###### Abstract  
This paper presents a new approach to the nonlinear model predictive control (NMPC) of an underactuated overhead crane system developed using a data-driven prediction model obtained utilizing the regularized genetic programming-based symbolic regression method. Grammar-guided genetic programming combined with regularized least squares was applied to identify a nonlinear autoregressive model with an exogenous input (NARX) prediction model of the crane dynamics from input-output data. The resulting prediction model was implemented in the NMPC scheme, using a particle swarm optimization (PSO) algorithm as a solver to find an optimal sequence of the control actions satisfying multi-objective performance requirements and input constraints. The feasibility and performance of the controller were experimentally verified using a laboratory crane actuated by AC motors and compared with a discrete-time feedback controller developed using the pole placement technique. A series of experiments proved the effectiveness of the controller in terms of robustness against operating condition variation and external disturbances. a 2024 2024 2024 2024 2024 2024 2024 2024 20  
real-time MPC method with a linearized model of a mobile harbor boom crane that is hydraulically actuated was developed in [19] and tested on a LIEBHERR harbor mobile crane with a load capacity of 104 tons and a rope length of up to 70 m. This work is further developed in [20], where the nonlinear behavior of the system is simplified by applying exact linearization and input-output linearization. [PERSON] et al. [21] proposed combining a Lyapunov-based controller to stabilize the pendulum dynamics and an NMPC scheme used to control the position of a small-scale knuckle boom crane. An NMPC-based scheme was designed in [22] to optimize the pendulum motion driven by a mechatronic cart-winch system. In [23], the dynamics of a 3D overhead crane system were decoupled into two second-order systems, and two separate NMPC schemes were developed for simultaneously positioning a payload along the two motion planes of a crane's bridge and trolley, respectively. Experiments carried out on a small laboratory-scale overhead crane confirmed the effectiveness of this strategy. In [24], the MPC approach is applied to minimize an objective function that is formulated as the integration of energy consumption and swing angle. In [25], the authors developed a path-following controller for a tower crane using nonlinear model predictive control with a fast suboptimal solution and verified the algorithm in simulations and on a small experimental stand. In [26], the authors proposed a model predictive controller for an overhead crane. The model was linearized around the equilibrium point, and the sway constraints were converted to input constraints using the kinematic equation of the crane system. The MPC strategy is employed in [27] to optimize the crane velocity profile when the maximum position overshoot is given by the crane operator. The aforementioned studies are mostly based on physics-based models of underactuated crane dynamics. However, the accurate analytical modeling of complex coupled crane dynamics can be difficult and time-consuming; thus, some recent works have proposed data-driven modeling approaches. An MPC strategy involving a discrete-time linear model, recursive least-squares parameter estimation, and a PSO solver of a multi-objective control optimization problem was proposed and tested on a laboratory overhead crane driven by DC motors in [28]. This linear MPC scheme is based on a straightforward approach that assumes a parametric model of crane dynamics, thereby reducing the identification task to parameter estimation using the RLS algorithm with parameter projection. The parametric identification procedure assumes there is an adequate model structure representation with uncertain parameters that are subject to optimization.