Distributed coordination algorithms for multiple fractional-order systems

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

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Realization of a fractional-order RLC circuit via constant phase element

International Journal of Dynamics and Control ◽

10.1007/s40435-021-00778-4 ◽

2021 ◽

Author(s):

Riccardo Caponetto ◽

Salvatore Graziani ◽

Emanuele Murgano

Keyword(s):

Experimental Data ◽

Carbon Black ◽

Fractional Order ◽

Constant Phase Element ◽

Polymeric Matrix ◽

Fractional Order Systems ◽

New Device ◽

Rlc Circuit ◽

Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

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Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0267 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Xindong Si ◽

Hongli Yang

Keyword(s):

Feedback Control ◽

Fractional Order ◽

State Feedback Control ◽

Invariant Sets ◽

Linear Feedback ◽

Control Law ◽

Optimization Approach ◽

Fractional Order Systems ◽

Linear Feedback Control ◽

Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

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An ADRC-based backstepping control design for a class of fractional-order systems

ISA Transactions ◽

10.1016/j.isatra.2021.03.033 ◽

2021 ◽

Author(s):

Fatemeh Doostdar ◽

Hamed Mojallali

Keyword(s):

Fractional Order ◽

Control Design ◽

Backstepping Control ◽

Fractional Order Systems

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