含有迟滞的随机非光滑三明治系统的滤波与状态估计

A class of non-smooth nonlinearities with multi-valued mapping,i.e.hysteresis, often exists in phase-locked loops of communication as well as weak signal detection systems, microwave radio-frequency circuits, sensing and measurement systems as well as electromechanical actuators etc.It is known that those non-smooth devices or subsystems do not exist isolately but connect with the other devices or subsystems in engineering applications. Therefore, most of those systems can be deascribed by so-called non-smooth sandwich models with hysteresis. In this archietecture, non-smooth nonlinear block is embedded between the input and output linear dynamic blocks. Usually, the systems are affected by stochastic noises, in this case, the states of the system will also be contaminated by the noises. This project mainly focuses on the investigation of characteristic of the system affected by non-smooth nonlinearities inherent in the case of existence of stochastic noises. Then, the corresponding noise models under the effect of hysteresis and the stochastic sandwich state space functions with hysteresis to describe the system behavior in stochastically noisy case are constructed, respectivley. After that, this project will develop the corresponding non-smooth dynamic filtering and estimation methods of system states when the system is disturbed by noise.Moreover, this project will also implement the research on studying of adaptive non-smooth robust filtering and estimation strategies to handle the case of such class of systems with uncertainty in noise models and time-varying covariance matrices of stochastic noise.

在通信、微弱信号检测常用的锁相电路、微波射频电路、传感测量、压电致动等一大类工程系统中，存在具有迟滞特性的元器件或子系统，而迟滞是一类非光滑、多值映射的非线性。并且，在实际工程系统中这些非线性元件或子系统大部分不是单独存在的，而是与其它器件或子系统连接，这类系统可以用含有迟滞的非光滑三明治模型进行描述。这类模型的结构特点是：非光滑、多值映射的迟滞环节被夹在输入和输出线性动态子环节之间。通常由于系统所处的环境存在随机噪声干扰，因此系统本身的状态等亦会受到随机噪声污染。本项目主要研究：在存在随机噪声干扰情况下，分析这类系统受迟滞影响的特征；建立迟滞影响下随机噪声模型以及含有迟滞的随机三明治状态空间方程；研究当这类含有迟滞的非光滑三明治系统受随机噪声影响时，对系统状态进行非光滑动态滤波与估计的方法；对噪声模型存在不确定性和噪声协方差阵时变的情况，研究自适应非光滑鲁棒滤波方法。

本课题根据项目拟定的研究计划，对大量存在于电子、机械、生物系统中存在的含有迟滞特性的非光滑三明治系统，在随机噪声环境下的动态滤波问题模型进行了研究。所做的主要工作有：.1、在存在随机噪声干扰情况下，分析这类系统受迟滞影响的特征。.2、建立迟滞影响下随机噪声模型以及含有迟滞的随机三明治状态空间方程；分别建立了随机情况下，含有迟滞的维纳模型、含有迟滞的Hammerstein模型和含有迟滞的三明治模型。.3、研究了这类三明治系统的能控能观性问题；给出了能控能观性的判别方法。.4、研究当这类含有迟滞的非光滑三明治系统受随机噪声影响时，对系统状态进行非光滑动态滤波与估计的方法，证明了滤波器的稳定性，并将有关方法用于精密机电系统的状态估计与随机噪声滤波，取得了令人满意的结果。