Fixed-Time and Robust Algebraic Distributed Pseudo-State Estimation for Fractional-Order Systems With Partially Connected Topology

In this work, by developing a set of reduced-order local estimators at the networked sensor nodes, we propose a fixed-time and robust algebraic distributed pseudo-state estimation method for fractional-order linear systems. To begin, we introduce a recovered set to construct an invertible transformation at each node, based on an assumption relaxer than the strongly connected assumption. Leveraging this transformation, at each node, the unobservable pseudo-state is recovered, and the relationship between the entire pseudo-state and local observable pseudo-states of the nodes in its recovered set is established. Building upon this framework, we develop the fractional-order modulating functions method to formulate a type of fixed-time pseudo-state estimators using initial-condition-independent algebraic integral formulas to estimate each node's local observable pseudo-state. Subsequently, by collaborating with a group of local observable estimations, the fixed-time distributed estimation for the entire pseudo-state is achieved. The error analysis in noisy cases is also conducted to demonstrate the robustness of our method. Finally, two numerical examples are provided to illustrate the efficacy and scalability of the developed distributed estimation scheme.