Fixed-Time and Prescribed-Time State Estimation of Multi-layer Complex Dynamical Network with Incomplete Measurements

In practical engineering applications, we hope to achieve the state estimation of the multi-layer complex dynamical network in the fixed-time or prescribed-time instead of the infinite time. At the same time, due to the influence of unreliable communication factors, the incomplete measurement of transmission between nodes is inevitable. In this paper, the fixed-time and prescribed-time state estimation problems of the multi-layer complex dynamical network with incomplete measurements is investigated. First, we establish an original network model and design an appropriate observer network, assume that the incomplete data measurement exists in the node transmission between the original network and the observer network. When the incomplete measurement happens, we adopt the compensation strategy of replacing the original network outputs with the observer network outputs. Second, based on the fixed-time and prescribed-time stability theories, we estimate the state information of the original network in the fixed-time and prescribed-time by constructing adaptive controllers and applying the Lyapunov stability theory. Finally, some numerical simulations are developed to illustrate the efficiency of the proposed method.