Switching Prescribed-Time Adaptive Second-Order Sliding Mode Control Subject to Unknown State-Dependent Uncertainties

In this article, a switching prescribed-time adaptive second-order sliding mode (ASOSM) control framework is proposed for a category of nonlinear systems with unknown time-varying parameters. The design procedure is systematically conducted in three steps. First, by appropriately constructing the sliding variables, the original uncertain system is transformed into a new sliding mode dynamics that alleviates the restrictive relative-degree requirement and reduces input-channel uncertainties. Second, leveraging a time-scaling transformation and a modified adding a power integrator (API) technique, a switching prescribed-time ASOSM controller integrated with parameter adaptation mechanisms is constructed. Third, a rigorous Lyapunov-based stability analysis is provided, showing that the sliding variables are driven into an arbitrarily small neighborhood of the origin within a user-assigned prescribed time, independently of the initial conditions, and subsequently stabilized to the equilibrium point in a finite time. The distinctive merit of the proposed switching control scheme is its capability to handle both matched and mismatched uncertainties, without requiring prior knowledge of their state-dependent bounds. Finally, two representative examples are provided to illustrate the effectiveness of the developed switching control strategy.