Distributed adaptive control for nonlinear multi-agent systems with nonlinear parametric uncertainties

Meiqiao Wang; Wuquan Li; Meiqiao Wang; Wuquan Li

doi:10.3934/mbe.2023576

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12908-12922. doi: 10.3934/mbe.2023576

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Distributed adaptive control for nonlinear multi-agent systems with nonlinear parametric uncertainties

Meiqiao Wang ,
Wuquan Li ^,

School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China

Received: 11 April 2023 Revised: 17 May 2023 Accepted: 25 May 2023 Published: 05 June 2023

This paper considers the distributed tracking control problem for a class of nonlinear multi-agent systems with nonlinearly parameterized control coefficients and inherent nonlinearities. The essential of multi-agent systems makes it difficult to directly generalize the existing works for single nonlinearly parameterized systems with uncontrollable unstable linearization to the case in this paper. To dominate the inherent nonlinearities and nonlinear parametric uncertainties, a powerful distributed adaptive tracking control is presented by combing the algebra graph theory with the distributed backstepping method, which guarantees that all the closed-loop system signals are global bounded while the range of the tracking error between the follower's output and the leader's output can be tuned arbitrarily small. Finally, a numerical example is provided to verify the validity of the developed methods.
- distributed adaptive tracking,
- nonlinear multi-agent systems,
- nonlinear parametric uncertainties,
- unstable linearization,
- global bounded,
- arbitrarily small
Citation: Meiqiao Wang, Wuquan Li. Distributed adaptive control for nonlinear multi-agent systems with nonlinear parametric uncertainties[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12908-12922. doi: 10.3934/mbe.2023576

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Abstract

This paper considers the distributed tracking control problem for a class of nonlinear multi-agent systems with nonlinearly parameterized control coefficients and inherent nonlinearities. The essential of multi-agent systems makes it difficult to directly generalize the existing works for single nonlinearly parameterized systems with uncontrollable unstable linearization to the case in this paper. To dominate the inherent nonlinearities and nonlinear parametric uncertainties, a powerful distributed adaptive tracking control is presented by combing the algebra graph theory with the distributed backstepping method, which guarantees that all the closed-loop system signals are global bounded while the range of the tracking error between the follower's output and the leader's output can be tuned arbitrarily small. Finally, a numerical example is provided to verify the validity of the developed methods.

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