Study On System Model Order Reduction Based On Rank Constraints Approximation

The order-reduction problem of system model based on rank constraint approximation in H? norm was researched in this paper. In order to reduce the descending order error of the lower order system and the original system, the rank constraint condition of the non-convex was approximated to be a differentiable linear matrix inequality constraint;making the original non-convex model became convex optimization model; and the corresponding algorithm is established. In order verify its validity the numerical experiments were carried out. The main work of this paper includes the following three aspects.The first, for continuous systems, based on the reduced order model proposed by Daniel Ankelhed 2007, in order to overcame the disadvantages of the existence of discontinuous and non-differentiable rank constraint conditions, as well as the difficulty of solving and reducing order effect are poor, by using the relation of rank function,nuclear norm, spectral norm and linear matrix inequality, the non-convex rank constraint condition was approximated with convex linear matrix inequality condition, and the system reducing order model based on rank constraint approximation was established. The corresponding solution algorithm was developed to calculate the lower order system. The validity of the experiment was verified by numerical example.The second, the problem of non-convex rank constraint conditions in the model reduction of discrete systems was also presented. The approximation method used in the descending order of continuous system was applied to the descending order of discrete system. The non-convex rank constraint condition was used to approximate the convex linear inequality, and the reduced order of discrete system model based on rank constraint approximation was established. The algorithm was developed to calculate the lower order system, and the numerical example were carried out verified the validity of the method. Thus, the method was also effective for the reduction of the discrete system.The third, the application of matrix rank constraint is very extensive.The system descending order problem in this paper can be transformed into a model with rank constraint, image processing, and the problem of matrix complement can also be transformed into a rank constraint model.The algebraic properties of matrix rank function constraint were summarized and preliminarily researched in this paper. The equivalence conditions of rank constraint and bound of rank constraint were obtained.Finally, the main contents in the paper were summarized and the further research work were put forward.