随机多模态驱动系统的混合频段鲁棒滤波

Robust filtering has been attracting much attention as one of important fields in control theory and engineering application, and most of the results have the requirement that the filtering error systems have the same disturbace rejection capability in overall frequency domain. In many practical applications, however, different design performance indices varying form one frequency interval to others should be considered specifically to fulfill various practical desired objectives in different frequency interval, which makes the traditional robust filtering approaches relatively conservative. As finite frequency filtering technique has the ability to describe and deal with the performance index specific to certain frequency interval, it owns strong application background. Large amounts of the existing effort have been primarily confined to the control systems with single modal, which limits the capacity of solving practical problems. Therefore, this proposal aims to develop a new field of mixed frequency interval filtering theory for stochastic multimodal-driven systems. Firstly, the single-frequency interval filtering algorithm is improved to address the multi-frequency interval filtering with multi-indices to meet the engineering demand. Secondly, to reduce the conservativeness, the mixed frequency interval filtering is proposed by considering the frequency characteristic of subsystems. Thirdly, on the basis of modal jump frequency, the mixed frequency interval robust filtering is suggested by relaxing the stability requirement of the filtering error systems. What is more, the optimal frequency is found to improve the filtering accuracy. Finally, the obtained results are extended to solve the mixed frequency interval filtering problems for complicated dynamics, such as dual stochastic process, nonlinearities, time-delays and so on.

鲁棒滤波在控制理论发展及工程实践中一直独具魅力，成果丰富，但大多要求误差系统对全频段的噪声有同样的干扰抑制能力。而工程中往往只需针对有限频段或对不同频段使用不同滤波指标进行设计，传统方法由于不能凸显有限频段特性可能保守性较大。有限频段滤波能直接刻画和处理特定频段性能指标，具有很强的应用背景，但现有结果基本局限于单一模态系统，处理和解决实际问题的能力有限。本项目以随机多模态驱动系统为对象，开拓其混合频段滤波理论研究新领域。改进单一频段滤波算法，结合多项性能指标，进行多频段多指标滤波，以满足实际需要；考虑各子系统的频率特性，有针对性的在特定频段分别设计，提出混合频段下的鲁棒滤波算法，降低设计的保守性；放宽对误差系统稳定性的要求，从模态跳变频率角度解决混合频段鲁棒滤波问题，并寻找最优分频点，提高滤波精度。最后集成阶段性研究成果，获得双重随机、非线性、时滞等复杂动态下混合频段滤波器的状态空间实现。

鲁棒滤波在控制理论发展及工程实践中一直独具魅力，成果丰富，但大多要求误差系统对全频段的噪声有同样的干扰抑制能力。而工程中往往只需针对有限频段或对不同频段使用不同滤波指标进行设计，传统方法由于不能凸显有限频段特性可能保守性较大。有限频段滤波能直接刻画和处理特定频段性能指标，具有很强的应用背景，但现有结果基本局限于单一模态系统，处理和解决实际问题的能力有限。本项目以随机多模态驱动系统为对象，开拓其混合频段滤波理论研究新领域。改进单一频段滤波算法，结合多项性能指标，进行多频段多指标滤波，以满足实际需要；考虑各子系统的频率特性，有针对性的在特定频段分别设计，提出混合频段下的鲁棒滤波算法，降低设计的保守性；放宽对误差系统稳定性的要求，从模态跳变频率角度解决混合频段鲁棒滤波问题，并寻找最优分频点，提高滤波精度。最后集成阶段性研究成果，获得双重随机、非线性、时滞等复杂动态下混合频段滤波器的状态空间实现。该项目具有丰富的研究内容和深刻的理论意义，从而推动随机多模态驱动系统理论.研究的进一步发展，开拓广阔的应用前景。同时，混杂系统动态机理的复杂性、信息估计问题的多样性、滤波算法的鲁棒性、精度、以及工程应用的保守性等，还将衍生出一系列极具挑战性的课题，从而丰富和发展现代控制理论及工业应用。