Interval Consensus of Heterogeneous High-Order Multiagent Systems

This article focuses on the interval consensus problem, which is characterized by the constraint that each agent has a lower and upper bound on the achievable consensus value. Such constraint is realized by setting saturation for neighbors' positions in agent dynamics. By using a novel system transformation, the heterogeneous high-order interval consensus problem then can be transformed into a first-order one, thus restoring the monotonic property, and further facilitating the analysis of the position interval consensus. We introduce a fully distributed absolute damping gain design. When the intersection of the intervals imposed by the agents is nonempty, the resulting positions must converge to a common value inside that intersection. When the intersection of the intervals is empty, there exists a unique, and globally asymptotically stable equilibrium. Numerical simulations have been presented to validate the efficacy of the proposed algorithms.