(eng): This paper is focused on parameter identification for Model Predictive Control (MPC). Two identification techniques for parameters of Auto Regressive model with eXogenous input (ARX model) are considered: namely the identification based on Particle Swarm Optimisation (PSO) and Least Square (LS) method. PSO is investigated and LS is presented in square-root form as a reference method for comparison, respectively. The following points are elaborated and discussed: i) parameters’ estimation of ARX model, ii) design of PSO and LS procedures, iii) design of data-driven MPC algorithm in square-root form, iv) concept of possible use of PSO for semiautomatic fine tuning or retuning of MPC parameters. The proposed theoretical procedures are demonstrated using simply reproducible simulation experiments. Application possibilities are discussed towards robotics and mechatronics.