475 research outputs found
A Partition-Based Implementation of the Relaxed ADMM for Distributed Convex Optimization over Lossy Networks
In this paper we propose a distributed implementation of the relaxed
Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization
of a separable convex cost function, whose terms are stored by a set of
interacting agents, one for each agent. Specifically the local cost stored by
each node is in general a function of both the state of the node and the states
of its neighbors, a framework that we refer to as `partition-based'
optimization. This framework presents a great flexibility and can be adapted to
a large number of different applications. We show that the partition-based
R-ADMM algorithm we introduce is linked to the relaxed Peaceman-Rachford
Splitting (R-PRS) operator which, historically, has been introduced in the
literature to find the zeros of sum of functions. Interestingly, making use of
non expansive operator theory, the proposed algorithm is shown to be provably
robust against random packet losses that might occur in the communication
between neighboring nodes. Finally, the effectiveness of the proposed algorithm
is confirmed by a set of compelling numerical simulations run over random
geometric graphs subject to i.i.d. random packet losses.Comment: Full version of the paper to be presented at Conference on Decision
and Control (CDC) 201
A Formal Approach to Cyber-Physical Attacks
We apply formal methods to lay and streamline theoretical foundations to
reason about Cyber-Physical Systems (CPSs) and cyber-physical attacks. We focus
on %a formal treatment of both integrity and DoS attacks to sensors and
actuators of CPSs, and on the timing aspects of these attacks. Our
contributions are threefold: (1) we define a hybrid process calculus to model
both CPSs and cyber-physical attacks; (2) we define a threat model of
cyber-physical attacks and provide the means to assess attack
tolerance/vulnerability with respect to a given attack; (3) we formalise how to
estimate the impact of a successful attack on a CPS and investigate possible
quantifications of the success chances of an attack. We illustrate definitions
and results by means of a non-trivial engineering application
Asynchronous Distributed Optimization over Lossy Networks via Relaxed ADMM: Stability and Linear Convergence
In this work we focus on the problem of minimizing the sum of convex cost
functions in a distributed fashion over a peer-to-peer network. In particular,
we are interested in the case in which communications between nodes are prone
to failures and the agents are not synchronized among themselves. We address
the problem proposing a modified version of the relaxed ADMM, which corresponds
to the Peaceman-Rachford splitting method applied to the dual. By exploiting
results from operator theory, we are able to prove the almost sure convergence
of the proposed algorithm under general assumptions on the distribution of
communication loss and node activation events. By further assuming the cost
functions to be strongly convex, we prove the linear convergence of the
algorithm in mean to a neighborhood of the optimal solution, and provide an
upper bound to the convergence rate. Finally, we present numerical results
testing the proposed method in different scenarios.Comment: To appear in IEEE Transactions on Automatic Contro
Relativistic Celestial Metrology: Dark Matter as an Inertial Gauge Effect
In canonical tetrad gravity, it is possible to identify the gauge variables, describing relativistic inertial effects, in Einstein general relativity. One of these is the York time, the trace of the extrinsic curvature of the instantaneous nonâEuclidean 3âspaces (global Euclidean 3âspaces are forbidden by the equivalence principle). The extrinsic curvature depends both on gauge variables and on dynamical ones like the gravitational waves after linearization. The fixation of these gauge variables is done by relativistic metrology with its identification of time and space. Till now, the International Celestial Reference Frame ICRF uses Euclidean 3âspaces outside the Solar System. It is shown that York time and nonâEuclidean 3âspaces may explain the main signatures of dark matter in ordinary spaceâtime before using cosmology. Also dark energy may be connected to these inertial gauge effects, because both redâshift and luminosity distance depend on them
Multi-agents adaptive estimation and coverage control using Gaussian regression
We consider a scenario where the aim of a group of agents is to perform the
optimal coverage of a region according to a sensory function. In particular,
centroidal Voronoi partitions have to be computed. The difficulty of the task
is that the sensory function is unknown and has to be reconstructed on line
from noisy measurements. Hence, estimation and coverage needs to be performed
at the same time. We cast the problem in a Bayesian regression framework, where
the sensory function is seen as a Gaussian random field. Then, we design a set
of control inputs which try to well balance coverage and estimation, also
discussing convergence properties of the algorithm. Numerical experiments show
the effectivness of the new approach
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