Data-driven iterative learning consensus control for linear parabolic distributed parameter multi-agent systems

Lanlan Liu; Xisheng Dai; Lanlan Liu; Xisheng Dai

doi:10.3934/math.2026522

AIMS Mathematics

2026, Volume 11, Issue 5: 12687-12704. doi: 10.3934/math.2026522

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Research article

Data-driven iterative learning consensus control for linear parabolic distributed parameter multi-agent systems

Lanlan Liu ¹,
Xisheng Dai ^{2,3
,
,}

1.
School of Business, Chongqing College of Finance and Economics, Chongqing 402160, China
2.
School of Computer Science, Guangdong University of Finance, Guangzhou 510520, China
3.
School of Automation, Guangxi University of Science and Technology, Liuzhou 545616, China

Received: 13 February 2026 Revised: 09 April 2026 Accepted: 15 April 2026 Published: 08 May 2026
MSC : 93A16, 93C20, 68T07

To address the consensus control challenge in model-unknown linear parabolic distributed parameter multi-agent systems, this paper proposes a novel data-driven iterative learning control (DDILC) method. A forward difference scheme is adopted to discretize the spatiotemporal dynamics, thereby establishing a data-driven input-output model that eliminates reliance on precise mathematical formulations. Neural network approximates the unknown linear operators, and an error-driven iterative learning law updates the network weights online to compensate for unmodeled dynamics and uncertainties. Rigorous Lyapunov-based analysis verifies the boundedness of the weight errors and the exponential convergence of the consensus tracking errors. Numerical simulations with one virtual leader and four followers confirm that all agents achieve precise consensus tracking within 20 iterations, with errors converging to within 0.01. This method overcomes the limitations of traditional model-based control, offering an efficient solution for consensus control in engineering applications such as UAV swarms and intelligent industrial collaboration.
- data-driven iterative learning control,
- distributed parameter multi-agent systems,
- neural network,
- consensus control
Citation: Lanlan Liu, Xisheng Dai. Data-driven iterative learning consensus control for linear parabolic distributed parameter multi-agent systems[J]. AIMS Mathematics, 2026, 11(5): 12687-12704. doi: 10.3934/math.2026522

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Abstract

To address the consensus control challenge in model-unknown linear parabolic distributed parameter multi-agent systems, this paper proposes a novel data-driven iterative learning control (DDILC) method. A forward difference scheme is adopted to discretize the spatiotemporal dynamics, thereby establishing a data-driven input-output model that eliminates reliance on precise mathematical formulations. Neural network approximates the unknown linear operators, and an error-driven iterative learning law updates the network weights online to compensate for unmodeled dynamics and uncertainties. Rigorous Lyapunov-based analysis verifies the boundedness of the weight errors and the exponential convergence of the consensus tracking errors. Numerical simulations with one virtual leader and four followers confirm that all agents achieve precise consensus tracking within 20 iterations, with errors converging to within 0.01. This method overcomes the limitations of traditional model-based control, offering an efficient solution for consensus control in engineering applications such as UAV swarms and intelligent industrial collaboration.

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