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针对一类由偏微分方程建模的多智能体系统一致性控制问题，提出了一类空间边界耦合方法。边界耦合方法与传统的状态耦合方法相比具有更为灵活和有效的特性。首先，研究了2种不同的Neumann边界耦合形式：同位边界耦合和异位边界耦合，这2种耦合形式为多智能体系统提供了更为多样化的协作机制。然后，在控制设计中引入状态观测器来对系统状态进行预估，状态观测器能有效地捕捉系统动态，并在一定程度上减少由于信息传递延迟而带来的负面影响。同时采用Lyapunov理论和积分不等式方法来保证系统的观测误差和一致性误差以指数形式收敛，得出在2种边界耦合下系统一致性的2个充分条件。最后，通过2个具体的例子验证了所提出的空间边界耦合方法的有效性。实验结果表明：在不同的边界耦合形式下，多智能体系统均能实现较好的一致性控制，进一步证明了边界耦合在多智能体系统中的潜在应用价值。
Abstract：A spatial boundary coupling approach is developed for consensus control in multi-agent systems governed by partial differential equations, demonstrating enhanced flexibility and efficiency relative to conventional state coupling techniques. Two Neumann boundary coupling variants — isostatic and heterotopic — are analyzed, each facilitating distinct cooperative interactions among agents. A state observer is incorporated into the control framework to estimate system states, capturing dynamic behavior and attenuating the effects of information transmission delays. Lyapunov theory and integral inequalities are applied to establish exponential convergence of observation and consensus errors,yielding two sufficient conditions for achieving consensus under the respective coupling schemes. Validation is conducted through two examples, with experimental outcomes confirming effective consensus across both coupling configurations, highlighting the applicability of boundary coupling to multi-agent systems.
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基本信息:
DOI：10.12194/j.ntu.20240722001
中图分类号:TP13
引用信息:
[1]万兴龙,杨成东,李振兴等.一类基于观测器的多智能体系统一致性边界耦合方法[J].南通大学学报(自然科学版),2025,24(01):40-50.DOI:10.12194/j.ntu.20240722001.
基金信息:
国家自然科学基金面上基金项目（62476117）; 云南省科技厅科技发展计划项目（202302AD080006）; 山东省自然科学基金项目（ZR2022MF222）