Asymptotically fast polynomial matrix algorithms for multivariable systems

We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer algebra techniques, minimal basis computations and matrix fraction expansion/reconstruction, and to polynomial matrix multiplication. Such reductions eventually imply that all these problems can be solved in about the same amount of time as polynomial matrix multiplication

Non-linear predictive control for manufacturing and robotic applications

The paper discusses predictive control algorithms in the context of applications to robotics and manufacturing systems. Special features of such systems, as compared to traditional process control applications, require that the algorithms are capable of dealing with faster dynamics, more significant unstabilities and more significant contribution of non-linearities to the system performance. The paper presents the general framework for state-space design of predictive algorithms. Linear algorithms are introduced first, then, the attention moves to non-linear systems. Methods of predictive control are presented which are based on the state-dependent state space system description. Those are illustrated on examples of rather difficult mechanical systems

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