Adaptive Prescribed-Time SOSM Controller Design for Nonlinear Systems With Prescribed Performance

The paper is devoted to the design of a prescribed-time adaptive second-order sliding mode (ASOSM) controller for a class of nonlinear systems with prescribed performance constraints. First, a time-varying prescribed performance barrier Lyapunov function (PPBLF) and a scaling function (SF) are introduced to handle the issues of prescribed performance constraint and prescribed-time stability, respectively. Subsequently, by combining the PPBLF and SF with the backstepping-like technique, an ASOSM controller, which ensures that the whole sliding mode dynamics is prescribed-time stable and satisfies the prescribed performance constraints, is systematically designed. Significantly, the proposed ASOSM controller contains two variable parameters, which are respectively used to reconstruct the upper bound of the state-dependent structure of uncertainty and generate the adaptive control gains. At last, a practical case is provided to validate the effectiveness of the developed scheme.