式（LMI）条件作为特例加以涵盖。数值算例证明了非线性反馈控制比线性反馈控制在ldi中的优越性。通过数值计算还发现，非线性控制策略有助于大大减少控制工作量。
This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions (LDIs). A recently introduced non-quadratic Lyapunov function, the convex hull of quadratics, will be used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least L2gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Numerical examples demonstrate the advantages of using nonlinear feedback control over linear feedback control for LDIs. It is also observed through numerical computation that nonlinear control strategies help to reduce control effort substantially.