Adaptive neural hierarchical sliding mode control for uncertain switched underactuated nonlinear systems against unmodeled dynamics and input delay

In this article, the issue of adaptive control for switched underactuated systems subject to input delay and unmodeled dynamics is investigated. Unlike traditional backstepping methods, this paper introduces a hierarchical sliding mode control (HSMC) approach that can improve the response rate and robustness of the controlled plant. Under the framework of this control method, a top hierarchical sliding mode surface (HSMS) containing all the information of state variables and an effective controller consisting of switching control laws and equivalent control laws are constructed. In the control design process, an auxiliary system and a hyperbolic tangent function are introduced to compensate for the impact of input delay while avoiding singularity problems. In addition, a dynamic signal is designed to compensate the effect of the unmodeled dynamics. The designed controller can ensure that all signals of the closed-loop system, including states of the auxiliary system, are bounded. Finally, the benefits of the proposed HSMC approach are confirmed by two simulation examples.