## 5 Conclusions  
Model Predictive Controller design requires incorporating good ship dynamics in the predictive model. A large amount of data for the identification procedure may be obtained in two ways: during non-linear ship model simulations or during real-time lake trials. We should obtain reliable data where all modes of the plant will be excited. Lake identification trials should be done without any disturbances such as wind, waves, and current. There is also difficulty with all modes of excitation without bringing the training ship into circulation. These trials are time-consuming and susceptible to severe errors. Thus, a method that combines simulation test and real-time trial validation data is presented. This method reduces the number of lake trials by about four times and gives acceptable results, indicating it is a good predictive model for further usage. Regularization is a straightforward procedure allowing for better control of the identification process. It allows for minimizing the standard deviations of particular coefficients and maximizing fitness function values. The GA procedure quickens **R** matrix and \(\lambda\) parameters search. It also brings their sub-optimal values, which are hard to find during conventional computations. Use of modern computers, with high computation power, allows for on-line parameter search. The obtained model may be modified during automatic MPC control, when ship parameters are changing, for example during underway replenishment, when the ship's metacentric height, draught, and load displacement change. Overall, the GA and conventional model qualities are measured by acceptable STDs and the validation fitness function value. The model whose coefficient STDs are bigger than 10% of their value is rejected. They are treated as unreliable. In addition, models causing high-frequency oscillations in the output signals are useless. GA regularization prevents the appearance of the above-mentioned unwanted STDs and oscillations. Parameters such as dynamic, output, and noise component matrices, whether or not GA regularization has been used, have STDs less than 10%. However, input matrix coefficients, when identification was done on the basis of the simulation data, had STDs exceeding even 100% of the coefficient value. GA regularization usage minimizes them to the values amounting to a small percent. Only the STD for the \(b_{3}\) coefficient (\(b_{3 STD}=27.68\%\)) exceeded 10%, but it did not reach 50%, which is acceptable for a single parameter for MPC design purposes. Moreover, use of GA regularization prevents oscillations in output signals. Therefore, the method presented in this paper can be used to predict future plant outputs for MPC. The minimal fit to validation data, in order to get a reliable predictive model for future control purposes, was equal to 80% for short-time and 65% for long-time predictions. GA regularization resulted in a model with predictive capabilities exceeding the reference short- and long-time prediction ability by 9 and 11 percentage points, respectively. The non-tuned model did not meet the reference values. Thus, significant prediction performance was achieved, which reached 18.5 and 21.1 percentage points for short- and long-time predictions, respectively. This algorithm is a good tool for identification of the real plant indirectly based on simulation data associated with real experiments. It may be used not only for ships, but for all nonlinear and nonholomical control objects. It gives a reliable prediction model, which may be applied to the MPC algorithm for future automatic control systems. The project was financed within the program of the Polish Ministry of Science and Higher Education called \"Regional Initiative of Excellence\" for the years 2019-2020, project number 006/RID/2018/19 financing amount 11,870,000 PLN. Not applicable. Data Availability StatementData available on request due to privacy. The author declares no conflict of interest. The following abbreviations are used in this manuscript: