Iterative generation of optimal input of a manipulator

We present a new algorithm that generates a suitable input for a manipulator to track the desired predetermined trajectory after repeating trials. It is ensured that the error between the desired trajectory and that of the manipulator becomes zero in a certain sense as the number of trials approaches infinite. In the proposed algorithm a kind of dual systems is used for recurrsively making new input and that system can be simply designed. The proposed algorithm is based on functional analysis.