Distributed convex optimization of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints

Yuhang Yao; Jiaxin Yuan; Tao Chen; Xiaole Yang; Hui Yang; Yuhang Yao; Jiaxin Yuan; Tao Chen; Xiaole Yang; Hui Yang

doi:10.3934/mbe.2023770

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 9: 17296-17323. doi: 10.3934/mbe.2023770

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Research article

Distributed convex optimization of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints

1.
School of Air Transportation, Shanghai University of Engineering Science, Shanghai 201620, China
2.
College of Engineering, China Agricultural University-East Campus, Beijin 100083, China

Academic Editor: Yang Kuang

Received: 14 July 2023 Revised: 16 August 2023 Accepted: 28 August 2023 Published: 07 September 2023

This article investigates a penalty-based distributed optimization algorithm of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints. The proposed method addresses the distributed optimization problem by designing a penalty function in the form of a quadratic function, which is the sum of the global objective function and the consensus constraint. Moreover, the observer is presented to address the unmeasurable state of each agent. Radial basis function neural networks (RBFNN) are employed to approximate the unknown nonlinear functions. Then, by integrating RBFNN and dynamic surface control (DSC) techniques, an adaptive backstepping controller based on the barrier Lyapunov function (BLF) is proposed. Finally, the effectiveness of the suggested control strategy is verified under the condition that the state constraints are not broken. Simulation results indicate that the output trajectories of all agents remain within the upper and lower boundaries, converging asymptotically to the global optimal signal.
- multi-agent systems,
- distributed optimization,
- bipartite containment control,
- state constraints,
- dynamic surface control
Citation: Yuhang Yao, Jiaxin Yuan, Tao Chen, Xiaole Yang, Hui Yang. Distributed convex optimization of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 17296-17323. doi: 10.3934/mbe.2023770

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Abstract

This article investigates a penalty-based distributed optimization algorithm of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints. The proposed method addresses the distributed optimization problem by designing a penalty function in the form of a quadratic function, which is the sum of the global objective function and the consensus constraint. Moreover, the observer is presented to address the unmeasurable state of each agent. Radial basis function neural networks (RBFNN) are employed to approximate the unknown nonlinear functions. Then, by integrating RBFNN and dynamic surface control (DSC) techniques, an adaptive backstepping controller based on the barrier Lyapunov function (BLF) is proposed. Finally, the effectiveness of the suggested control strategy is verified under the condition that the state constraints are not broken. Simulation results indicate that the output trajectories of all agents remain within the upper and lower boundaries, converging asymptotically to the global optimal signal.

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