On convergence of the Monotone Structural Evolution

The paper studies convergenceof the Monotone Structural Evolution (MSE), a computational method of optimal control. The principles of MSE are described and an expository example presents the method in action. It is then proved that under appropriate assumptions the method is convergent to the decision space stationarity conditions. Observations on finite convergence and on connections with Pontryagin’s maximum principle are also provided

Analysis of multivariable Smith predictors using MATLAB Containers

Containers are structured m-files which allow `data' and `methods' to be stored persistently. Containers have a user-defined class structure, so that one can have several Containers of the same class, all structurally similar, and there is a mechanism for interaction with Containers in the style of database transactions. The use of MATLAB Containers to analyze multivariable Smith predictors is discussed

Nonlinear Cross Gramians

We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results

Model order reduction for nonlinear IC models

Model order reduction is a mathematical technique to transform nonlinear dynamical models into smaller ones, that are easier to analyze. In this paper we demonstrate how model order reduction can be applied to nonlinear electronic circuits. First we give an introduction to this important topic. For linear time-invariant systems there exist already some well-known techniques, like Truncated Balanced Realization. Afterwards we deal with some typical problems for model order reduction of electronic circuits. Because electronic circuits are highly nonlinear, it is impossible to use the methods for linear systems directly. Three reduction methods, which are suitable for nonlinear differential algebraic equation systems are summarized, the Trajectory piecewise Linear approach, Empirical Balanced Truncation, and the Proper Orthogonal Decomposition. The last two methods have the Galerkin projection in common. Because Galerkin projection does not decrease the evaluation costs of a reduced model, some interpolation techniques are discussed (Missing Point Estimation, and Adapted POD). Finally we show an application of model order reduction to a nonlinear academic model of a diode chain