Abstract-The problem considered in the present article is optimal design of network topologies in multi-agent systems in order to make communication on the network as efficient as possible for the continuous-time average-consensus protocol. The network design problem can be posed in two different ways.(1) Assuming that the maximum communication cost, i.e. the maximum number of communication links, is known, the goal is to find the network topology which results in the fastest convergence to the consensus (in presence of communication time delays on the links). (2) If a minimum performance of the protocol is required, the design problem can be posed as finding the network with lowest possible communication cost which fulfills the required performance. In both approaches, we formulate the problem of finding the optimal communication graph among a class of directed graphs, strongly balanced digraphs, as a Mixed Integer Semidefinite Program (MISDP). By solving this MISDP, the optimal graph and the weights on communication links are obtained. The average-consensus algorithm mainly developed in [5] has received tremendous attention in recent years due to its applicability and elegance. Authors in [5] have studied the convergence and performance of the average-consensus algorithm under different conditions. It is shown that the convergence speed of the average-consensus protocol is determined by the second smallest eigenvalue of the Laplacian matrix of the mirror graph of the network which is itself determined by the topology of the network. A natural question that arises is how to choose the weights on communication links, the entries of the adjacency matrix of the graph, in order to achieve the best performance. In most cases, the network designer can also determine which agents communicate with each other. Therefore, one can go even further and investigate the best communication topology, i.e. the communication graph as well as the weights on the links, so that the performance of the consensus algorithm is optimized.Since the development of the average-consensus algorithm, extensive efforts have been made to improve the
Cultivation environment can be effective on the degree of limitations in crop evapotranspiration and yield, as a result of water shortage and salinity. The purpose of this study was to determine and compare the impact of different irrigation regimes (daily, weekly and every two weeks) combined with different water salinities (0.8, 2.5, 5.0 and, 7.0 dS m -1 ) on eggplant yield (Y) and evapotranspiration (ETc) in outdoor and greenhouse cultivation. Daily ETc values were measured by diurnal weighting of microlysimeters throughout the growing season (from May 19th to September 5th, 2012 and June 1st to September 22nd, 2013) placed in a plastic greenhouse and outdoor basins. Measurements showed apparent variations between different irrigation regimes×water salinity treatments, during the early growing season in both years. Both water deficit and salinity factors had significant effects on ETc, ECe, Y, fruit diameter and shoot dry weight in both environments. The applicability of Doorenbos-Kassam linear crop-water production function along with Maas-Hoffman salt tolerance model was investigated in the greenhouse and outdoor conditions. The Ky coefficient obtained for outdoor and greenhouse eggplants treatments were 0.97 and 1.03 in the first year and 0.91 and 0.93 in the second year, respectively. Higher sensitivity of greenhouse eggplants to salinity was later demonstrated for both years, obtaining higher values of b and lower values of ECe threshold in the greenhouse eggplants.
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