Optimization Based On Non Commutative Maps
Download Optimization Based On Non Commutative Maps PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Optimization Based On Non Commutative Maps book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Optimization based on Non-Commutative Maps
Author: Jan Feiling
language: en
Publisher: Logos Verlag Berlin GmbH
Release Date: 2022-01-20
Powerful optimization algorithms are key ingredients in science and engineering applications. In this thesis, we develop a novel class of discrete-time, derivative-free optimization algorithms relying on gradient approximations based on non-commutative maps–inspired by Lie bracket approximation ideas in control systems. Those maps are defined by function evaluations and applied in such a way that gradient descent steps are approximated, and semi-global convergence guarantees can be given. We supplement our theoretical findings with numerical results. Therein, we provide several algorithm parameter studies and tuning rules, as well as the results of applying our algorithm to challenging benchmarking problems.
Design of Distributed and Robust Optimization Algorithms. A Systems Theoretic Approach
Author: Simon Michalowsky
language: en
Publisher: Logos Verlag Berlin GmbH
Release Date: 2020-04-17
Optimization algorithms are the backbone of many modern technologies. In this thesis, we address the analysis and design of optimization algorithms from a systems theoretic viewpoint. By properly recasting the algorithm design as a controller synthesis problem, we derive methods that enable a systematic design of tailored optimization algorithms. We consider two specific classes of optimization algorithms: (i) distributed, and (ii) robust optimization algorithms. Concerning (i), we utilize ideas from geometric control in an innovative fashion to derive a novel methodology that enables the design of distributed optimization algorithms under minimal assumptions on the graph topology and the structure of the optimization problem. Concerning (ii), we employ robust control techniques to establish a framework for the analysis of existing algorithms as well as the design of novel robust optimization algorithms with specified guarantees.
Determining input-output properties of linear time-invariant systems from data
Author: Anne Koch
language: en
Publisher: Logos Verlag Berlin GmbH
Release Date: 2022-02-08
Due to their relevance in systems analysis and controller design, this thesis considers the problem of determining input-output properties of linear time-invariant systems. While obtaining a suitable mathematical model describing the input-output behavior of a dynamical system can be a difficult task, data of the system in form of input-output trajectories is often and increasingly available. This thesis therefore introduces three complementary data-driven analysis methods to determine input-output properties directly from data without deriving a mathematical model first. In particular, the results of this thesis include iterative methods, where data is actively sampled by performing experiments on the unknown system, as well as approaches based on available (offline) data. All these approaches are simple to apply, come with low requirements on the data, and provide rigorous theoretical guarantees. Systems analysis not only provides insights into the system and allows to do controller design with guaranteed stability, but it can also validate a given controller or its closed-loop performance. By developing different methods to determine input-output properties directly from data on the basis of a rigorous mathematical analysis, this thesis contributes to a sound mathematical framework for data-driven systems analysis and control theory.