Barrier Function-Driven Robust Fixed-Time Leader–Follower Consensus with Variable Exponent Control

Abstract

This paper presents a fixed-time sliding mode control (FXT-SMC) scheme for multi-agent systems (MASs) having double-integrator dynamics to address the leader-follower consensus (LFC) problems. The proposed consensus strategy employs a variable exponent which depends on the state to ensure fixed-time convergence under the SMC framework. A barrier-function-based adaptive algorithm is introduced to avoid overestimation of gain. This mechanism dynamically regulates the discontinuous control gain and prevents unnecessary gain overestimation, thereby reducing chattering in the control input. The input-to-state stability (ISS) of the fixed-time protocol for leader–follower consensus dynamics is rigorously proven through Lyapunov-based analysis. Finally, simulation studies are carried out to demonstrate and validate the performance and feasibility of the introduced control design approach.