The extremum control methods which are developed up to date are classified as follows; (a) the method based on the linear approximation of performance index (P. I.) of the controlled object (e. g. gradient method), and (b) the method based on the higher order approximation of P. I. (e. g. extrapolation method). Each of them has its merits as well as shortcomings.
The first half of this paper investigates the theoretical as well as experimental convergence properties of the two methods based on gradient and extrapolation schemes respectively, as they are applied to optimizing problems with the quadratic form models of P. I.. In the latter half, a new optimizing method is proposed, which is essentially based on the combination of these two methods. During the initial stages of this optimizing process, the modified gradient method is applied to examine whether it is possible to approximate P. I. with a quadratic model. When this is found possible, a proper quadratic form model is constructed using the results of experimental searches. Finally the extrapolation method is applied to this model.
As this method is characterized by these dual functions, it is expected that it has following two desirable characteristics. Firstly, it can optimize a controlled object with general form of P. I. as the gradient method. Secondly, it does not have the weak point of the gradient method that the steps of manipulated variables become too small near the ridge of P. I.. In the simulated optimization study, it is shown that this method has the properties just described above.
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