Adaptive tracking control for impact oscillator systems with uncertain parameters

In nonlinear dynamics, the impact oscillator system exhibits complex dynamical behaviours and has extensive engineering applications. It is highly sensitive to initial conditions, external disturbances, and parameter variations. Therefore, tracking control of the oscillator is of vital importance. This paper innovatively integrates multiple control theories to propose a new adaptive tracking control method under parameter uncertainties. The control strategy handles unknown parameters through an adaptive mechanism and optimises the control law. Based on Lyapunov's theorem, a rigorous stability analysis framework for nonsmooth systems is established, and stability conditions are derived. Numerical simulations show that the system achieves effective tracking control for multiple periodic solutions, with errors asymptotically converging to zero, thus validating the effectiveness of the proposed strategy. This study provides a new solution for the stability control of nonsmooth dynamical systems.