Fixed-time convergent observer-based tracking control with variable exponential coefficients for high-order multiagent systems under directed interaction topology

This paper investigates the fixed-time consensus tracking control problem for high-order multiagent systems under directed interaction topology. To address the limitation of constant exponential coefficients in existing studies, a novel distributed state observer is proposed, whose core feature is the state-dependent exponential coefficients. Specifically, the exponents in the observer are designed as functions of the observation state, enabling them to adapt dynamically based on the magnitude of the state, rather than remaining constant. This adaptive adjustment mechanism contributes to enhanced estimation convergence performance. Building upon this observer, a corresponding distributed fixed-time tracking protocol with the same variable exponential philosophy is designed. Theoretical analysis proves fixed-time convergence independent of initial conditions. Simulation results demonstrate that this variable exponential strategy achieves a faster convergence speed compared to the traditional constant exponential approach.