网络环境下非线性时变随机系统的最优递推滤波研究

This project will discuss the design of the optimal recursive filters for the nonlinear time-varying stochastic systems in network environment. By summarizing the existing methods of characterizing the network-induced phenomena (NIP), the mathematical models will be given for the newly emerging NIP (including the fading measurements, multiple fading measurements and randomly occurring signal quantizations etc.). Considering the physical plant involving the features of nonlinear, time-varying as well as stochastic and the NIP, the nonlinear stochastic dynamic models and measurement models will be established. Subsequently, the recursive filters will be constructed in terms of the network-induced information for special/general nonlinear time-varying stochastic systems. By employing the techniques of Riccati-like difference equations, innovation analysis approach and unscented transformation, the existence of the recursive filtering with the specified performance indices will be given and the algorithms of the optimal/suboptimal recursive filters will be developed. Also, the critera will be proposed to ensure the stability, robustness and convergence of the developed filtering algorithms. The monotonicity of the missing probabilities, the robustness of the fading coefficients and the sensibility of the quantization limit for the filtering error covariance will be poninted out, respectively. Moreover, the relationship between the computational complexity and the filtering performance will be studied. This research will contribute to the development of theories of networked systems, nonlinear stochastic systems and time-varying systems. The obtained results will provide an effective means to investigate the signal estimations for the complex dynamic networked systems.

本项目研究网络环境下的非线性时变随机系统的最优递推滤波器设计问题。首先归纳描述现有网络诱导现象的方法，建立刻画测量衰减、多重测量衰减、随机发生信号量化等新型现象的数学模型。综合考虑具有非线性性、时变性和随机性的物理对象及网络诱导现象，建立相应的非线性随机动力学模型与测量模型。接着，分别针对网络环境下的特殊/一般非线性时变随机系统构造依赖于网络诱导信息的递推滤波器。利用黎卡提型差分方程方法、新息分析方法、无损变换等技术，得到满足既定性能指标的递推滤波器的存在性条件及最优/次优递推滤波器的设计算法，给出保证滤波算法稳定性、鲁棒性与收敛性的判别条件，分别揭示滤波误差协方差对丢失概率的单调性、对衰减系数的鲁棒性和对量化极限的敏感性规律，并讨论计算复杂度和滤波性能之间的关系。本研究将有利于促进网络化系统、非线性随机系统和时变系统理论的发展，可为复杂动态网络化系统的信号估计提供有效的方法。

本项目研究了网络化环境下非线性随机系统的递推滤波、状态估计、故障估计与最优控制等问题。归纳了描述现有网络诱导现象的方法，建立刻画测量衰减、多重测量衰减、随机发生信号量化等新型现象的数学模型。综合考虑具有非线性性、时变性和随机性的物理对象及网络化诱导现象，建立了相应的非线性随机动力学模型与测量模型。给出了新的网络化时变随机系统的递推滤波算法（最优滤波、非脆弱滤波、事件触发滤波等），得到了新的非线性网络化系统的状态估计策略（方差受限状态估计、事件触发分布式状态估计、采样 H-infinity 状态估计等），提出了新的非线性时变网络化系统的最优保成本可靠控制方法；此外，将提出的理论结果应用于解决网络化环境下非线性时变随机系统的故障估计问题，给出了具有随机发生非线性和随机发生欺骗攻击的故障估计方法、抗网络诱导不确定性和数据丢包的故障估计策略、具有传感器饱和与随机发生故障的状态与故障联合估计算法等。本项目给出了保证算法鲁棒性、有界性等性能的充分性判别条件。特别地，探讨了数据包丢失现象对滤波算法性能的影响，从理论上揭示了数据包丢失概率与所获得的最优上界的迹的单调性关系。本项目推动了网络化系统和非线性随机系统理论的进一步发展，研究成果为解决非线性网络化随机系统的分析和综合问题提供有效的理论与方法。..在本项目资助下，出版英文专著1部（Springer出版社），授权发明专利1项，获黑龙江省高校科学技术奖一等奖1项，发表论文19篇，其中SCI检索论文16篇，EI检索论文3篇，SCI他引次数为146次。在项目执行期间，项目负责人担任美国《数学评论》评论员和5个国际期刊编委/副编辑，作为客座编辑组织3个国际期刊专刊，并培养了一批优秀的研究生。.

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