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

This article introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-α. ALADIN-α is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. It is user interface is convenient for rapid prototyping of non-convex distributed optimization algorithms. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization with reduced information exchange. A collection of examples from different applications fields including chemical engineering, robotics, and power systems underpins the potential of ALADIN-α

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

Implementação em FPGA de estratégias de controle preditivo para um quadrirrotor

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2019.Uma das técnicas de controle que mais impactou tanto a indústria quanto a academia nos últimos anos foi a estratégia de controle conhecida como Controle Preditivo baseado em Modelo (MPC). A principal razão para o interesse nesse tipo de controlador é o fato de o mesmo ser capaz de controlar um sistema respeitando as restrições que são impostas ao mesmo, independente da natureza delas (normas de segurança, faixa de operação dos atuadores, normas de qualidade de um produto, etc.), ao mesmo tempo que encontra uma solução ótima que satisfaz os objetivos de controle desejados. Entretanto, o MPC possui uma grande desvantagem: seu elevado custo computacional. Isso limita a implementação do MPC a sistemas de dinâmicas mais lentas, o que tem levado a um aumento no estudo de técnicas de otimização e no desenvolvimento de sistemas mais rápidos e com mais recursos, capazes de acelerar o MPC para aplicá-lo a sistemas de dinâmicas mais rápidas. Neste cenário, este trabalho apresenta o desenvolvimento de uma arquitetura em hardware do MPC, utilizando FPGA (do inglês, Field Programmable Gate Array) para sua implementação. Este tipo de dispositivo reconfigurável tem ganho notoriedade na literatura por permitir a aceleração de algoritmos, por meio da paralelização dos mesmos ao implementá-los diretamente em hardware. A aplicação escolhida para este trabalho consiste em um Veículo Aéreo Não Tripulado (VANT) quadrirrotor, um tipo de sistema amplamente utilizado em diversas áreas e muito estudado na atualidade, já que é considerado um problema de controle desafiador para a aplicação do controlador MPC, devido às dimensões do seu modelo e suas dinâmicas rápidas, que também são acopladas e inerentemente instáveis. Neste trabalho, são apresentados resultados referentes à implementação do MPC sem aplicação de restrições e com aplicação de restrições implementados em FPGA, com o objetivo de rastrear trajetórias pré-definidas para o quadrirrotor. Todos os algoritmos são desenvolvidos manualmente e implementados utilizando artimética em ponto flutuante. Os resultados mostram que o MPC sem restrições consome menos recursos de hardware do que a solução com restrições, mas não é capaz de lidar com cenários nos quais restrições não podem ser violadas. Por outro lado, O MPC com restrições respeita essas restrições, ao custo de um consumo de hardware maior. Por conta da sua complexidade, o MPC com restrições também exige maior precisão em ponto flutuante, de forma que os melhores resultados foram alcançados utilizando tamanho de dados de 32 bits em ponto flutuante.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).One of the most impactful control techniques both in industry and academia through the last years is the control strategy known as Model Predictive Control (MPC). The main reason for such interest on this type of controller is due to the fact that it is capable of controlling a system while handling constraints imposed to it, regardless of the nature of such constraints (security, operation range of the actuators, quality norms of a product, etc.), while still finding an optimal solution that satisfies the desired control objectives. However, MPC has a major drawback: its elevated computational cost. This limits MPC implementation to systems with slower dynamics, which has lead to an increase of studies regarding new optimization techniques and the development of faster and more resourceful systems, capable of accelerating MPC in order to apply it to systems with faster dynamics. Regarding this scenario, this work presents the development of a hardware architecture for MPC, using FPGA (Field Programmable Gate Array) for its implementation. This type of reconfigurable device has gained notoriety in literature for allowing the speedup of embedded algorithms, by parallelising and implementing them directly in hardware. The chosen application for this work consists of a quadrotor Unmanned Aerial Vehicle (UAV), a type of system that has been widely used today in many fields of application and vastly studied, as it is considered a challenging control problem for MPC, due to the dimensions of its model and fast dynamics, which are also coupled and inherently unstable. In this work, results regarding both unconstrained MPC and constrained MPC implemented using FPGA are presented, with the goal of tracking predefined trajectories for the quadrotor. All control algorithms were developed manually and using floating point arithmetic. The results obtained show that unconstrained MPC consumes less hardware resources than the constrained solution, but it is not capable of handling scenarios in which constraints must not be violated. On the other hand, constrained MPC is capable of handling these constraints, at the cost of a higher hardware consumption. Due to its complexity, constrained MPC also demands a higher floating point precision, so that the best results were obtained using a 32 bits data width in floating point

Fast distributed MPC based on active set method

Modern chemical plants are characterized by their large-scale, strong interactions and the presence of constraints. With its ability to systematically handle these issues, distributed model predictive control (DMPC) is a promising approach for the control of such systems. However, the problem of how to efficiently solve the resulting distributed optimization problem is still an open question. This paper develops a novel fast DMPC approach based on a distributed active set method and offline inversion of the Hessian matrix to efficiently solve a constrained distributed quadratic program. A dual-mode optimization strategy based on the value of unconstrained optimal solution is developed to accelerate the computation of control action. The proposed method allows for the optimization to be terminated before convergence to cope with the fast sampling periods. Furthermore, a warm-start strategy based on the solution of the previous sampling instant is integrated with the approach to further improve convergence speed. The approach is highly parallelized as constraints can be checked in parallel. The approach is demonstrated using an academic example as well as a chemical process network control. © 2014 Elsevier Ltd