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Register a new userAverage Consensus on Arbitrary Strongly Connected Digraphs with Time-Varying Topologies
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Added by
Kai Cai
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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We have recently proposed a surplus-based algorithm which solves the multi-agent average consensus problem on general strongly connected and static digraphs. The essence of that algorithm is to employ an additional variable to keep track of the state changes of each agent, thereby achieving averaging even though the state sum is not preserved. In this note, we extend this approach to the more interesting and challenging case of time-varying topologies: An extended surplus-based averaging algorithm is designed, under which a necessary and sufficient graphical condition is derived that guarantees state averaging. The derived condition requires only that the digraphs be arbitrary strongly connected in a emph{joint} sense, and does not impose balanced or symmetric properties on the network topology, which is therefore more general than those previously reported in the literature.
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We study a new variant of consensus problems, termed `local average consensus, in networks of agents. We consider the task of using sensor networks to perform distributed measurement of a parameter which has both spatial (in this paper 1D) and temporal variations. Our idea is to maintain potentially useful local information regarding spatial variation, as contrasted with reaching a single, global consensus, as well as to mitigate the effect of measurement errors. We employ two schemes for computation of local average consensus: exponential weighting and uniform finite window. In both schemes, we design local average consensus algorithms to address first the case where the measured parameter has spatial variation but is constant in time, and then the case where the measured parameter has both spatial and temporal variations. Our designed algorithms are distributed, in that information is exchanged only among neighbors. Moreover, we analyze both spatial and temporal frequency responses and noise propagation associated with the algorithms. The tradeoffs of using local consensus, as compared to standard global consensus, include higher memory requirement and degraded noise performance. Arbitrary updating weights and random spacing between sensors are analyzed in the proposed algorithms.
Let $G$ be a digraph with adjacency matrix $A(G)$. Let $D(G)$ be the diagonal matrix with outdegrees of vertices of $G$. Nikiforov cite{Niki} proposed to study the convex combinations of the adjacency matrix and diagonal matrix of the degrees of undirected graphs. Liu et al. cite{LWCL} extended the definition to digraphs. For any real $alphain[0,1]$, the matrix $A_alpha(G)$ of a digraph $G$ is defined as $$A_alpha(G)=alpha D(G)+(1-alpha)A(G).$$ The largest modulus of the eigenvalues of $A_alpha(G)$ is called the $A_alpha$ spectral radius of $G$, denoted by $lambda_alpha(G)$. This paper proves some extremal results about the spectral radius $lambda_alpha(G)$ that generalize previous results about $lambda_0(G)$ and $lambda_{frac{1}{2}}(G)$. In particular, we characterize the extremal digraph with the maximum (or minimum) $A_alpha$ spectral radius among all $widetilde{infty}$-digraphs and $widetilde{theta}$-digraphs on $n$ vertices. Furthermore, we determine the digraphs with the second and the third minimum $A_alpha$ spectral radius among all strongly connected bicyclic digraphs. For $0leqalphaleqfrac{1}{2}$, we also determine the digraphs with the second, the third and the fourth minimum $A_alpha$ spectral radius among all strongly connected digraphs on $n$ vertices. Finally, we characterize the digraph with the minimum $A_alpha$ spectral radius among all strongly connected bipartite digraphs which contain a complete bipartite subdigraph.
Connected and automated vehicle (CAV) technology is one of the promising solutions to addressing the safety, mobility and sustainability issues of our current transportation systems. Specifically, the control algorithm plays an important role in a CAV system, since it executes the commands generated by former steps, such as communication, perception, and planning. In this study, we propose a consensus algorithm to control the longitudinal motion of CAVs in real time. Different from previous studies in this field where control gains of the consensus algorithm are pre-determined and fixed, we develop algorithms to build up a lookup table, searching for the ideal control gains with respect to different initial conditions of CAVs in real time. Numerical simulation shows that, the proposed lookup table-based consensus algorithm outperforms the authors previous work, as well as van Arems linear feedback-based longitudinal motion control algorithm in all four different scenarios with various initial conditions of CAVs, in terms of convergence time and maximum jerk of the simulation run.
Let $A_alpha(G)$ be the $A_alpha$-matrix of a digraph $G$ and $lambda_{alpha 1}, lambda_{alpha 2}, ldots, lambda_{alpha n}$ be the eigenvalues of $A_alpha(G)$. Let $rho_alpha(G)$ be the $A_alpha$ spectral radius of $G$ and $E_alpha(G)=sum_{i=1}^n lambda_{alpha i}^2$ be the $A_alpha$ energy of $G$ by using second spectral moment. Let $mathcal{G}_n^m$ be the set of non-strongly connected digraphs with order $n$, which contain a unique strong component with order $m$ and some directed trees which are hung on each vertex of the strong component. In this paper, we characterize the digraph which has the maximal $A_alpha$ spectral radius and the maximal (minimal) $A_alpha$ energy in $mathcal{G}_n^m$.
Classical approaches for asymptotic convergence to the global average in a distributed fashion typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions are not necessarily valid in practical settings due to varying delays that might affect transmissions at different times, as well as possible changes in the underlying interconnection topology (e.g., due to component mobility). In this work, we propose protocols to overcome these limitations. We first consider a fixed interconnection topology (captured by a - possibly directed - graph) and propose a discrete-time protocol that can reach asymptotic average consensus in a distributed fashion, despite the presence of arbitrary (but bounded) delays in the communication links. The protocol requires that each component has knowledge of the number of its outgoing links (i.e., the number of components to which it sends information). We subsequently extend the protocol to also handle changes in the underlying interconnection topology and describe a variety of rather loose conditions under which the modified protocol allows the components to reach asymptotic average consensus. The proposed algorithms are illustrated via examples.
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