Average Consensus and Stability Analysis in Networked Dynamic Systems

This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is a high dimensional vector as a solution of the highly nonlinear first order dynamics with and without drift terms. This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is high Under the proposed interaction rules, agreements as a common average value or an average trajectory are reached, solving finitetime average consensus and the multisystem equilibrium is controlled leading to the finitetime stability of each system origin. Sufficient conditions are achieved using the Lyapunov techniques and the graph theory. In networked dynamic systems, the theoretical results of the paper cover a large class of underactuated autonomous systems as formation flight, multivehicle coordination, and heterogeneous multisystem behaviors. Some examples are introduced in simulation which approves the proposed protocols.

Distributed Mechanism for Detecting Average Consensus with Maximum-Degree Weights in Bipartite Regular Graphs

In recent decades, distributed consensus-based algorithms for data aggregation have been gaining in importance in wireless sensor networks since their implementation as a complementary mechanism can ensure sensor-measured values with high reliability and optimized energy consumption in spite of imprecise sensor readings. In the presented article, we address the average consensus algorithm over bipartite regular graphs, where the application of the maximum-degree weights causes the divergence of the algorithm. We provide a spectral analysis of the algorithm, propose a distributed mechanism to detect whether a graph is bipartite regular, and identify how to reconfigure the algorithm so that the convergence of the average consensus algorithm is guaranteed over bipartite regular graphs. More specifically, we identify in the article that only the largest and the smallest eigenvalues of the weight matrix are located on the unit circle; the sum of all the inner states is preserved at each iteration despite the algorithm divergence; and the inner states oscillate between two values close to the arithmetic means determined by the initial inner states from each disjoint subset. The proposed mechanism utilizes the first-order forward and backward finite-difference of the inner states (more specifically, five conditions are proposed) to detect whether a graph is bipartite regular or not. Subsequently, the mixing parameter of the algorithm can be reconfigured the way it is identified in this study whereby the convergence of the algorithm is ensured in bipartite regular graphs. In the experimental part, we tested our mechanism over randomly generated bipartite regular graphs, random graphs, and random geometric graphs with various parameters, thereby identifying its very high detection rate and proving that the algorithm can estimate the arithmetic mean with high precision (like in error-free scenarios) after the suggested reconfiguration.