Fixed-Time Control of Nonlinear Systems With Experimental Verification

This article proposes the design of a fixed-time nonsingular backstepping controller for second-order nonlinear systems. We adopt a variable exponent coefficient for the design of the backstepping controller, which can render fixed-time stability. The estimate of the settling time is obtained through the Lyapunov stability analysis using level sets. The proposed method overcomes the limitations of singularity in control law, which is generally observed in fixed-time backstepping control framework. The controller structure is then applied to solve the tracking problem of Euler-Lagrange systems in the presence of uncertainty. A robust fixed-time control scheme is presented with variable exponent backstepping and integral sliding mode control. The stability of the overall closed-loop system is presented using Lyapunov analysis. The verification of the proposed control scheme is done through simulation and experimental studies.