This paper aims to address the consensus problem for multi-agent systems (MASs) with unknown states, parameter and nonlinear delay functions, where each agent’s dynamics are governed by coupled ordinary and hyperbolic partial differential equations.
A Luenberger-type boundary observer is designed via swapping transformations integrated with a least-squares parameter adaptation law using boundary measurements. An event-triggered boundary controller is developed relying solely on boundary states from neighboring agents and the agent’s own states. Adaptive and convergence analyses are conducted under an undirected communication topology using Yapunov methods and graph theory.
When the feedback gain and a positive definite matrix satisfy certain linear matrix inequalities, both the system states and parameter estimation errors converge exponentially. Asymptotic consensus is achieved without Zeno behavior. The effectiveness of the scheme is verified through numerical simulations of a three-lane highway traffic flow system modeled by the Aw–Rascle–Zhang equations.
This study addresses coupled MASs characterized by realistic complexities, including unknown states, uncertain parameter and nonlinear time delays. The proposed Luenberger-type boundary observer and least-squares adaptation law rely only on boundary measurements, reducing implementation complexity. The event-triggered controller utilizes limited neighbor information, lowering communication burden. Stability is rigorously proven using Lyapunov and graph-theoretic tools, ensuring exponential convergence and exclusion of Zeno behavior. The application to traffic flow systems underscores its practical relevance.
