Neuro-adaptive fixed-time non-singular fast terminal sliding mode control design for a class of under-actuated nonlinear systems

This paper presents a fixed-time neuro-adaptive control design for a class of uncertain under-actuated nonlinear systems (UNS) using a non-singular fast terminal sliding mode control (TSMC) with a radial basis function (RBF)-based estimator to achieve the convergence and robustness against the uncertainties. The mathematical model of the considered class is reduced into an equivalent regular form. A fast TSMC is designed for the transformed form to improve the control performance and annihilate the associated singularity problem of the conventional TSMC. Lyapunov stability theory ensures the steering of the sliding manifold and system states in fixed time. RBF neural networks are adaptively estimate the nonlinear drift functions. The theoretical design, analysis, and simulations of cart-pendulum and quadcopter demonstrate the feasibility and benefits of the regular form transformation and the designed control design. Comparing the proposed synthesis with the standard literature presents the attractive nature of proposed method for such a class.