A new modulating functions-based non-asymptotic state estimation method for fractional-order systems with MIMO

Wang, Lei; Liu, Da‐Yan; Gibaru, Olivier

doi:10.1007/s11071-022-08128-5

Cited by 8 publications

(3 citation statements)

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“…For Riemann-Liouville FOLSs, [29]- [30] applied the FOMFs method to the state-space representation, deriving formulas for fractional integrals of state variables to achieve state estimation. In the case of Caputo FOLSs, [31] focused on estimating the initial conditions to realize state estimation.…”

Section: A Centralized Formulas For States Of Observable Folssmentioning

confidence: 99%

“…Inspired by [30], the desired FOMFs used in Theorem 2 are designed by the following proposition. Proposition 1.…”

Section: A Centralized Formulas For States Of Observable Folssmentioning

confidence: 99%

“…, κ j ), are assured. • Owing to the properties of the formulas for η js derived from Theorem 2, the designed distributed state estimator (30) is also irrelevant to the system's initial condition. Hence, our proposed method enables a fixed-time distributed state estimation for the FOLS (7) within an arbitrarily predefined time.…”

Section: B Fixed-time and Robust Distributed State Estimator For Folssmentioning

confidence: 99%

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

Zhang,

Liu,

Boutat

et al. 2024

Preprint

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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.

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Section: A Centralized Formulas For States Of Observable Folssmentioning

confidence: 99%

“…Inspired by [30], the desired FOMFs used in Theorem 2 are designed by the following proposition. Proposition 1.…”

Section: A Centralized Formulas For States Of Observable Folssmentioning

confidence: 99%

Section: B Fixed-time and Robust Distributed State Estimator For Folssmentioning

confidence: 99%

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