A finite-time consensus algorithm with simple structure for fixed networks

In this paper, a continuous-time consensus algorithm with guaranteed finite-time convergence is proposed. Using homogeneity theory, finite-time consensus is proved for fixed topologies. The proposed algorithm is computationally simpler than other reported finite-time consensus algorithms, which is an important feature in scenarios of energy efficient nodes with limited computing resources such as sensor networks. Additionally, the proposed approach is compared on simulations with existing consensus algorithms, namely, the standard asymptotic consensus algorithm and the finite-time and fixed-time convergent algorithms, showing, in cycle graph topology, better robustness features on the convergence with respect to the network growth with less control effort. Indeed, the convergence time of other previously proposed consensus algorithms grows faster as the network grows than the one herein proposed whereas the control effort of the proposed algorithm is lower

Design and Analysis of Distributed Averaging with Quantized Communication

Consider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some value close to that average. Such an algorithm is called generically "distributed averaging," and our goal in this paper is to study the performance of a subclass of deterministic distributed averaging algorithms where the information exchange between neighboring nodes (agents) is subject to uniform quantization. With such quantization, convergence to the precise average cannot be achieved in general, but the convergence would be to some value close to it, called quantized consensus. Using Lyapunov stability analysis, we characterize the convergence properties of the resulting nonlinear quantized system. We show that in finite time and depending on initial conditions, the algorithm will either cause all agents to reach a quantized consensus where the consensus value is the largest quantized value not greater than the average of their initial values, or will lead all variables to cycle in a small neighborhood around the average. In the latter case, we identify tight bounds for the size of the neighborhood and we further show that the error can be made arbitrarily small by adjusting the algorithm's parameters in a distributed manner

Fixed-time Distributed Optimization under Time-Varying Communication Topology

This paper presents a method to solve distributed optimization problem within a fixed time over a time-varying communication topology. Each agent in the network can access its private objective function, while exchange of local information is permitted between the neighbors. This study investigates first nonlinear protocol for achieving distributed optimization for time-varying communication topology within a fixed time independent of the initial conditions. For the case when the global objective function is strictly convex, a second-order Hessian based approach is developed for achieving fixed-time convergence. In the special case of strongly convex global objective function, it is shown that the requirement to transmit Hessians can be relaxed and an equivalent first-order method is developed for achieving fixed-time convergence to global optimum. Results are further extended to the case where the underlying team objective function, possibly non-convex, satisfies only the Polyak-\L ojasiewicz (PL) inequality, which is a relaxation of strong convexity.Comment: 25 page

Symmetrizing quantum dynamics beyond gossip-type algorithms

Recently, consensus-type problems have been formulated in the quantum domain. Obtaining average quantum consensus consists in the dynamical symmetrization of a multipartite quantum system while preserving the expectation of a given global observable. In this paper, two improved ways of obtaining consensus via dissipative engineering are introduced, which employ on quasi local preparation of mixtures of symmetric pure states, and show better performance in terms of purity dynamics with respect to existing algorithms. In addition, the first method can be used in combination with simple control resources in order to engineer pure Dicke states, while the second method guarantees a stronger type of consensus, namely single-measurement consensus. This implies that outcomes of local measurements on different subsystems are perfectly correlated when consensus is achieved. Both dynamics can be randomized and are suitable for feedback implementation.Comment: 11 pages, 3 figure