ECC 2016 Workshop

Distributed and Stochastic Optimization: Theory and Applications

 

Date: June 28, 2016

Location: Room Laugsstuen, Aalborg Congress & Culture Center, Aalborg, Denmark

 

Organizers

Kostas Margellos – University of Oxford, UK

Maria Prandini – Politecnico di Milano, Italy

 

Objectives

The aim of the workshop is to  provide a concise, yet complete, exposition to the topic of distributed and stochastic optimization, with an in depth understanding of the mathematical and algorithmic mechanisms underlying it, of the potential communication and computational savings of such implementations, and of how uncertainty can be dealt with in a rigorous manner. This comprehensive introduction to the machinery underlying distributed and stochastic optimization will  encourage the development of new results and the investigation of several important issues in the future of distributed optimization and control over uncertain networks, possibly through novel collaborations.

Merging distributed optimization algorithms with stochastic optimization techniques that allow for a rigorous treatment of uncertainty is a quite challenging problem.

We believe that this full-day workshop will help building the appropriate background to address it, by demonstrating recent advances on the broad topic of distributed and stochastic optimization, offering attendees the opportunity to get exposed to recent algorithmic developments as well as to applications of contemporary interest like smart grid  monitoring and control, control of cyber-physical systems, and wireless networks.

The workshop brings together a diverse group of internationally recognized researchers, who are affiliated with outstanding institutions in Europe and in the United States. Attendees will be exposed to cutting edge research on the field, acquire a comprehensive awareness of the literature, and get some insight on the potential connections and complementarities among different algorithmic alternatives as well as new vistas on the field.

 

Target audience and prerequisites

The workshop aims at attracting graduate students and researchers with an interest in optimization-based control, to get them exposed to the fundamentals of distributed and stochastic optimization, and to point out recent advances and open research directions in the field. Target audience involves also researchers that are more inclined towards applications than only theoretical aspects. Emphasis will be given on illustrating the potential of applying the theoretical machinery to different problems in the energy sector, highlighting its importance in transiting from centralized power management to smart-grid control concepts, facilitating the integration of intermittent energy sources like renewables.

The topic of the workshop is quite broad, however, there are no particular prerequisites for attendees, and any graduate level control engineer should be able to fruitfully attend it, not only grasping the main concepts but also achieving some deep level of understanding. It would be beneficial, however, if attendees have a strong mathematical background, possibly being familiar with optimization in its various forms, so as to gain the maximum from what the workshop can offer. Attendees from other disciplines than control (e.g., operations research, power engineering) are also qualified to attend the workshop, since the talks are expected to be self-contained, introducing some necessary control engineering prerequisites.

 

Presentations: titles and abstracts

Distributed Learning in Graphs

Angelia Nedich, University of Illinois at Urbana-Champaign, USA

We will consider the problem of distributed cooperative non-Bayesian learning in a network of agents, where the agents are repeatedly gaining partial information about an unknown random variable whose distribution is to be jointly estimated. The joint objective of the agent system is to globally agree on a hypothesis (distribution) that best describes the observed data by all agents in the network. Interactions between agents occur according to an unknown sequence of time-varying graphs. We highlight some interesting aspects of Bayesian learning and stochastic approximation approach for the case of a single agent, which has not been observed before and it allows for a new connection between optimization and statistical learning. Then, we discuss and analyze the general case where subsets of agents have conflicting hypothesis models, in the sense that the optimal solutions are different if the subset of agents were isolated. Additionally, we provide a new non-Bayesian learning protocol that converges an order of magnitude faster than the learning protocols currently available in the literature for arbitrary fixed undirected graphs. Our results establish consistency and a non-asymptotic, explicit, geometric convergence rate for the learning dynamics.

 

Proximal algorithms for distributed optimization over uncertain networks

Kostas Margellos, University of Oxford, UK , and Maria Prandini, Politecnico di Milano, Italy

We provide a proximal minimization based algorithm for distributed convex optimization over time-varying multi-agent networks, in the presence of constraints and uncertainty. We first focus on the deterministic case, develop an iterative algorithm and show that agents reach consensus, and in particular, that they convergence to some optimizer of the centralized problem.

Our approach is then extended to the case where the agents' constraint sets are affected by a possibly common uncertainty vector. To tackle this problem we follow a scenario-based methodology and offer probabilistic guarantees regarding the feasibility properties of the resulting solution.

We illustrate how this distributed methodology can be applied to the problem of energy management in building networks affected by stochastic uncertainty.

 

Distributed convex optimization algorithms robust to asynchronous computation and lossy communication

Luca Schenato, University of Padova, Italy

 

In this talk I will present some recent results on distributed convex algorithms in the context of multi-agent systems where computation is asynchronous and communication is subject to packet loss and random delay. I will consider two different scenarios. In the first scenario all agents are required to compute the same minimizer of a global cost functions which is given by the sum of local cost functions, while in the second scenarios each agent is required to compute only some local components of the global minimizer. Applications which are relevant to the former scenario include logistic regression, kernel regression and map-building, while applications which are relevant to the latter scenario are area-based state estimation in smart grids and robot localization from relative measurements. Although asynchronous distributed convex optimization has a long history and many results are available, the inclusion of lossy communication where the transmitter agent is not aware whether the message is received or loss, is still at infancy. Indeed, naive extensions of popular algorithms such as ADMM in this context may provide poor performance or even fail to converge. We will present some algorithms which are robust also in the presence of lossy communication and provide some sufficient conditions for convergence, and we will show their performance with realistic numerical simulations.

 

Scenario-based model predictive control applied to building automation systems

Karl Henrik Johansson, KTH Stockholm, Sweden

Improving energy efficiency of heating, ventilation and air conditioning (HVAC) systems is a primary objective for the society. Model predictive control (MPC) techniques can naturally account for several important aspects of a more efficient HVAC system, such as weather and occupancy forecasts, comfort ranges, and actuation constraints. Developing effective MPC for HVAC systems is challenging, however, since building dynamics are nonlinear and affected by various uncertainties. Further, the complexity of the MPC problem and the burden of on-line computations can lead to difficulties in implementing the scheme in real building management systems.

We propose to address the computational issue by designing a scenario-based explicit MPC strategy, i.e., a controller that is simultaneously based on explicit representations of the MPC feedback law and accounts for uncertainties in the occupancy patterns and weather conditions by using the scenario paradigm. The main advantages of this approach are the absence of a-priori assumptions on the distributions of the uncertain variables, the applicability to any type of building, and the limited on-line computational burden, enabling practical implementations on low-cost hardware platforms. We illustrate the proposed controller on a building automation testbed at KTH, showing its effectiveness and computational tractability.

The talk will be  based on joint work with Alessandra Parisio, Marco Molinari, Damiano Varagnolo and other collaborators.

 

Model Predictive Control for Jump-Markov-Linear Systems

Olaf Stursberg, University of Kassel, Germany

Systems are suitably modeled by Jump-Markov-Linear-Systems (JMLS) if they exhibit uncertainties of the type that switching between different linear dynamics appears randomly and can be quantified probabilistically. Applications for which transitions into fault modes are possible, are an example to motivate the use of JMLS. Recent developments have led to schemes of model predictive control (MPC) for optimizing the behavior of JMLS. In the first part, the talk will present MPC schemes for discrete-time JMLS with input constraints and constraints for the expectancy of the state trajectory. Tailored recursive prediction schemes allow the transformation

into quadratic programs which can be solved with small computational effort and thus be applied

to large systems. In parallel efforts, methods of distributed model predictive control have been advanced such that for deterministic distributed linear systems fundamental concepts and limits are known. The second part of the talk will report on these developments, and will in particular point to possibilities to combine the work on JMLS with principles of distributed model predictive control to arrive at a scheme of distributed stochastic MPC.

 

Randomized proximal gradient methods for asynchronous distributed optimization

Giuseppe Notarstefano, University of Salento, Italy

Large-scale cyber-physical network systems have become ubiquitous in everyday life. Social-networks, smart grids, cooperative robots, sensor networks are just few examples. An important prerequisite for numerous estimation, learning, decision and control tasks arising in such complex systems is the distributed solution of optimization problems in an asynchronous, peer-to-peer framework. In this talk we will present a class of distributed algorithms to solve general convex optimization problems with composite, possibly non-smooth, cost function. The algorithms are based on randomized, coordinate-descent methods for the solution of large-scale and big-data problems. The proposed techniques work under a symmetric, event-triggered communication protocol, in which the processor updates are ruled by local timers. The node updates use local step-sizes so that no centralized tuning is needed. Moreover, the algorithms can handle general optimization problems including both regularization terms and local constraints.

 

Distributed Control Approaches in Emerging Electrical Energy Systems

Christoforos Hadjicostis, University of Cyprus, Cyprus

In this talk, we will describe distributed control approaches and their applications in emerging electrical energy systems. The progression of technology and the continuous drive to an ever-increasing penetration of sensing and networking devices is revolutionizing the ways in which we monitor, operate and utilize energy resources and power distribution systems. However, in order to overcome current limitations and fully utilize the flexibility provided in these emerging systems, one has to develop appropriate distributed strategies that are easily adaptable and can overcome faulty/malicious operation at some of the components, while ensuring provably optimal (or at least acceptable) operation. The talk will consider two control problems of interest: (i) a distributed architecture for generation control in islanded ac microgrids, with both synchronous generators and inverter-interfaced power supplies, and (ii) a distributed control architecture that ensures stable and synchronized operation at a specific frequency. Both proposals rely on distributed algorithms that adhere to a communication network interconnecting the  controllers present at each bus and eliminate the reliance on a centralized computer and the need to communicate measurements/commands to/from this centralized computer.

 

An optimization-on-manifold approach to the design of distributed feedback control in smart grids

Florian Dörfler and Saverio Bolognani, ETH Zurich, Switzerland

By introducing an implicit model for the power flow equations, we will cast optimal power flow (OPF) problems into the framework of optimization on manifolds. Based on this formulation, and on a structure-preserving linear approximation of the model, we show how this approach allows to design distributed feedback control laws that drive the system to the solution of the original OPF problem. We illustrate this procedure via an example (optimal reactive power compensation for voltage regulation) and we examine the distributed nature and the communication requirements of the resulting control strategy. Finally, we discuss how to extend this feedback control design approach to general OPF problems.

 

Download the agenda in pdf form.