Second-order consensus in networks of dynamic agents with communication time-delays

This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.

Dynamic Analysis of a Turret-Moored Tanker

In this paper, the second-order perturbation method in frequency domain is used to calculate RAO and spectra of motion and mooring line tension of a turret-moored tanker in ballast condition. The calculated results are compared with corresponding experiment results. In the experiment the wave heading is 180 degrees, and the wave spectra is the P-M spectrum and white noise spectrum. In the theoretical calculations, the damping coefficient of slow oscillation of the tanker is determined on the basis of the damping obtained from a test of irregular waves where the mooring system is replaced by a nonlinear spring with nonlinear stiffness similar to that of the mooring system. From the comparison between theoretical calculations and experiment al results, it can be found that the theoretical results obtained by the second-order perturbation method in frequency domain are in good agreement with the experimental results, indicating that the damping coefficient of slow oscillation of the tanker required in frequency domain calculation can be determined by reference to the damping coefficient of the tanker moored by a spring system in irregular waves, and the second-order perturbation method can be used to analyze the dynamic response of a turret-moored tanker.

Second-Order Consensus in Networks of Agents with Delayed Dynamics

This paper proposes second-order consensus protocols and gives a measure of the robustness of the protocols to the time-delays existing in the dynamics of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states achieve second-order consensus asymptotically for appropriate time-delay if the topology of the network is connected. Particularly, a nonconservative upper bound on the fixed time-delay that can be tolerated is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which makes the proposed protocols scalable. It reduces the complexity of connections among agents significantly. Simulation results are provided to verify the effectiveness of the theoretical results for second-order consensus in networks in the presence of time-delays existing in the dynamics of agents.