###### Abstract  
To enhance riding comfort for drivers of heavy-duty vehicles, this paper introduces a novel adaptive prescribed performance control (APPC) for active seat suspension systems. The model incorporates dynamic friction and hysteresis damping effects to capture the complex behavior of the seat suspension. The accuracy of the proposed model is validated through experimental data. The controller utilizes a prescribed performance function (PPF) to regulate the dynamic response of the system, combined with an adaptive backstepping control (ABC) method to account for system uncertainties, such as variations in driver weight, friction, suspension stiffness, and damping coefficients. A set of parameter estimators, governed by innovative adaptive laws, compensates for estimation errors. Furthermore, the stability of the controlled system is rigorously demonstrated. Both simulation and experimental tests, including bump and random excitation tests, are conducted to assess the controller performance in both time and frequency domains. The results confirm that the proposed controller effectively mitigates vibrations in the driver-seat system and demonstrates robustness against system uncertainties. S Date: 20  
However, it is widely believed that active seat suspension is more efficient in isolating the vibration [5]. It is worth noting that many studies on vehicle suspension can be used as valuable references for seat suspension design due to their similar topologies. From the perspective of control method, one can observe that most of the advanced control scheme for active suspension are designed using H-infinity control [6; 7; 8; 9], backstepping control [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20], sliding mode control (SMC) [21; 22; 23; 24], fuzzy control [25; 26; 27], Linear-Quadratic-Gaussian (LQG) control [28; 29; 30], and hybrid control methods [31; 32; 33; 34; 35; 36; 37; 38; 39]. In the review of these literatures, one can find that a major difficulty in controlling the suspension is the uncertainties of system parameters, such as the variation of sprung mass (passenger weight) and suspension characteristics. The stiffness and damping coefficients of a conventional suspension may vary with the application environment, such as the temperature, fatigue, and aging process [12]. In order to deal with the uncertain parameters, the adaptive control method is widely employed. By incorporating the backstepping control or SMC, adaptive control has proved its effectiveness in handling parameter uncertainties [11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. In [31; 32; 34], neural networks (NNs) are adopted to estimate unknown nonlinear dynamics and uncertain parameters in active suspension systems. These studies commonly employ adaptive control frameworks in which NNs approximate the system's uncertainties, such as sprung mass variation, nonlinear spring-damper forces, or unmodeled disturbances. By integrating NN-based estimation with advanced control schemes--such as barrier Lyapunov functions, prescribed performance functions, or robust observers--they ensure boundedness or the convergence of tracking errors while satisfying system constraints. The Takagi-Sugeno (T-S) fuzzy method provides an alternative way to handle these uncertainties without designing adaptive laws. In [37; 38], dynamic sliding-mode controllers based on T-S fuzzy models are developed to handle nonlinearities and uncertainties in active suspension systems. The results show improved ride comfort and robustness, while ensuring suspension deflection and road-holding constraints under varying vehicle conditions. In [38; 40], an approximation-free control method is presented, which can deal with uncertainties without using an estimator. The performance of the active suspension relies heavily on the dynamic behavior of the actuator. In many of the existing studies, such as [10; 11; 40], the actuator is modelled as a simple linear function of the control signal.