Distributed containment control with predefined performance of high-order multi-agent systems with unknown heterogeneous non-linearities

This study presents a predefined performance design approach for the distributed containment control of heterogeneous non-linear strict-feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbours of only a subset of the followers. It is assumed that all followers´ non-linearities unmatched in the control input are unknown. The performance bounds, which characterise the convergence rate and maximum overshoot of control errors, are incorporated into the control error vectors, in order to ensure the predefined transient and steady-state performance of containment control errors. On the basis of these error vectors, the authors design a simple distributed containment control system without employing any function approximators to estimate unknown non-linearities and calculating the repeated derivatives of virtual controllers. It is shown from Lyapunov stability theorem that all followers nearly converge to the dynamic convex hull spanned by the dynamic leaders and the containment control errors are preserved within certain given predefined bounds.