Figure 9
The horizontal axis is labeled “Prediction Horizon (H)” and ranges from 5 to 25 with an interval of 5. The left vertical axis is labeled “R-squared Score” and ranges from negative 2.5 to 2 with an interval of 0.5, and the right vertical axis is labeled “Computation Time per Step (milliseconds)” and ranges from 0 to 60 with an interval of 10. Four curves are plotted and identified in the legend. The “Nonlinear M P C R-squared” curve is shown as a solid orange line with square markers. It appears only at higher horizons, starting from H equals 20 at negative 2.5 of score and rising vertically to around negative 0.2 and then sloping downward toward the right at H equals 25 around negative 0.5 score. The “D K-M P C R-squared” curve is shown as a solid green line with circular markers. It remains constant at a value of 1 across all horizons from 5 through 25, forming a horizontal line. The “Nonlinear M P C Time” curve is shown as a dashed blue line with square markers. It starts near about 15 milliseconds at H equals 5, increases to around 20 milliseconds at H equals 10, rises further to about 39 milliseconds at H equals 15, peaks near 58 milliseconds at H equals 20, and then decreases to about 48 milliseconds at H equals 25, forming a rising, then slightly falling, trend. The “D K-M P C Time” curve is shown as a dashed purple line with circular markers. It remains low across all horizons, starting near about 2 milliseconds at H equals 5 and gradually increasing slightly to around 3 milliseconds by H equals 25. The curves are clearly separated by color and marker style, with R-squared values referenced to the left axis and computation time values referenced to the right axis. Note: All numerical data values are approximated.Comparison of DK-MPC and nonlinear MPC performance across varying prediction horizon lengths (H = 5 to 25). The left y-axis shows the R2 score, indicating tracking accuracy, while the right y-axis shows the computation time per control step in milliseconds. DK-MPC maintains consistently high R2 scores and low computation time across all horizons, while Nonlinear MPC exhibits significant instability in both accuracy and runtime. In the nonlinear MPC approach where H < 20, the R2 error is significantly negative, implying that predictions are very far off from the actual values, failing to find solutions