An essentially decentralized interior point method for control

Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems with non-convex constraints for which classical decentralized optimization algorithms lack convergence guarantees. Moreover, classical decentralized algorithms usually exhibit only linear convergence. This paper presents an essentially decentralized primal-dual interior point method with convergence guarantees for non-convex problems at a {super}linear rate. We show that the proposed method works reliably on a numerical example from power systems. Our results indicate that the proposed method outperforms ADMM in terms of computation time and computational complexity of the subproblems

Load Flow Solution of Distribution Systems - A Bibliometric Survey

In this paper, Bibliometric Survey has been carried out on ‘Load Flow Solution of Distribution Systems’ from 2012 to 2021. Scopus database has been used for the analysis. There were total 1711 documents found on this topic. The statistical analysis is carried out source wise, year wise, area wise, Country wise, University wise, author wise, and based on funding agency. Network analysis is also carried out based on Co-authorship, Co-occurrence. Results are presented. During 2020 and 2018, there were 263 documents published which is the highest. ‘IEEE Transactions on Power Systems’ has published 90 documents during the period of study which is the highest in terms of articles under the category of sources. Highest citations were received by the article authored by Hung and Mithulanathan with 484 citations in the collected database with the chosen key words. VOSviewer 1.6.16 is the software that is used for the statistical analysis and network analysis on the database. It provides a very effective way to analyze the co-authorship, co-occurrences, citation and bibliometric analysis etc. The Source for all Tables and figures is www.scopus.com, The data is assessed on 6th July, 2021

ALADIN-α\alpha -- An open-source MATLAB toolbox for distributed non-convex optimization

This paper introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-$\alpha$. ALADIN-$\alpha$ is a MATLAB implementation of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm, which is tailored towards rapid prototyping for non-convex distributed optimization. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization. A collection of application examples from different applications fields including chemical engineering, robotics, and power systems underpins the application potential of ALADIN-$\alpha$

Distributed Optimization with Application to Power Systems and Control

In many engineering domains, systems are composed of partially independent subsystems—power systems are composed of distribution and transmission systems, teams of robots are composed of individual robots, and chemical process systems are composed of vessels, heat exchangers and reactors. Often, these subsystems should reach a common goal such as satisfying a power demand with minimum cost, flying in a formation, or reaching an optimal set-point. At the same time, limited information exchange is desirable—for confidentiality reasons but also due to communication constraints. Moreover, a fast and reliable decision process is key as applications might be safety-critical. Mathematical optimization techniques are among the most successful tools for controlling systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization control the subsystems in a distributed or decentralized fashion, reducing or avoiding central coordination. These methods have a long and successful history. Classical distributed optimization algorithms, however, are typically designed for convex problems. Hence, they are only partially applicable in the above domains since many of them lead to optimization problems with non-convex constraints. This thesis develops one of the first frameworks for distributed and decentralized optimization with non-convex constraints. Based on the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm, a bi-level distributed ALADIN framework is presented, solving the coordination step of ALADIN in a decentralized fashion. This framework can handle various decentralized inner algorithms, two of which we develop here: a decentralized variant of the Alternating Direction Method of Multipliers (ADMM) and a novel decentralized Conjugate Gradient algorithm. Decentralized conjugate gradient is to the best of our knowledge the first decentralized algorithm with a guarantee of convergence to the exact solution in a finite number of iterates. Sufficient conditions for fast local convergence of bi-level ALADIN are derived. Bi-level ALADIN strongly reduces the communication and coordination effort of ALADIN and preserves its fast convergence guarantees. We illustrate these properties on challenging problems from power systems and control, and compare performance to the widely used ADMM. The developed methods are implemented in the open-source MATLAB toolbox ALADIN-—one of the first toolboxes for decentralized non-convex optimization. ALADIN- comes with a rich set of application examples from different domains showing its broad applicability. As an additional contribution, this thesis provides new insights why state-of-the-art distributed algorithms might encounter issues for constrained problems