Synthesis for Spatially Interconnected Systems with Distributed Output Feedback Controllers
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摘要: 讨论了一类由若干个连续时间线性系统组成的强耦合的空间关联系统的分布式控制器设计问题. 该类系统在实际中有广泛应用, 如高速路车辆控制系统, 电网系统及计算机网络系统. 提出了混合Lyapunov判据和混合有界实引理对该类大系统的稳定性和H无穷性能进行了分析. 给出了基于LMI的分布式动态输出反馈控制器设计方法, 从而保证了闭环大系统的稳定性和H无穷性能. 在控制器的求解过程中, 引入了更为高效和计算可靠性更高的变量替换法进行求解, 试验结果表明, 一些通过消元法无解的问题借助变量替换法可以得到很好的解决. 最后, 通过具体实例说明了分布式控制系统在动态性能指标上优于分散控制系统.Abstract: This paper considers the design of distributed control architecture for spatially interconnected systems that are composed of several similar interconnected sub-units. Each sub-unit is a linear continuous time system and directly interacts with its nearest neighbors. This class of systems exists in several applications such as automated highway systems, power systems, and computer networks. Hybrid Lyapunov criterion and the hybrid real bounded lemma are derived to determine the stability and H∞ performance of the overall system. In order to stabilize this class of systems, distributed dynamic output feedback controllers are considered, and tractable linear matrix inequality (LMI)-based algorithms for the derivation of distributed controllers are presented. The change variable approach is introduced in the LMI-based algorithms due to its higher efficiency and numerically stable implementation than the elimination algorithm as introduced in previous works. It is shown through a numerical example that the distributed H∞ controllers developed in this article are superior to decentralized controllers in several aspects.
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