Intermediate Observer-Based Robust Distributed Fault Estimation for a Complex Network of Dynamical Systems

In this paper, we focus on the robust distributed fault estimation problem for a complex network of dynamical systems with nonlinear terms, a novel intermediate observer design method is proposed to estimate the system states and faults based on local output measurements and estimation error from its neighbors. Compare with the existing results, the fault estimation method does not need to satisfy the observer-matching conditions and the upper bound of the fault also could be unknown. Besides, a nonlinear term has been added to the design of intermediate variable to eliminate the influence of the artificial selected parameters in the coefficient matrix of the coupling term. The intermediate variable parameters constructed by artificial parameters can be adjusted according to different fault types to ensure the robustness of the global error system. Based on Shur complement lemma, the calculation method of observer parameters is presented, and converted the matrix inequality into linear matrix inequality. Finally, simulation results demonstrate the effectiveness of the method. Note to Practitioners—With the increasing requirement of dynamical systems, it is essential to design a fault estimation method that can be adapted to a wider range of system models. The motivation of this paper is to further improve the intermediate observer based on the specific structure of the network of dynamical systems. In conventional method, the artificial selected parameters in intermediate variables are selected as the same constant and can not be selected separately, besides, intermediate variables exist in the coefficient matrix of the coupling term, making the selection of single artificial parameter difficult. This paper proposed an improved intermediate observer design method to estimate the faults in the complex network of dynamical systems. Under this method, a nonlinear term is introduced to eliminate the effect of coupling terms and the artificially selected parameters can be selected separately according to different faults types, meanwhile, compared with the traditional method, the distributed estimation error is introduced to expand the application range of observer and also improve estimation performance.