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Distributed coordination algorithms (DCA) carry out information processing processes among a group of networked agents without centralized information fusion. Though it is well known that DCA characterized by an SIA (stochastic, indecomposable, aperiodic) matrix generate consensus asymptotically via synchronous iterations, the dynamics of DCA with asynchronous iterations have not been studied extensively, especially when viewed as stochastic processes. This paper aims to show that for any given irreducible stochastic matrix, even non-SIA, the corresponding DCA lead to consensus successfully via random asynchronous iterations under a wide range of conditions on the transition probability. Particularly, the transition probability is neither required to be independent and identically distributed, nor characterized by a Markov chain.
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This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order conditions for optimality is observed in the numerical experiments. Next, for a starting point, an asynchronous N-block PCPM algorithm is proposed to solve linearly constrained N-block convex optimization problems. The numerical results demonstrate the sub-linear convergence rate under the bounded delay assumption, as well as the faster convergence with more short-time iterations than a synchronous iterative scheme.
Many problems can be solved by iteration by multiple participants (processors, servers, routers etc.). Previous mathematical models for such asynchronous iterations assume a single function being iterated by a fixed set of participants. We will call such iterations static since the systems configuration does not change. However in several real-world examples, such as inter-domain routing, both the function being iterated and the set of participants change frequently while the system continues to function. In this paper we extend Uresin & Duboiss work on static iterations to develop a model for this class of dynamic or always on asynchronous iterations. We explore what it means for such an iteration to be implemented correctly, and then prove two different conditions on the set of iterated functions that guarantee the full asynchronous iteration satisfies this new definition of correctness. These results have been formalised in Agda and the resulting library is publicly available.
We consider asynchrono
Consensus protocols for asynchronous networks are usually complex and inefficient, leading practical systems to rely on synchronous protocols. This paper attempts to simplify asynchronous consensus by building atop a novel threshold logical clock abstraction, which enables upper layers to operate as if on a synchronous network. This approach yields an asynchronous consensus protocol for fail-stop nodes that may be simpler and more robust than Paxos and its leader-based variants, requiring no common coins and achieving consensus in a constant expected number of rounds. The same approach can be strengthened against Byzantine failures by building on well-established techniques such as tamper-evident logging and gossip, accountable state machines, threshold signatures and witness cosigning, and verifiable secret sharing. This combination of existing abstractions and threshold logical clocks yields a modular, cleanly-layered approach to building practical and efficient Byzantine consensus, distributed key generation, time, timestamping, and randomness beacons, and other critical services.
This paper presents a distributed optimization algorithm tailored for solving optimal control problems arising in multi-building coordination. The buildings coordinated by a grid operator, join a demand response program to balance the voltage surge by using an energy cost defined criterion. In order to model the hierarchical structure of the building network, we formulate a distributed convex optimization problem with separable objectives and coupled affine equality constraints. A variant of the Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) method for solving the considered class of problems is then presented along with a convergence guarantee. To illustrate the effectiveness of the proposed method, we compare it to the Alternating Direction Method of Multipliers (ADMM) by running both an ALADIN and an ADMM based model predictive controller on a benchmark case study.
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