Sliding-Mode Control of Full-State Constraint Nonlinear Systems: A Barrier Lyapunov Function Approach

This study presents the design of a robust control based on the sliding-mode theory to solve both; the stabilization and the trajectory tracking problems of nonlinear systems subjected to a class of full-state restrictions. The selected nonlinear system satisfies a standard Lagrangian structure affected by nonparametric uncertainties. A barrier Lyapunov function is used to ensure the state constraints by designing a time-varying gain, which guarantees the fulfillment of the predefined state constraints even under external perturbations. The proposed design methodology for the barrier sliding-mode control (BSMC) ensures the convergence of the sliding surface in finite time to the origin. Consequently, the asymptotic convergence of the states to the corresponding equilibrium point is achieved. The finite-time stability of the origin in the closed-loop system with the proposed controller has been demonstrated using the second Lyapunov stability method. The suggested controller was evaluated on a two-link robotic manipulator. Then, the obtained results showed better stabilization and tracking performances (while the restrictions are satisfied) than the traditional first-order sliding-mode or linear state feedback controllers.