**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

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.
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.
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.
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.
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.
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.
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.
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.
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.
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. |