The concept of the adaptive system working on the principle of minimizing the output power under the constrained response to specified directions is introduced. Theoretical analysis and computer simulation experiments on this directional constraint system are also presented. By comparison with the computer experiment, the differential equation approach is shown to be useful to predict the behavior of the system. The effect of error in setting the constraint direction is investigated, and it is demonstrated that the system is not very sensitive to such error. This margin can be made even greater by adopting the double directional constraints system. This system is also analyzed theoretically and experimented by computer simulation. History of output power components during adaptation is shown, which enables the comprehension of the behavior of the system.
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Takao et al. (1976) studied this question.