Horizon length

Horizon length was of no great importance to the performance of the NMPC or the OIC. All horizon lengths between 30 and 45 time steps had similar performance. Horizon lengths between 25 and 30 had problems with the cart crashing to the walls. Horizons shorter than 25 time steps could not reliably perform the swing-up task because the reference signal became too unrealistic. Very long horizons were also problematic. First of all, they increase the computational burden of the algorithm. The increase in the number of the parameters often also leads into increase in the number of local minima, which makes the optimisation problem more involved. In addition, because only an approximative model of the system is available, predictions far to the future become more unreliable. This can lead the algorithm to choose an optimisation strategy which is not feasible in practice.