Neural-Network-Based Filtering for A General Class of Nonlinear Systems under Dynamically Bounded Innovations Over Sensor Networks
Lifeng Ma, Zidong Wang, Hongjian Liu, Fuad E. Alsaadi, Fawaz E. Alsaadi
Abstract
In this paper, the design problem of distributed filters is studied for nonlinear systems over sensor networks. At each sensor node, filters are designed by making use of both local measurements and innovation information sent from the neighboring nodes via interaction network. To mitigate adverse effects from abnormal data during transmissions, in the constructed local filters, a mechanism is proposed which utilizes a saturation function to constrain the propagated innovations within a dynamically changeable bound. A neural-network-based algorithm is used for the approximation of the nonlinear dynamics, where the weight matrix is co-designed with the filter gains. By resorting to certain convex optimization techniques, sufficient conditions are determined with respect to the solvability of our addressed problem, which ensure that 1) the estimation errors at each sensor node are confined within a pre-specified ellipsoidal region; and 2) the finite-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance specification is achieved. Moreover, within the established framework, an optimal problem is established to determine a locally optimal filter gain. Finally, a simulation example is given to demonstrate the correctness of the proposed filtering algorithm.