Fixed-time sliding-mode distributed consensus and formation control of disturbed fractional-order multi-agent systems

ISA Trans. 2023 Jul:138:37-48. doi: 10.1016/j.isatra.2023.03.010. Epub 2023 Mar 17.


In this paper, fixed-time consensus and formation control for fractional-order multi-agent systems with a dynamic virtual leader in the presence of external disturbances is investigated. Consensus is achieved in fixed-time, i.e., with a finite settling time whose upper bound is independent of the initial conditions of the agents' states. A new distributed sliding-mode control with neighborhood-based error variable is proposed to track a virtual leader in order to achieve a desired consensus in the presence of disturbances. Furthermore, the fractional Lyapunov stability theorem has been employed to prove the fixed-time stability and to estimate the upper bound of convergence. The formation of agents has also been investigated for the agents of fractional-order. Finally, several numerical simulations are provided to determine the effectiveness of the design method.

Keywords: Fixed-time convergence; Fractional-order multi agent systems; Sliding-mode; Virtual leader.