Abstract
To construct an optimal state regulator for a nonlinear system with quadratic performance index, several approximation methods are investigated, namely, the perturbation method, the method of instantaneous linearization, and the method of parameter optimization.
The perturbation method or the ε-parameter method, previously established by the present authors, is briefly outlined and some practical difficulties are remarked. The method of instantaneous linearization, proposed by Pearson, is based on the idea to use a technique similar to that for linear systems. This idea much simplifies the calculation. However, the best possible solution can not necessarily be obtained, because of the arbitrariness in the system description. In order to correct this serious shortcoming, the present paper proposes to use a parameter optimization technique jointly. According to the idea, the nonlinear system is represented by a linearized state-dependent model which contains a set of adjustable parameters. Secondly the values of these parameters are determined so as to minimize the performance index by the gradient method.
Three examples attached illustrate and compare the perturbation method and the method of instantaneous linearization improved by parameter optimization technique. In the first and the third examples which permit the exactly optimal control, the applications of the two methods are examined analytically, while in the second example the results of numerical calculations are compared.
