## 1 Introduction  
Hydropneumatic suspensions have superior nonlinear stiffness and damping characteristics, and interconnected hydropneumatic suspensions can achieve different performance requirements through different interconnection forms, such as anti-roll, anti-pitch, and anti-vertical functions. Hydropneumatic suspensions are often used in special vehicles. Compared with those of ordinary heavy vehicles, the road conditions of special vehicles are complex and changeable, and they require greater mobility. Passive X-type interconnected hydropneumatic suspensions can provide both anti-roll and anti-pitch moments, with superior performance, a simple structure, and easy implementation. After being designed and installed, their stiffness and damping can be fixed. When road excitation changes and depending on whether the load is empty or full, the corresponding optimal stiffness and damping are different. The suspension may be too hard or too soft, which limits the performance improvement of special vehicles. In addition, if the hydropneumatic suspension works under a high load for a long time, it may also cause accidents such as leakage, thereby shortening the service life of the suspension and reducing safety. Active suspensions can control the filling and discharging of oil and gas spring cylinders through an external oil source, achieving the active control of interconnected hydropneumatic suspensions. This effectively improves the smoothness and stability of a vehicle under different road excitations or empty as opposed to full loads. Scholars globally have directed their attention to control methodologies. [PERSON] et al. [1] constructed a semi-vehicle dynamic model and devised a fuzzy PID controller to regulate the active hydropneumatic suspension's output force, leading to notable enhancements in suspension performance. [PERSON] et al. [2] created a two-DOF (degrees of freedom) active suspension model for a quarter-car setup, formulated fuzzy control rules, and engineered fuzzy controllers accordingly. [PERSON] et al. [3] examined the influence of SMC (sliding-mode control)-based active suspension on automotive performance. [PERSON]. [4] introduced an MPC active suspension system, utilizing body state identification to determine the braking model and thereby manage the suspension damping force. [PERSON] et al. [5] proposed an LQR controller optimized by a particle swarm optimization algorithm, simulating both passive and adaptive dynamic models of air suspension systems. [PERSON] and colleagues [6] crafted a fuzzy PID controller tailored to a quarter-vehicle model featuring active air suspension. [PERSON] et al. [7] incorporated fuzzy control into a seven-DOF model of a hydropneumatic suspension. [PERSON] [8] proposed an active hydraulic interconnected suspension system based on robust \(H\infty\) control. The above single-control method often has difficulty in meeting the performance requirements of heavy-duty special vehicles, and the composite control theory combined with a variety of control strategies can lead to more efficient, accurate, and stable system control. An active controller leveraging both ESO and MPC was devised to overcome the challenges posed by the passive X-type interconnected hydropneumatic suspension's limited adaptability to diverse road surfaces and the inadequate performance of traditional single-mode control strategies. The improved controller for MPC based on the ESO accurately controls the output force of the hydropneumatic suspension, and the hydropneumatic suspension's performance is refined, resulting in improved ride comfort and stability for special vehicles. Compared with fuzzy PID, ESO-MPC can handle multivariable and nonlinear systems, estimate unmodeled dynamics, and external disturbances of the system through an extended state observer (ESO) and has stronger disturbance resistance [9]. MPC can explicitly handle constraints (such as input and state constraints) by optimizing future state trajectories [10].