Safe Sliding Mode Controllers for Nonlinear Uncertain Systems

Abstract: In this study, we present a novel sliding mode safety-critical controller designed to address both stability and safety concerns in a class of nonlinear uncertain systems. The controller features two feedback loops: an inner loop designed by conventional sliding mode techniques and an outer safeguarding loop aimed at enhancing system safety. The inner loop, while ensuring asymptotic stability of the closed-loop system, may not guarantee compliance with safety constraints. To overcome this limitation and ensure both stability and safety, the outer loop introduces a correction term known as the safeguarding control signal. This signal is added to the unsafe control signal generated by the inner loop, effectively modifying it to meet the required safety constraints. To design the safeguarding control law, we integrate the system dynamics with an additional state variable. The dynamics of this augmented state are derived based on a stability constraint obtained from Lyapunov theory. By utilizing a control barrier function for the augmented system, we determine the safeguarding control signal, which ensures the system operates within the defined safety constraint. The proposed safety-critical controller exhibits finite-time convergence to the sliding manifold. To mitigate interference between the inner and outer loops, strategies such as defining risky sets are employed, limiting the impact of the safeguarding loop on the functionality of the inner loop. A closed-form solution for designing safeguarding control laws is derived to eliminate the necessity for solving any quadratic problems in real-time. Simulation case studies validate the effectiveness of the proposed controller in maintaining stability and safety.