Application-Oriented Input Design and Optimization Methods Involving ADMM

This thesis is divided into two main parts. The first part considers application-oriented input design, specifically for model predictive control (MPC). The second part considers alternating direction method of multipliers (ADMM) for ℓ1 regularized optimization problems and primal-dual interior-point methods. The theory of system identification provides methods for estimating models of dynamical systems from experimental data. This thesis is focused on identifying models used for control, with special attention to MPC. The 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. The 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. The 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. The 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. These limitations inhibit the use of a central computational unit to solve the problems. We derive a distributed method for solving them instead. The method is a primal-dual interior-point method that uses ADMM to distribute all the calculations necessary to solve the optimization problem at hand.QC 20160602