## 1 Introduction  
Electrohydraulic systems are currently utilized extensively in a variety of industrial and transport applications [1, 2, 3, 4, 5, 6], e.g., construction machines [7], robot manipulators [8], load simulators [9], and steering systems [10]. Hydraulic pressure control performance is critical in particular situations, e.g., tunneling boring machine thrust force control and hydraulic press forming force control. In general, two kinds of hydraulic system configurations are used for these applications. One feasible method is to regulate the supply flow to the cylinder chamber by using an electrohydraulic servo/proportional valve [1, 11, 12, 13, 14, 15], which enables satisfactory dynamic behavior. Another approach is to regulate flow using a variable flow pump; this solution offers better energy efficiency [16], but the system bandwidth is restricted by the response speed of the pump, in which the moving parts' inertia is much larger than that of the servo/proportional valve. A solution was proposed by combining an electrohydraulic servo valve with a variable displacement pump [17]. In this configuration, the pump drives the cylinder together with the valve. To obtain better dynamic performance for electrohydraulic cylinder control, various control methods have been used [18, 19, 20]. A strategy featuring double closed-loop compound robust control was proposed to deal with the underperformance of double pump-double valve-controlled motors due to external interference, such as poor stability of output speed, low controllability, and difficulties in managing synchronous output [21]. A sliding-mode controller of a single-channel motor was designed for the inner loop, while double-channel cross-coupled closed-loop control was applied to the outer loop. A novel pump-valve compound drive system was designed in [22], and a force control method combining tracking error compensation and load compensation control was designed. In [23], a time-sharing controller was proposed for motor pump-valve control systems. During the high-flow period, the cylinder is controlled by adjusting the speed of the control motor, while during the low-flow period, the cylinder is controlled by the form of the valve-controlled cylinder. Valve-pump parallel variable mode control for hydraulic speed regulation systems, which established a flexible control mechanism using pump control and valve control, was proposed in [24]. In [25], valve-pump parallel variable structure control was proposed for a variable speed hydraulic system. Leaking parallel valve control was applied to improve low-speed performance at the start and stop stages by increasing damping ratios and compensating for the reduction in damping ratios due to the negative friction slope. In these studies, linear control strategies were employed, but the control performance was often unsatisfying if the working conditions varied dramatically [26]. To increase tracking performance, sliding mode control was used for electrohydraulic cylinder pressure control [27; 28; 29], but chattering phenomena may excite unwanted frequency modes and degrade the tracking performance. [PERSON] [11] showed that by accounting for the nonlinear behavior and parameter uncertainties of the plant, a high tracking performance could be achieved, and this control strategy was also verified in [30; 31]. In general, many control strategies for a dual-actuator-driven electrohydraulic actuator mainly focus on parameter uncertainties and disturbances in the system, but the actuator constraints, e.g., the stroke and velocity limit of the control valve and variable displacement pump, are not considered. If these constraints are violated, the closed-loop system control performance will significantly degrade. Figure 1 depicts the electrohydraulic system considered in this paper. It consists of a proportional valve and variable displacement pump.