Adaptive neural predefined-time hierarchical sliding mode control of switched under-actuated nonlinear systems subject to bouc-wen hysteresis

For switched under-actuated systems subject to bouc-wen hysteresis, an adaptive neural predefined-time control scheme is presented first time in this paper. To improve the robustness and response rate of the system under consideration, a hierarchical sliding mode control technique is introduced. Based on a predefined-time stability criterion, the stabilization time of the system can be directly preset under the designed controller. Besides, the convergence time depends only on the preset value and is independent of all other parameters. The projection algorithm is introduced to avoid the singularity problem in the controller design process. Meanwhile, it is proved that all signals of the closed-loop system are bounded after a preset time through the Lyapunov stability theory. Finally, a simulation example and a comparison example are given to further illustrate the effectiveness and superiority of developed control approach.