Machine Behavior Design And Analysis by Yinyan Zhang & Shuai Li

Author:Yinyan Zhang & Shuai Li
Language: eng
Format: epub
ISBN: 9789811532313
Publisher: Springer Singapore

5.4 Computer Simulations

In this section, to evaluate the behavior of the discrete-time biased min-consensus protocol under different situations, we discuss the simulation results under different settings.

For the sake of illustration, we use the graph shown in Fig. 5.2 to conduct the simulations, for which the set of leader nodes is . The synchronous discrete-time biased min-consensus protocol (5.2) is applied to the nodes on the graph, where the initial node states are given as , ∀i ∈{1, 2, ⋯ , 8}. From Fig. 5.3a, it can be find that after about three time instants, the state variables of the nodes reach the equilibrium at which and , in which p il denotes the length of a shortest path from node i to node l in set {1, 2, 3}. The result is consistent with Theorem 5.1. We also evaluate the case with bounded time delays. For this case, the randomly varying time delays τ ij within interval (1, 10) are considered. As seen from Fig. 5.3b, under time delays, the same equilibrium is still reached although more time instants are took, which is consistent with Theorem 5.2.

Fig. 5.2A undirected connected graph consisting of eight nodes where the set of leaders is

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