Consensus in multi-agent systems with time-delays

Different consensus problems in multi-agent systems have been addressed in this thesis. They represent improvements with respect to the state of the art. In the first part of the thesis in luding Chapters 2, 3, and 4, the state of the art of the representation and stability analysis of consensus problems, time-delay systems, and sampled-data systems have been presented. Novel contributions have been illustrated in Chapters 5-8. Particularly, in Chapter 5 we reported the results of Zareh et al. (2013b), where we investigated the consensus problem for networks of agents with double integrator dynamics affected by time-delay in their coupling. We provided a stability result based on the Lyapunov-Krasovskii functional method and a numerical proc edure based on an LMI condition which depends only on the algebraic connectivity of the considered network topologies, thus reducing greatly the computational complexity of the procedure. Obviously, this result implies the existence of a minimum dwell time such that the proposed consensus protocol is stable for slow swit things between network topologies with suffient algebraic connectivity. Future work will involve actually computing such a dwell time by adopting a multiple Lyapunov function method and evaluating the worst case sider only delayed relative measurements instead of delayed absolute values of the neighbors' state variables. The results of Zareh et al. (2013a) were addressed in Chapter 6, in which a on- tinuous time version of a consensus on the average protocol for arbitrary strongly connected directed graphs is proposed and its convergence properties with respect to time delays in the local state update are characterized. The convergenc e properties of this algorithm depend upon a tuning parameter that an be made arbitrary small to prove stability of the networked system. Simulations have been presented to corroborate the theoretical results and show that the existenc e of a small time delay an a tually improve the algorithm performance. Future work will include an extension of the mathematical characterization of the proposed algorithm to consider possibly heterogeneous or time-varying delays. In Chapter 7 we proposed a PD-like consensus algorithm for a second-order multi- agent system where, at non-periodic sampling times, agents transmit to their neighbors information about their position and veloc ity, while each agent has a perfect knowledge of its own state at any time instant. Conditions have been given to prove onsensus to a ommon xed point, based on LMIs verification. Moreover, we also show how it is possible to evaluate an upper bound on the de ay rate of exponential convergence of stable modes. In Chapter 8, mainly based on our paper Zareh et al. (2014b), we considered the same problem as in Chapter 7. The main contribution consists in proving consensus to a common fixed point, based on LMIs verification, under the assumption that the network topology is not known and the only information is an upper bound on the connectivity. Two are the main directions of our future research in this framework. First, we want to compute analytically an upper bound on the value of the second largest eigenvalue of the weighted adjacency matrix that guarantees consensus, as a function of the other design parameters. Second, we plan to study the case where agents do not have a perfect knowledge of their own state

Consensus in multi-agent systems with non-periodic sampled-data exchange and uncertain network topology

In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded inter-sampling intervals. It is assumed that each agent has exact knowledge of its own state at any time instant. The considered local interaction rule is PD-type. Sufficient conditions for stability of the consensus protocol to a time-invariant value are derived based on LMIs. Such conditions only require the knowledge of the connectivity of the graph modeling the network topology. Numerical simulations are presented to corroborate the theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:1407.300

Consensus in multi-agent systems with second-order dynamics and non-periodic sampled-data exchange

In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded inter-sampling intervals. It is assumed that each agent has exact knowledge of its own state at all times. The considered local interaction rule is PD-type. The characterization of the convergence properties exploits a Lyapunov-Krasovskii functional method, sufficient conditions for stability of the consensus protocol to a time-invariant value are derived. Numerical simulations are presented to corroborate the theoretical results.Comment: The 19th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA'2014), Barcelona (Spain

Palladium supported on bis(indolyl)methane functionalized magnetite nanoparticles as an efficient catalyst for copper-free Sonogashira-Hagihara reaction

A novel heterogeneous catalyst based on palladium nanoparticles supported on 3,3′-bisindolyl(4-hydroxyphenyl)methane functionalized magnetite (Fe3O4) nanoparticles was synthesized, characterized and used as catalyst for Sonogashira-Hagihara reaction. The alkynylation of a variety of aryl iodides and aryl bromides with terminal alkynes was carried out at 60 °C under copper and phosphane-free conditions using N,N-dimethyl acetamide as solvent, DABCO as base and low Pd loadings (0.18 mol%) under air. In the case of aryl chlorides, the reaction was carried out at 120 °C in the presence of tetra-n-butylammonium bromide (TBAB) and 0.36 mol% of Pd catalyst. The heterogeneous palladium catalyst introduced in this study is recoverable by an external magnet and it can be used for seven consecutive runs without a significant loss in catalytic activity.The authors thank Institute for Advanced Studies in Basic Sciences (IASBS) Research Council and Iran National Science Foundation (INSF-Grant number: 94010666) for financial support of this work. C. Nájera is also thankful to The Spanish Ministerio de Economia y Competitividad (MINECO) (projects CTQ2013-43446-P and CTQ2014-51912-REDC), FEDER, the Generalitat Valenciana (PROMETEOII/2014/017) and the University of Alicante for financial support

Decentralized biconnectivity conditions in multi-robot systems

The network connectivity in a group of cooperative robots can be easily broken if one of them loses its connectivity with the rest of the group. In case of having robustness with respect to one-robot failure, the communication network is termed biconnected. In simple words, to have a biconnected network graph, we need to prove that no articulation point exists. We propose a decentralized approach that provides sufficient conditions for biconnectivity of the network, and we prove that these conditions are related to the third smallest eigenvalue of the Laplacian matrix. Data exchange among the robots is supposed to be neighbor-to-neighbor

Distributed Laplacian Eigenvalue and Eigenvector Estimation in Multi-robot Systems

Distributed Laplacian Eigenvalue and Eigenvector Estimation in Multi-robot System

Enforcing biconnectivity in multi-robot systems

Connectivity maintenance is an essential task in multi-robot systems and it has received a considerable attention during the last years. However, a connected system can be broken into two or more subsets simply if a single robot fails. Then, a more robust communication can be achieved if the network connectivity is guaranteed in the case of one-robot failures. The resulting network is called biconnected. In [1] we presented a criterion for biconnectivity check, which basically determines a lower bound on the third-smallest eigenvalue of the Laplacian matrix. In this paper we introduce a decentralized gradient-based protocol to increase the value of the third-smallest eigenvalue of the Laplacian matrix, when the biconnectivity check fails. We also introduce a decentralized algorithm to estimate the eigenvectors of the Laplacian matrix, which are used for defining the gradient. Simulations show the effectiveness of the theoretical findings

Consensus on the average in arbitrary directed network topologies with time-delays

In this preliminary paper we study the stability property of a consensus on the average algorithm in arbitrary directed graphs with respect to communication/sensing time-delays. The proposed algorithm adds a storage variable to the agents' states so that the information about the average of the states is preserved despite the algorithm iterations are performed in an arbitrary strongly connected directed graph. We prove that for any network topology and choice of design parameters the consensus on the average algorithm is stable for sufficiently small delays. We provide simulations and numerical results to estimate the maximum delay allowed by an arbitrary unbalanced directed network topology

Consensus in multi agent systems with second order dynamics and non-periodic sampling time data exchange

In this paper consensus in second-order multi-agent system s with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded intersampling intervals. It is assumed that each agent has exact knowledge of its own state at all times. The considered local interaction rule is PD-type. The characterization of the convergence properties exploits a Lyapunov-Krasovskii functional method, sufficient conditions for stability of the consensu s protocol to a time-invariant value are derived. Numerical simulations are presented to corroborate the theoretical results