In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical in...
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In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase *** the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.
A standard assumption in control of network dynamical systems is that its nodes interact through pairwise interactions, which can be described by means of a directed graph. However, in several contexts, multibody, dir...
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A standard assumption in control of network dynamical systems is that its nodes interact through pairwise interactions, which can be described by means of a directed graph. However, in several contexts, multibody, directed interactions may occur, thereby requiring the use of directed hypergraphs rather then digraphs. For the first time, we propose a strategy, inspired by the classic pinning control on graphs, that is tailored for controlling network systems coupled through a directed hypergraph. By drawing an analogy with signed graphs, we provide sufficient conditions for controlling the network onto the desired trajectory provided by the pinner, and a dedicated algorithm to design the control hyperedges.
In this paper, we discuss the problem of motion synchronization for a formation of marine vessels with the unknown, external disturbance. A novel distributed control algorithm is proposed, which comprises a disturbanc...
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In this paper, we discuss the problem of motion synchronization for a formation of marine vessels with the unknown, external disturbance. A novel distributed control algorithm is proposed, which comprises a disturbance observer and a synchronization controller. The disturbance observer is constructed for estimating the unknown time-variant disturbance from the external environment, such as wind, wave, and ocean current. The synchronization controller is designed to compensate for the synchronization error between the vessels and the tracking error of the desired trajectory. By distributed, we mean that each vessel can execute the algorithm with only the knowledge of the local information broadcast by its neighbors within the communication network of the formation, though reasonably, certain bounds determined by limited centralized information are known. By modeling the network topology of the formation as a directed graph, we show that global synchronization of the vessel formation can be achieved if the gains in both disturbance observer and synchronization controller satisfy certain lower bounds. We further introduce a constant time delay to the communication process to validate the robustness of our proposed algorithm. The simulations of a four-vessel formation are provided to verify the effectiveness of our proposed algorithm.
A notion of scaled consensus is defined, wherein network components' states approach dictated ratios in the asymptote. A linear network dynamics that achieves scaled consensus for a prescribed interaction graph is...
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A notion of scaled consensus is defined, wherein network components' states approach dictated ratios in the asymptote. A linear network dynamics that achieves scaled consensus for a prescribed interaction graph is introduced, and an equivalence with the class of (negative) singular M-matrices is explored. A few further characterizations of the scaled synchronization process are given, and finally a modification that allows tracking on the stable manifold is presented. (C) 2014 Elsevier Ltd. All rights reserved.
We consider an individual-based model where agents interact over a random network via first-order dynamics that involve both attraction and repulsion. In the case of all-to-all coupling of agents in this system has a ...
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We consider an individual-based model where agents interact over a random network via first-order dynamics that involve both attraction and repulsion. In the case of all-to-all coupling of agents in this system has a lowest energy state in which an equal number of agents occupy the vertices of the -dimensional simplex. The purpose of this paper is to sharpen and extend a line of work initiated in [56], which studies the behavior of this model when the interaction between the agents occurs according to an ErdAs-R,nyi random graph instead of all-to-all coupling. In particular, we study the effect of randomness on the stability of these simplicial solutions, and provide rigorous results to demonstrate that stability of these solutions persists for probabilities greater than . In other words, only a relatively small number of interactions are required to maintain stability of the state. The results rely on basic probability arguments together with spectral properties of random graphs.
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