具有随机丢包的网络控制系统不定二次多项式滤波与控制问题研究

Network control is the objective demand of the complex control systems and the remote control systems, one of its main problem is the presence of random packet dropout. This proposal aims to investigate the problem of nonlinear (polynomial) filtering and control based on indefinite quadratic performance index for networked control systems with random packet dropouts. The polynomial filtering problem is proposed based on indefinite quadratic index. By using Kronecker algebra and Krein space linear estimation theory, the analytical solutions are given for the indefinite quadratic polynomial filtering problem of linear and Lipschitz nonlinear networked control systems. Moreover, the polynomial control problem is proposed based on indefinite quadratic index. By constructing the duality principle between the polynomial filtering problem and the polynomial control problem, the analytical solutions are obtained for the indefinite quadratic polynomial control problem of linear and Lipschitz nonlinear networked control systems. Though appling the proposed approach to the H∞ polynomial filter and controller design for networked control systems, sufficient conditions for the existence of H∞ polynomial filter (controller) are proposed and the filter (controller) is derived.The main contents of this proposal belong to one of the unsolved advanced topics in control area. The results can improve the robustness and accuracy of filtering and control for networked control systems. Thus, it has important theoretical and practical significance.

网络化控制是复杂控制系统和远程控制系统的客观需求，其面临的主要问题之一是随机数据丢包的存在。本项目以受随机数据丢包影响的网络控制系统为研究对象，旨在研究其在不定二次性能指标下的非线性（多项式）滤波与控制问题。提出基于不定二次型的多项式滤波问题，利用Kronecker代数定义增广系统，进而运用Krein空间线性估计理论，得到线性和Lipschitz非线性网络控制系统不定二次多项式滤波问题的解析解。提出基于不定二次型的多项式控制问题，通过建立不定二次多项式滤波与控制问题的对偶关系，给出线性和Lipschitz非线性网络控制系统多项式控制问题的解析解。将上述结论应用于网络控制系统H∞多项式滤波器与控制器的设计，给出H∞多项式滤波器（控制器）的解及其存在的充分条件。本项目的研究内容是控制领域尚未解决的前沿课题之一，所得结果可提升网络控制系统滤波与控制的鲁棒性和精确性，具有重要的理论意义和现实意义。

网络控制系统可应用于几乎任何带有控制器的分布设备需要进行数据交换的场合，是现代化工业的基础，国内外对其滤波和控制问题研究很重视。我们针对一类具有测量数据丢失的线性广义网络控制系统，设计了H∞故障检测器；解决了一类线性网络控制系统的非高斯噪声二阶多项式估计问题，并对估计器的稳定性进行了分析；针对一类离散时间Lipschitz非线性系统，提出了一种基于Krein空间估计理论的H∞自适应平滑器设计方法；分析了一类高阶非线性脉冲混杂系统的Hyers-Ulam稳定性和Hyers-Ulam-Rassias稳定性；基于多项式滤波理论，针对一类具有观测随机丢包的线性网络控制系统，设计了二阶多项式反卷积滤波器和固定滞后平滑器；基于Krein空间投影公式和新息分析方法，解决了一类单边Lipschitz非线性系统的H∞多步预测问题。这些成果进一步完善了多项式滤波（控制）理论，并提升了网络控制系统滤波与控制的精确度与鲁棒性，有一定的理论与应用价值。