On Safe Sliding Mode Control Design for Nonlinear Uncertain Systems

This article introduces a safe sliding mode controller designed to ensure both stability and safety in nonlinear uncertain systems. The proposed architecture combines two feedback loops: an inner sliding mode controller that ensures robust asymptotic stability, and an outer safeguarding loop that enforces safety constraints. By augmenting the system with a state variable whose dynamics are derived from Lyapunov theory, we establish a control barrier function (CBF) framework that guarantees finite-time convergence to a stabilizing sliding manifold while maintaining safety. The method features two key innovations: 1) a noninvasive safeguarding control that limits interference with the robust stability objective by employing a risk-set-triggered mechanism, and 2) closed-form expressions for the control input, which eliminate the need for solving quadratic programs (QP), significantly reducing computational burden. Theoretical analysis proves that the proposed controller ensures system stability and provides robust safety assurances under matched uncertainties. Simulation studies validate the approach across three representative scenarios. Results show the controller maintains safety without significant performance degradation, while outperforming QP-based safety-critical controllers in terms of computational efficiency.