Design of reduced-order controller by using real-coded genetic algorithm

There exist a direct and an indirect methods in designing reduced-order H_∞ controller. The former method is difficult and there exists no effective way presently. The latter method has been used conventionally. However, the resultant controller may be conservative. We propose a method of designing a less conservative reduced-order controller by using genetic algorithm (GA). Since it is difficult to search reduced-order controller directly, we search for the full-order controller whose reduced-order controller has approximate performance of the optimal full-order H_∞ controller. Then, it is reduced by the reduction technique. In order to search the desired full-order controller effectively, Glover´s parameterization is applied. Furthermore, we propose the coding which searches only optimal full-order controllers, since the desired full-order controller is expected to be one of numerous optimal full-order controllers. In order to show the effectiveness of the proposed method, an numerical example is given.