Sun Yanxiu, Wen Yu, Li Hong, Du Ying
Basic Course Department, Shenyang Institute of Technology, Fushun, China.
College of Sciences and Mathematics, Handan University, Handan, China.
PLoS One. 2025 Apr 29;20(4):e0320912. doi: 10.1371/journal.pone.0320912. eCollection 2025.
In this study, the problem of the robust control of interconnected systems was investigated. A controller design method based on a state observer is proposed for nonlinear discrete interconnected systems with disturbance terms. In the proposed method, the observer and controller of the interconnected systems are designed separately, and sufficient conditions for the existence of the gain matrix are provided. In the design of the state observer, considering the convergence rate of the observation error, the performance of the state observer was improved by adding constraints. The influence of the external disturbance of the system on the state estimation is reduced by introducing a performance index, which provides the necessary theoretical basis for the design of the controller. In the controller design, based on the disk stability lemma and control theory, sufficient conditions for the existence of the controller are provided, and robust stabilization of the feedback closed-loop system was realized. In this study, the separate design method of the controller was compared with the centralized design method, which demonstrated the superiority of the separate design of the observer and controller. Finally, a numerical example is discussed, in which the separation design method of the robust controller was tested, and the effectiveness of the method was verified.
在本研究中，对互联系统的鲁棒控制问题进行了研究。针对具有干扰项的非线性离散互联系统，提出了一种基于状态观测器的控制器设计方法。在所提方法中，互联系统的观测器和控制器分别进行设计，并给出了增益矩阵存在的充分条件。在状态观测器设计中，考虑观测误差的收敛速度，通过添加约束条件提高了状态观测器的性能。引入一个性能指标，降低了系统外部干扰对状态估计的影响，为控制器设计提供了必要的理论依据。在控制器设计中，基于圆盘稳定性引理和控制理论，给出了控制器存在的充分条件，实现了反馈闭环系统的鲁棒镇定。在本研究中，将控制器的分离设计方法与集中设计方法进行了比较，证明了观测器和控制器分离设计的优越性。最后，讨论了一个数值例子，对鲁棒控制器的分离设计方法进行了测试，验证了该方法的有效性。
