Adaptive SOSM Control for Nonlinear Systems with Parametric Uncertainties and Time-Varying Asymmetric Output Constraints

In this article, a new adaptive second-order sliding mode (SOSM) controller is designed for a type of nonlinear systems with parametric uncertainties and time-varying asymmetric output constraints. There are two notable features in the obtained results. One feature is that a two-layer adaptive mechanism is established to reconstruct the upper bound of the unknown uncertainty, where the uncertainty is bounded by an unknown state-dependent structure rather than an unknown constant. The other is that a universal tangent-type barrier Lyapunov function (Tan-BLF) is constructed to address the time-varying asymmetric output constraint requirements. By combining the designed Tan-BLF, adaptive control and revamped adding a power integrator techniques together, a novel design procedure is introduced to systematically construct an adaptive SOSM controller. A rigorous Lyapunov analysis indicates that under the developed control framework, the finite-time stability of the whole system and the realization of the prescribed constraints can be guaranteed. Finally, two simulation cases containing a practical one are provided to demonstrate the effectiveness of the proposed control scheme. Note to Practitioners - This article is motivated by the desire to deal with nonlinear systems in the presence of parameter uncertainties and time-varying output constraints. In practical applications, on the one hand, parameter uncertainties are an unavoidable problem for real-world systems, and on the other hand, output constraints are widely present in many engineering systems due to safety considerations and inherent physical constraints. Until now, these issues have not been solved effectively. Therefore, to resolve these issues, a new adaptive SOSM controller is constructed in this article by using the adaptive control technique, adding a power integrator method, time-varying asymmetric Tan-BLF and Lyapunov finite-time stability theory. The proposed control strategy not only ensures the finite-time stability of the resulting closed-loop system, but also guarantees that the system output satisfies the preset time-varying output constraints. In the future, we will attempt to apply the proposed method to more practical systems.