In recent, the development of the automotive semi-active suspension (SAS) system with the nonlinear hydraulic adjustable damper (HAD) has attracted widely attention due to its superiorities of low energy consumption, fast response, durable, reliable and simple structure. Many existing SAS researches focus on control algorithms for limited objectives and assume the control signal is the damping force, but very few of them discusses how to realize the calculated damping force. To solve this problem, the unknown regulating mechanism of the nonlinear HAD should be modeled and a complex multi-objective control of the SAS system should be designed. Aiming at modeling the regulating mechanism of the nonlinear HAD, this work constructs a novel compensation system by using fuzzy neural network or grey neural network algorithm in order to realize the desired damping force by regulating the stepper motor angle adaptively. Meanwhile, a new multi-objective control strategy, particle swarm optimization based sliding mode control method, is originally proposed to calculate the desired damping force to achieve exact damping force control of the SAS system. To realize the practical application of the SAS system with the nonlinear HAD, an online hardware-in-the-loop test is conducted on a quarter car test rig. Numerical and experimental results illustrate that the modeled regulating mechanism of the nonlinear HAD and the proposed multi-objective control of SAS system are effective to improve the vertical performance of the vehicle and feasible in practical applications.