Cancellation algorithm

We discuss now how one can construct the transformation for one step in the iterative algorithm. An equation to determine D and W can be obtained by expanding Eq. (77) in powers of s and requiring that the 0-dependent terms of order s cancel out. This leads to the two equations... 

The order of an integration method is the degree to which the Taylor series expansion. Equation (7.2), is truncated it is the lowest term that is not present in the expansion. The order may not always be apparent from the formulae used. For example, the highest-order derivative that appears in the Verlet formulae is the second, a(f), yet the Verlet algorithm is, in fact, a fourth-order method. This is because the third-order terms, which cancel when Equation (7.6) is added to Equation (7.7), are still implied in the expansion ... 

Tracing back the running list, there exists a residual cancelation sequence with a single element (move 4), that is, the corresponding complement move 4 will be set tabu and the running of the algorithm is continued. 

The design of incremental control algorithms can become complex when a human controller is controlling a computer, which is controlling the actual physical process, in a stressful and busy environment, such as a military aircraft. If one of the commands in an incremental control sequence cannot be executed within a specified period of time, the human operator needs to be informed about any delay or postponement or the entire sequence should be canceled and the operator informed. At the same time, interrupting the pilot with a lot of messages that may not be critical at a busy time could also be dangerous. Careful analysis is required to determine when multistep controller inputs can be preempted or interrupted before they are complete and when feedback should occur that this happened [90]. 

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