This article attempts to clarify the question of what the essential difference between the optimal and “clipped-optimal” control is that the Hamilton–Jacobi–Bellman or Hamilton–Jacobi–Isaacs partial differential equation is linear or nonlinear. An adaptive optimal control based on policy iteration to the constrained semi-active vehicle suspension system with a magnetorheological damper is presented. The problem of improving the optimal performance of semi-active control suspension system is converted to L₂-gain optimal control problem. A two-player policy iteration scheme is employed to solve the Hamilton–Jacobi–Isaacs equation by use of neural networks to approximate optimal policies and value functions in the admissible global region. Simulation results demonstrate that the adaptive optimal controlled semi-active vehicle suspension system outperforms greater than that of the clipped-LQR controlled.

The ride stability and driving comfort of vehicles are highly dependent on the performance of the damping system. The fatigue life prediction of damping components using rubber as the core damping material has become a research hotspot in the field of vehicle vibration isolation. Taking an automotive engine rubber isolator as the research carrier, this paper jointly carries out finite element simulation analysis and structural component fatigue life tests. A dual-parameter mapping framework is proposed, which integrates maximum strain energy density and cyclic energy dissipation instead of using a single damage indicator. This approach comprehensively accounts for the coupling effect of energy storage and energy dissipation coexisting under actual service conditions. Through uniaxial tensile tests on rubber specimens, combined with finite element simulations and physical model parameters, a quantitative mapping relationship between laboratory specimens and full-scale engine rubber isolators is established. Based on this mapping, the fatigue life curve of the isolator is derived from the specimen-based failure characteristics. Validation tests under two randomly selected operating conditions yield prediction errors of 7.5% and 6.9%, demonstrating that the proposed model can accurately achieve equivalent fatigue life transformation from small specimens to actual components. Unlike conventional direct extrapolation methods, this approach does not require complex multiaxial fatigue tests on the component itself; it only needs simple specimen fatigue data, significantly reducing development costs, while providing a reliable theoretical basis for material selection, fatigue performance optimization, and forward structural design of rubber isolators.