\(H_{\infty }\) filtering with randomly occurring sensor saturations and missing measurements.

*(English)*Zbl 1244.93162Summary: In this paper, the \(H_{\infty }\) filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, Randomly Occurring Sensor Saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional \(H_{\infty }\) filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the \(H_{\infty }\)-norm requirement is satisfied. Note that the regional \(l_{2}\) gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semidefinite program method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.

##### MSC:

93E11 | Filtering in stochastic control theory |

93B36 | \(H^\infty\)-control |

93C55 | Discrete-time control/observation systems |

93C10 | Nonlinear systems in control theory |

90C22 | Semidefinite programming |

##### Keywords:

randomly occurring sensor saturations (ROSS); missing measurements; nonlinear systems; regional \(H_{\infty }\) filters; random incomplete information
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