Simultaneous Design of Controller and Structure: A New Look at Optimizing Generalized Structural Parameters
Koji Teraoka, March 1999 (in Japanese)

In order to achieve better performance of a control system, one should choose carefully not only the controller but also structural parameters which the plant may have. In ordinary control systems synthesis, one first designs structural parameters of a plant regardless of controllers, and a controller is selected design afterwards. In this approach, structural parameters are not chosen by taking into account the total performance of the whole system. The controller and structural parameters must be designed simultaneously in order to achieve a more advanced level of control performance.

This thesis focuses on such a simultaneous design of controllers and {\it Generalized Structural Parameters}. The class of generalized structural parameters are defined as structural parameters which appear in the mathematical model of a system in a Linear Fractional Transformation fashion. A physical parameter does not always appear affinely, but also appear as inverse and their combinations in the state--space model. For example, the mass of a mechanical system has its inverse in the state--space realization. The mass not only has much effect on the performance of control, but also is important and useful as structural parameters in various situations. Thus, generalized structural parameters which encompass the above situations are practically important. From the viewpoint of solving the design as optimization, the simultaneous design with generalized structural parameters is non--convex in parameters, which is, in general, a mathematically hard problem.

An attempt at solving the simultaneous design problem was made by Tanaka and Sugie(1997). They proposed using a descriptor representation to reduce the problem into a problem which is affine in structural parameters. The transformed problem is, however, not simultaneous affine in all parameters for controller and structure design so that the optimization problem is still non--convex. Their resulting non--convex optimization has more parameters to be sought than the problem originally has. In practice, increase of parameters may significantly slow down optimization computation.

This experience motivated the authors' research. The idea of this thesis is to bypass the intermediate step which only results in another non--convex problem of large size. It is shown that the design problem can be successfully reduced into a nice tractable problem without introducing redundant parameters in optimization. Thereby, this thesis proposes an computationally effective method for the simultaneous design. A lot of numerical examples are provided to illustrate various aspects of optimization for the simultaneous design and the effectiveness of the proposed method.