Estimator-Based Second-Order Sliding Mode Control Design for Nonlinear Systems With Unknown Input Delay

In this article, we propose an estimator-based second-order sliding mode (SOSM) controller tailored for uncertain nonlinear systems with unknown input delay. Distinct from existing SOSM control methods, this work tackles two principal challenges: 1) the difficulty of dealing with unknown input delay, especially given the discontinuity of sliding mode controllers; and 2) the uncertainties in the nonlinear systems bounded by functions rather than widely-used constants. We begin by establishing the SOSM dynamics with input delay and uncertainties, followed by the introduction of an auxiliary compensation system. Then, we design an input delay estimator suitable for discontinuous controllers by enhancing the convex optimization method. Leveraging this, a novel estimator-based SOSM controller is constructed by adding a power integrator technique to address the input delay issue. Rigorous Lyapunov analysis is conducted to confirm the finite-time stability of the closed-loop control system. Finally, comparative simulations validate the superiority of the proposed SOSM controller.