The pseudo-spectral approach implemented in this paper is essentially an approximate method; hence, there is an error. This error materializes as an error in computing the optimal control. In all the previous figures, the results are accurate since they are a simulation for the computed control with the dynamic model. Yet the performance might not be optimal due to the approximations in the pseudo-spectral approach. The approximation error varies depending on the problem. For instance, the approximation error in the constraint problem is different from that in the unconstraint problem. To see that, consider the results presented in Fig. 21. The energy captured from surge and pitch in the constrained motion case is 3.724 × 10^{4} J and it is higher than the energy captured in the unconstrained motion case (3.455 × 10^{4} J, see Fig. 8), which is not expected. The reason for that is the approximation error in pseudo-spectral method. In this case, the approximation error in the unconstrained motion case is higher and hence the solution is not as close to the optimal solution as that of the constrained motion case. For verification, the error in each state between the simulated true values and the approximated values is computed. Figure 24 shows this error for one state (the surge velocity), for different surge constrain values (Constraint in Fig. 24 is the maximum allowed surge). As can be seen from Fig. 24, the unconstrained case has higher error than the constrained ones, in this case. It is noted here that this conclusion would vary from one test case to another. In this test case for instance, the surge reaches a maximum of about 0.5 m when it is unconstraint. In other test cases for other sea states, the conclusion might vary.