Feedback controlled adaptive time-stepping for energy preserving variational integration

High-fidelity physical simulation is a cornerstone of embodied intelligence, yet simulating high-dimensional nonlinear multi-body systems involves a fundamental trade-off between numerical stability and computational efficiency. Conventional explicit integrators suffer from energy drift in long-horizon tasks. Conversely, symplectic variational integrators (VIs) often have high computational costs due to implicit constraints. To bridge the gap, this paper reformulates the step-size adaptation as a dynamic closed-loop feedback control process instead of a rigid root-finding problem, proposing a Control-Theory-Inspired Adaptive Time-step Variational Integrator (C-ATSVI). A Lyapunov-based controller is designed to ensure asymptotic stability of the energy error, augmented by the Internal Model Principle (IMP) to eliminate steady-state residuals caused by numerical truncation. Simulations on a low-dimensional 2-DoF pendulum, a high-dimensional 7-DoF pendulum and a 7-DoF manipulator with external force are conducted. Numerical results demonstrate that C-ATSVI achieves energy fidelity comparable to adaptive schemes, while maintaining computational efficiency similar to explicit fixed-step methods. Therefore, the proposed method offers a robust solution for analyzing complex Hamiltonian dynamics.