Resilient containment control of fractional-order multi-agent systems with uncertainty and time delay via non-fragile approaches

Revathi Santhana Gopalan; Mallika Arjunan Mani; Jae Hoon Jeong; Revathi Santhana Gopalan; Mallika Arjunan Mani; Jae Hoon Jeong

doi:10.3934/math.2025879

AIMS Mathematics

2025, Volume 10, Issue 8: 19712-19737. doi: 10.3934/math.2025879

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Resilient containment control of fractional-order multi-agent systems with uncertainty and time delay via non-fragile approaches

1.
Department of Mathematics, School of Arts, Sciences, Humanities and Education, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India
2.
College of Computer and Software, Kunsan National University, 558 Daehak-ro, Gunsan-si, 54150, Jeollabuk-do, South Korea

Received: 23 July 2025 Revised: 12 August 2025 Accepted: 22 August 2025 Published: 27 August 2025
MSC : 26A33, 34B15, 34K37

This paper investigated resilient containment control ($ {\mathcal{CC}} $)-based consensus in fractional-order multi-agent systems ($ {\mathcal{FOMAS}s} $) subject to parametric uncertainties, communication time delays, and external disturbances. A non-fragile ($ \mathcal{NF} $) distributed control protocol was proposed to accommodate controller perturbations and delay variations simultaneously. By integrating fractional calculus, algebraic graph theory, and an improved Razumikhin technique, we derived concise algebraic conditions ensuring all followers asymptotically converge to the convex hull that the leaders form under worst-case uncertainties. The results cover non-delayed and delayed cases and are expressed as simple, verifiable matrix inequalities. At the end, we provide examples to demonstrate the feasibility of the proposed method, including a numerical case study, and we illustrate the applicability of the developed theoretical results through designing a controller for electronic circuits.
- Caputo fractional derivative,
- containment control,
- Razumikhin method,
- uncertain parameters,
- non-fragile,
- time delay,
- resilient control
Citation: Revathi Santhana Gopalan, Mallika Arjunan Mani, Jae Hoon Jeong. Resilient containment control of fractional-order multi-agent systems with uncertainty and time delay via non-fragile approaches[J]. AIMS Mathematics, 2025, 10(8): 19712-19737. doi: 10.3934/math.2025879

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Abstract

This paper investigated resilient containment control ($ {\mathcal{CC}} $)-based consensus in fractional-order multi-agent systems ($ {\mathcal{FOMAS}s} $) subject to parametric uncertainties, communication time delays, and external disturbances. A non-fragile ($ \mathcal{NF} $) distributed control protocol was proposed to accommodate controller perturbations and delay variations simultaneously. By integrating fractional calculus, algebraic graph theory, and an improved Razumikhin technique, we derived concise algebraic conditions ensuring all followers asymptotically converge to the convex hull that the leaders form under worst-case uncertainties. The results cover non-delayed and delayed cases and are expressed as simple, verifiable matrix inequalities. At the end, we provide examples to demonstrate the feasibility of the proposed method, including a numerical case study, and we illustrate the applicability of the developed theoretical results through designing a controller for electronic circuits.

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