Time-varying formation consensus for fractional-order multi-agent systems based on sliding mode control

This article addresses the problem of time-varying formation control when the fractional derivatives of the expected formation are different from the fractional multi-agent system. To achieve the infinite convergence of the relative position among agents, the synthetic error of the agent is introduced. Then according to the sliding mode control theory, the sliding mode function is designed based on the defined error. The time-varying formation control problem converts into the asymptotic stability problem of the system. Sufficient conditions for fractional-order multi-agent systems are derived by employing the Lyapunov stability theory, matrix theory, graph theory, and property of fractional-order systems. Finally, two numerical simulations are presented to validate the theoretical analysis.