非线性时滞系统参数辨识及其实验

The project is a fundamental research both in theory and application. The motivation is derives from dynamical structures subjected to active control and equipments for precision machining and also from new techniques modeled by those nonlinear delayed systems appearing in transportation, system biology, electronic and photonic communication, neural network, information technology. Four key scientific problems are focused, i. e. parameter identifiably analysis, identification method and its constructive algorithm for linear systems with delay coupling, parameter identification theory and method for nonlinear systems with time delay coupling, the excitation identification theory and method for delayed systems and experimental verification of algorithms. Universalization，completion and simplification will be considered as research goals. In identification model, some general methods are proposed to identify the delay and nonlinearity parameters in a versatile model not only for a special kind of mechanical system and but also for multi-degree-of-freedom systems. In algorithms, the given computation is required to identify the parameters with complete derivation, explicit iteration procedure and rapid convergence. In application, the identification method is required to build a friendly interface that requires least data input and simplest manual operation and it is easy to be understood and verified by experiments. In this project, it is expected to form initially some general methods or algorithms witch used to identify those nonlinear and time delay parameters in nonlinear delayed systems. Such achievement may not only establish a fundamental for further experiments in nonlinear delayed systems, but also provide a technical support for some applications in engineering. The present project not only lies in an integration of multiple scientific disciplines such as dynamics, control theory, signal processing and so on, is but also helpful for development and improvement in nonlinear delayed systems.

项目定位应用基础研究。针对主动控制动态结构、精密加工机械装备等近代技术中出现的各种非线性时滞系统，通过对时滞耦合线性系统的可辨识性分析及算法构造、时滞耦合非线性系统的辨识理论及算法构造、时滞耦合系统的载荷识别理论及算法构造和时滞耦合系统辨识算法实验验证四个科学问题研究，试图实现辨识模型通用化、算法完备化及应用简单化三项科研目标。在辨识模型方面，提出针对一般化模型的时滞和非线性参数辨识方法；在算法方面，给出推导完备、迭代程序明确、具有快速收敛的辨识计算方法，在应用简单化方面，给出需简单输入输出信息、无需过多人工干预过程研究结果通过实验进行验证。项目试图初步形成针对非线性时滞系统的非线性和时滞参数辨识一般性方法，为进一步开展针对非线性时滞系统的实验和某些工程应用研究奠定理论基础，研究意义在于理论上综合了动力学、控制理论、信号处理等诸多学科，有助于非线性时滞动力学理论的进一步发展和完善。

针对本项目的问题来源和问题带来的研究方面的挑战性，我们对四个科学即时滞耦合线性系统的可辨识性分析及算法构造、时滞耦合非线性系统的辨识理论及算法构造、时滞耦合系统的载荷识别理论及算法构造和时滞耦合系统辨识算法的实验验证进行了研究。针对时滞耦合线性系统的参数辨识问题，建立了非完备观测情形下时滞及反馈增益参数的可辨识性判据，提出了时滞参数辨识结果唯一性的必要条件，解决了非完备观测情形下时滞参数的辨识流程及算法构造问题；针对确定性信号过程，论证了时滞耦合非线性系统的参数可辨识性，提出了适用于弱非线性的脊线辨识方法、适用于强非线性的伽辽金法、拓扑自适应神经网络法和具有噪声自适应修正能力的参数辨识方法，解决了传统方法抗噪能力低、适用性差和鲁棒性等方面的缺点，为进一步推动时滞非线性系统参数辨识方法的工程应用奠定了理论和技术基础；针对建模误差产生的动态载荷和摩擦载荷辨识问题，构造了非光滑摩擦力的回归辨识算法、同步辨识法和数据驱动模型重构人工智能算法，特别是对动荷载辨识的同步法证明了收敛性，为动态载荷的辨识提供了一套新的方法；提出了一种数字式时滞控制技术，极大地提高了时滞控制的分辨率和参数调控范围，在此基础上，集成了时滞反馈控制系统，设计了模块化的线性、非线性结构，形成了完整的时滞非线性系统参数辨识方法实验验证平台。上述成果将形成一个时滞耦合动力学系统理论分析、算法构造与实验验证的研究框架。项目共发表期刊论文32篇，其中SCI索引26篇，EI索引2篇，北大中文核心2篇，CSSCI索引论文1篇。发表国际会议论文2篇。毕业博士研究生5人，硕士研究生1人，2名博士研究生获得国家奖学金。申请人受邀在国内外学术会议上做特邀报告11次。项目组成员参加国际学术会议14人次，参加国内学术会议24人次，举办国内学术会议/大会专题研讨会3次。项目组成员2人获得上海市青年科技英才杨帆计划资助，1人获得中国科协第四届托举人才工程资助，3人获得国家自然科学基金资助。