Optimizing the performance of the feedback controller for state-based switching bilinear systems
Optimizing the performance of the feedback controller for state-based switching bilinear systems
复制标题
优化基于状态的切换双线性系统反馈控制器的性能
DOI：
10.1002/oca.2639
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发表时间：
2020
影响因子：
1.8
通讯作者：
Schutter Bart
中科院分区：
文献类型：
--
作者：
Lin Shu;Li Dewei;Schutter Bart
本文研究了基于状态切换的双线性系统（SBLS）反馈控制器的设计和性能优化问题，其中子系统在不同的状态空间多面体中具有双线性系统的形式。首先，通过进一步将子区域划分为更小的区域，并在所得到的区域中设计区域相关的反馈控制器，SBLS可以被转换为相应的切换线性系统（SLS）。然后，对于这些SLS，通过对李雅普诺夫函数施加收缩性条件，可以得到无限水平二次成本的上界。优化这个上界产生控制器设计。将优化问题转化为一个线性矩阵不等式优化问题，可以有效地求解。最后，闭环系统的稳定性下所提出的控制器是逐步建立通过减少总的李雅普诺夫函数。
This article is concerned with the design and performance optimization of feedback controllers for state‐based switching bilinear systems (SBLSs), where subsystems take the form of bilinear systems in different state space polyhedra. First, by further dividing the subregions into smaller regions and designing region‐dependent feedback controllers in the resulting regions, the SBLSs can be transformed into corresponding switching linear systems (SLSs). Then, for these SLSs, by imposing contractility conditions on the Lyapunov functions, an upper bound on the infinite horizon quadratic cost can be obtained. Optimizing this upper bound yields the controller design. The optimization problem is formulated as a linear matrix inequalities optimization problem, which can be solved efficiently. Finally, the stability of the close‐loop system under the proposed controller is established step by step through a decreasing overall Lyapunov function.