Model Reduction Using Semidefinite Programming
In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to the algorithms is a number of frequency response samples of the original model. This makes the computational complexity relatively low for large-scale models. Extra properties on a reduced model can also be enforced, as long as the properties can be expressed as convex conditions. Semidefinite program are solved using the interior point methods which are well developed, making the implementation simpler. A number of extensions to the proposed methods were studied, for example, passive model reduction, frequency-weighted model reduction. An interesting extension is reduction of parameterized linear time invariant models, i.e. models with state-space matrices dependent on parameters. It is assumed, that parameters do not depend on state variables nor time. This extension is valuable in modeling, when a set of parameters has to be chosen to fit the required specifications. A good illustration of such a problem is modeling of a spiral radio frequency inductor. The physical model depends nonlinearly on two parameters: wire width and wire separation. To chose optimally both parameters a low-order model is usually created. The inductor modeling is considered as a case study in this thesis.
model reduction, convex optimization, semidefinite programming
Licentiate Thesis ISRN LUTFD2/TFRT--3247--SE, Department of Automatic Control, Lund University, Sweden, November 2009.