A kind of observer-based consensus boundary coupling method for multi-agent systems

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.