Finite-time tracking control of nonsmooth impact-vibration capsule systems

In light of the nonsmooth and complex dynamic characteristics of the impact capsule system, this paper proposes a novel finite-time tracking control strategy. Compared with conventional asymptotic control methods, the proposed approach not only effectively suppresses basin hopping induced by noise and significantly enhances system robustness but also enables the capsule robot to achieve fast and accurate trajectory tracking. Furthermore, through rigorous dynamic analysis and mathematical proof based on Lyapunov stability theory, this study establishes finite-time stability criteria for the closed-loop system, providing a theoretical basis for system performance evaluation. Numerical simulation results demonstrate that the designed controller excels in multistability regulation and chaos suppression. Regardless of whether the initial state lies in a multistable or chaotic region, the system can rapidly and accurately track the desired motion trajectory. The research outcomes also offer valuable insights for the control design of other nonsmooth dynamical systems.