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测量值异常下多时间尺度系统$H_{\infty}$滤波

马磊1,2, 张莹1,2, 杨春雨1,2, 王国庆1,2   

  1. 1. 中国矿业大学信息与控制工程学院, 徐州 221116;
    2. 地下空间智能控制教育部工程中心, 徐州 221116
  • 收稿日期:2022-01-27 修回日期:2022-04-27 发布日期:2022-08-31
  • 通讯作者: 杨春雨,Email:chunyuyang@cumt.edu.cn.
  • 基金资助:
    江苏省科技计划项目(BK20200631,BK20200633),国家自然基金(61873272,62073327,62003348),中国博士后基金面上项目(2020M681766),江苏省博士后科研资助项目.

马磊, 张莹, 杨春雨, 王国庆. 测量值异常下多时间尺度系统$H_{\infty}$滤波[J]. 系统科学与数学, 2022, 42(7): 1648-1659.

MA Lei, ZHANG Ying, YANG Chunyu, WANG Guoqing. $H_{\infty}$ Filter Design for Multi-Time-Scale Systems with Measurement Outliers[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(7): 1648-1659.

$H_{\infty}$ Filter Design for Multi-Time-Scale Systems with Measurement Outliers

MA Lei1,2, ZHANG Ying1,2, YANG Chunyu1,2, WANG Guoqing1,2   

  1. 1. School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116;
    2. Engineering Research Center of Intelligent Control for Underground Space, Ministry of Education, Xuzhou 221116
  • Received:2022-01-27 Revised:2022-04-27 Published:2022-08-31
复杂的工业系统中经常存在快、慢动态耦合运行的多时间尺度现象,通过引入时间尺度参数,这类系统被建模为多时间尺度系统.由于实际系统运行过程中通常会有外部干扰或者噪声存在,为了准确获取系统的状态,判断系统运行状态以及设计控制算法,$H_{\infty}$滤波器受到了广泛的研究关注.同时,系统在运行时可能产生传感器故障或者受到传感器攻击,引起了系统测量值的异常,导致滤波结果不精确无法满足滤波需求.因此,文章考虑测量值异常情形下的多时间尺度$H_{\infty}$滤波问题,通过引入饱和函数约束测量值上界,同时设计依赖于时间尺度参数的滤波器,实现了系统的状态估计并且满足给定的$H_{\infty}$性能,并且避免了设计过程中由于多时间尺度现象导致的“病态数值问题”.最后,通过仿真例子证明了文章所提方法的正确性和优越性.
The co-existence of slow and fast dynamics often occurs in many complicated industrial systems, which is also called the multi-time-scale phenomenon. Systems with multi-time-scale phenomenon are modeled as the multi-time-scale systems (MTTSs) by introducing a time scale parameter. To accurately obtain the state of the system dynamics, which can be used to evaluate the operation state of the system and design the control algorithms, the $H_{\infty}$ filter has received extensive research attention because of the existence of external interference or noise in the actual industrial system operation process. At the same time, sensor faults or sensor attacks may occur during system operation, as such measurement outliers occur in data packets from sensors, thereby resulting in inaccurate filtering. And therefore, in this paper, we focus on the $H_{\infty}$ filter design for the MTTSs. By introducing a saturation function to force the measurement within an upper bound and design a filter dependent on the time scale parameter, a filter design algorithm is proposed to achieve the pre-defined $H_{\infty}$ performance index of the filter error dynamics, while the possible ill-conditioned numerical issue is also avoided. Finally, the correctness and merits of the proposed method are demonstrated by a simulation example.

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