Fixed-time stabilisation and tracking control for nonlinear system

This paper proposes an adaptive fixed-time control scheme for high-order nonlinear systems, synergising a dual dynamic gain mechanism with a novel integral Lyapunov function. By introducing the improved integral Lyapunov function, the fixed-time controller is designed. Two dynamic gains with decoupled update laws are built to assist in stabilising the closed-loop systems. Theoretical analysis and simulation results demonstrate that the error signals of closed-loop system converge to zero within a prescribed fixed time independent of initial conditions, achieving superior convergence speed and tracking accuracy compared to existing methods.