Zonotopic distributed fusion for nonlinear networked systems with bit rate constraint

In this paper, the distributed fusion estimation problem is studied for a class of nonlinear networked systems subject to unknown-but-bounded (UBB) noises. A bit rate constraint is introduced to quantify the limited bandwidth of the communication channel, under which a bit rate allocation protocol is further designed by solving a certain off-line optimization problem. Based on the received data from the network, several local extended-Kalman-type estimators are constructed and zonotopic sets confining local estimation errors are then obtained. By designing the local estimator parameters, the F-radii of the obtained zonotopic sets are minimized. Subsequently, with the calculated local estimates and zonotopic sets, a zonotopes-based distributed fusion estimator is put forward by means of the matrix-weighted fusion method, and the global zonotope (i.e., the zonotope encompassing the error between the system state and the fused estimate) is derived. Moreover, under the proposed zonotopes-based fusion framework, the distributed fusion estimators are designed based on, respectively, the scalar-weighted fusion method and the diagonal-matrix-weighted fusion method. Finally, the effectiveness of the proposed distributed fusion method is illustrated through a numerical example.