Application-Oriented Input Design and Optimization Methods Involving ADMM

is thesis is divided into two main parts. e first part considers applicationoriented input design, specifically for model predictive control (MPC). e second part considers alternating direction method of multipliers (ADMM) for l1 regularized optimization problems and primal-dual interior-point methods. e theory of system identification provides methods for estimating models of dynamical systems from experimental data.is thesis is focused on identifying models used for control, with special attention to MPC. e objective is to minimize the cost of the identification experiment while guaranteeing, with high probability, that the obtained model gives an acceptable control performance. We use application-oriented input design to find such a model. We present a general procedure of implementing application-oriented input design to unknown, possibly nonlinear, systems controlled using MPC. e practical aspects of application-oriented input design are addressed and the method is tested in an experimental study. In addition, a MATLAB-based toolbox for solving application-oriented input design problems is presented. e purpose of the toolbox is threefold: it is used in research; it facilitates communication of research results; it helps an engineer to use application-oriented input design. Several important problems in science can be formulated as convex optimization problems. As such, there exist very efficient algorithms for finding the solutions. We are interested in methods that can handle optimization problems with a very large number of variables. ADMM is a method capable of handling such problems. We derive a scalable and efficient algorithm based on ADMM for two l1 regularized optimization problems: l1 mean and covariance filtering, and l1 regularized MPC. e former occurs in signal processing and the latter is a specific type of model based control. We are also interested in optimization problems with certain structural limitations. ese limitations inhibit the use of a central computational unit to solve the problems. We derive a distributed method for solving them instead. e method is a primal-dual interior-point method that uses ADMM to distribute all the calculations necessary to solve the optimization problem at hand.