Distributed finite‐time formation control of multiple Euler–Lagrange systems under directed graphs

This paper investigates the finite-time formation problem of multiple Euler-Lagrange systems subject to model uncertainties and external disturbances under directed graphs. An adaptive distributed control approach is developed by integrating dynamic gain control and adaptive control based on the consensus theory and the finite-time stability theory. Auxiliary scalar dynamics are constructed to facilitate dynamic gain design. It is shown that finite-time formation can be achieved via the proposed non-smooth controller characterized by fractional powers of the auxiliary dynamics, which is significantly different from most existing works on finite-time controllers where fractional powers of system states are adopted. Moreover, continuity of the proposed controller is guaranteed by adjusting one control parameter, of which range is proven explicitly. In addition, dynamic surface control is improved to remove acceleration information from finite-time controller design. In the end, the effectiveness of the proposed control approach is verified by numerical simulation.