Distributed observers design for a class of nonlinear systems to achieve omniscience asymptotically via differential geometry

Distributed observers are the framework of fusing observed data by constructing a cooperative observer network. This article renders a scheme of distributed observers for a class of nonlinear system. With this scheme, each local nonlinear observer in the cooperative network can estimate the whole states of the underlying system by their own output measurements and information obtained from their neighbor via communication network. The proposed distributed observers are constructed with Partial Observable Canonical Form, which is a technology studied in differential geometry. The common observable subspace pruning and the weight matrix with spatial transformation are innovatively developed to solve the problem that each local observer is not in the same space. The sufficient conditions are proposed to guarantee the achievement of asymptotical omniscience of distributed nonlinear observers. Furthermore, our distributed observers can also be applied to linear systems and systems with some zero outputs. In addition, comparing with some existing methods of distributed nonlinear observers, our method admits some unbounded systems. Four simulations including multi-Wen-bridge oscillator systems, multi-manipulators systems, unbounded nonlinear system and a linear system are employed to show the validity of the main result.