Fixed-time and robust distributed state estimation for fractional-order linear systems based on fractional-order modulating functions

Abstract

In this paper, we propose a fixed-time and robust distributed state estimation method for fractional-order linear systems by developing a set of reduced-order centralized estimators at the networked sensor nodes. To begin, we introduce a recovered set and a connectivity assumption weaker than strong connectivity, which are crucial for constructing an invertible transformation at each node. Leveraging this transformation, each node’s unobservable state can be represented, and the relationship between the entire state at each node and the observable states of the nodes in the recovered set can be established. Building upon this framework, the fractional-order modulating functions method is developed to estimate each observable part, and a type of fixed-time and robust centralized state estimators are formulated by initial condition-independent algebraic integral formulas. Subsequently, based on the established relationship, by collaborating a recovered set of local reduced-order centralized estimators, fixed-time and robust distributed state estimation in noisy cases is realized. Additionally, in the discrete noisy case, a distributed estimation algorithm for online applications is generated through vector products and a detailed stability analysis for distributed state estimation errors is conducted to complement our proposed methodology. Finally, two numerical examples are provided to demonstrate the efficacy of the developed distributed estimation scheme.