## 1 Introduction
### Related Works  
From a system and control point of view, the tractor-trailer is considered a complex and nonlinear system that has limitations on its articulation state as well as the steering input. Although the system is internally stable when moving forward, it becomes unstable and difficult to control when driving in reverse due to its under-actuation [1] and propensity for jackknifing. Additionally, there is a restricted range of articulation angle values beyond which it cannot be maneuvered in the backward direction. Hence, an in-depth treatment of the tractor-trailer maneuverability conditions and a jackknife prevention system are presented by [PERSON] et al. in ref. [2]. The literature on the topic of truck trailer systems presents a multitude of control methods for both forward motion and backward (reverse) driving. For the forward path-following problem, several controllers were adopted. To name a few, a Linear Quadratic Regulator (LQR) in ref. [1], robust controller via feedback linearization [3], back-stepping [4], Model Predictive Control (MPC) [5], and a Sliding mode approach for formation control [6] have been proposed. For backward movement, researchers tend to redesign the forward motion controllers to overcome the instability issues in backward motion. Some approaches use geometrical coordinate transformations to make the control algorithms simpler and allow for the application of methods used for forward driving [7; 8]. Other methods solve the nonlinear backing control problem directly, by utilizing concepts of artificial neural network controllers [9; 10; 11; 12], nonlinear feedback stabilization [13; 14; 15], fuzzy control and systems [16; 17; 18], or explicit Model Predictive Control [19; 20]. The control methods may vary based on the location of the hitch, with on-axle hitch vehicles being differentially flat, while off-axle hitch vehicles are not. These approaches have been successful in addressing the control challenges posed by tractor-trailer vehicles moving in reverse. Moreover, control methods for tractor-trailer vehicles could also be further classified based on the location of the hitch. Systems of articulated vehicles with hitches on the axle exhibit differential flatness, whereas those with hitches off the axle do not, as per previous research [21; 22]. Table 1 summarizes the literature review. Sliding mode is a robust control method that has been widely investigated for complex and nonlinear systems subject to uncertainties and disturbance [23; 24]. It has been a popular choice for truck trailer systems. [PERSON] et al. [25] explored how to prevent tractor semitrailers from rollover (jackknifing). A new algorithm is used to control a model of a tractor semitrailer. In addition, [PERSON] et al. [26] explored the path-tracking challenges of autonomous farming vehicles, especially concerning wheel slips common in agricultural environments. In scenarios demanding heightened stability for vehicles transporting liquids, [PERSON] et al. [27] employed an active roll control system, leveraging two distinct approaches. [PERSON] et al. [28] primarily focused on crafting an adaptive sliding mode controller (SMC) that can handle variations in trailer loads and cope with sensor noise. In another study, an active disturbance rejection control technique to enhance the stability of elongated articulated vehicles has been explored [29]. This was underpinned by a nineteen-degree-of-freedom dynamic model simulated in a virtual environment. In [30], the authors examine the adaptive back-stepping sliding mode control for tractor-trailer systems, specifically addressing input delays using an RBF neural network. This research emphasizes an adaptive sliding mode neural network control approach tailored for tractor-trailers that have two degrees of freedom and confront input delays. [PERSON] et al. [31] aim to devise a dynamic tractor model suitable for sloped terrains, introducing a robust control strategy anchored in sliding mode observers.