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首页> 外文期刊>IEEE Transactions on Automatic Control >On Nonlinear $H_{infty }$Filtering for Discrete-Time Stochastic Systems With Missing Measurements
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On Nonlinear $H_{infty }$Filtering for Discrete-Time Stochastic Systems With Missing Measurements

机译：缺少测量的离散时间随机系统的非线性$ H_ {infty} $滤波

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In this paper, the H infin filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper.
机译：在本文中，针对缺少测量值的一类非线性离散时间随机系统，研究了H infin滤波问题。所研究的系统不仅受状态相关的白噪声破坏，而且还受到外来输入的干扰。测量输出包含随机丢失的数据，该数据由具有已知条件概率的伯努利分布的白色序列建模。首先设计一个非常通用的滤波器，使得滤波过程是随机稳定的，并且在零初始条件下，对于所有可接受的缺失观测值和非零外生干扰，滤波误差均满足H infin性能约束。用二阶非线性不等式描述所需滤波器的存在条件。这种不等式可以分解为一些辅助的不等式，可以通过采用Lyapunov泛函的特殊形式来独立解决。结果，为了实际应用，讨论了线性时不变滤波器的设计问题，并获得了一些简化的条件。最后，给出了两个数值模拟例子来说明本文的主要结果。

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