Fuzzy $H_{\infty}$ Filtering for Nonlinear Networked Systems Subject to Sensor Saturations
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摘要: 研究了基于T-S模糊模型描述的非线性网络化系统$H_{\infty}$滤波器设计问题.由于网络诱导时滞的存在, 使得一个采样周期内, 到达接收端的数据可能是一个或多个, 也可能没有任何数据.提出传感器冗余策略解决由于饱和而引起的传感器件失效的问题.为降低结果的保守性, 选择模糊规则依赖的Lyapunov函数对滤波误差系统进行稳定性分析, 给出使滤波误差系统均方渐近稳定且具有指定$H_{\infty}$性能的充分条件, 滤波器参数通过求解一组线性矩阵不等式(Linear matrix inequalities, LMIs)得到.仿真研究结果表明算法的有效性.Abstract: The $H_{\infty}$ filter design problem is investigated for T-S fuzzy-model-based nonlinear networked systems. The existing of transmission delay makes that there may be one or multiple data, even no data arriving at the receiver side within one sampling period. A redundant strategy is proposed to solve the problem of sensor failure caused by sensor saturation. In order to reduce the conservatism, the fuzzy-dependent-basis Lyapunov function is chosen to analyze the stability of filtering error systems and a sufficient condition is given to make the filtering error system mean-square asymptotically stable with a specified $H_{\infty}$ performance. The parameters of the filter are obtained by solving a set of linear matrix inequalities (LMIs). The simulation results illustrate the effectiveness of the algorithm.
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Key words:
- Networked system /
- T-S fuzzy model /
- sensor saturation /
- H∞ filter /
- packet dropout /
- time delay
1) 本文责任编委 王占山 -
表 1 接收端接收数据情况举例
Table 1 An example case of the received data at the receiver side
$k $ $\xi_k^{(0)}$ $\xi_k^{(1)}$ $\tilde {y}_k$ 1 1 0 $y_1$ 2 1 1 $y_2$ 3 0 0 0 4 0 1 $y_3$ 5 1 1 $y_5+y_4 $ 
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表 2 模糊规则依赖与模糊规则独立的$\gamma^*$比较
Table 2 Comparison of $\gamma^*$ between fuzzy- basis-dependent and fuzzy-basis-independent methods
$ \xi_k^{(0)}$ 模糊规则依赖情况 模糊规则独立情况 0.1 5.8237 7.7774 0.3 5.7774 7.2734 0.5 5.1049 6.0407 0.7 4.1155 4.6130 0.9 3.2347 3.4826
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表 3 最优$H_{\infty}$性能指标与传感器饱和发生概率$\bar\delta$的关系
Table 3 Relation between optimal $H_{\infty}$ performance and the sensor saturation occurrence rate
$\bar\delta$ $\gamma^{*}$ 0.2 5.6159 0.4 5.7171 0.6 5.7774 0.8 5.8047 1 5.8116
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表 4 最大时滞为一步与两步时的$\gamma^*$比较
Table 4 Comparison of $\gamma^*$ between one-step and two-step maximum delays
${\bar\xi}_0/{\bar\xi}_1/{\bar\xi}_2$ $ P_{1d}$ $P_{2d}$ $ P_{drop}$ $\gamma^*$ 0.2/0.3 0.24 0 0.56 5.8221 0.2/0.1/0.2222 0.08 0.16 0.56 16.6811 0.4/0.3 0.21 0 0.42 5.7386 0.4/0.1/0.2222 0.07 0.14 0.42 13.6758 0.6/0.3 0.12 0 0.28 4.8987 0.6/0.1/0.2222 0.04 0.08 0.28 10.2688 0.8/0.3 0.06 0 0.14 3.7947 0.8/0.1/0.2222 0.02 0.04 0.14 8.2085
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