Composite Simpsons 13 Rule

The Gregory formula used here has the advantage that it requires no special considerations as to whether or not the integral involves an odd or even number of points, in contrast to other integration formulas such as the composite Simpson s rule. 

To implement the improvement strategy numerically, we split the time interval into N subintervals of equal length and use numerical integration [e. g., composite Simpson s 1/3 Rule given in Section 9.12 (p. 275) for even number... 

Evaluate the objective functional using the controls u s and the state variables y s. Using composite Simpson s 1/3 Rule, the objective functional value is given by... 

Using composite Simpson s 1/3 Rule, given that the state equations are satisfied. 

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