In frequency hopping (FH) wireless communications, finding an effective transmission strategy to properly mitigate jamming has been recently considered as a critical issue, due to the inherent broadcast nature of wireless communications. Recently, game theory has been proposed as a powerful tool for dealing with the jamming problem, which can be considered as a player (jammer) playing against a user (transmitter). Different from existing results, in this paper, a bimatrix game framework is developed for modeling the interaction process between the transmitter and the jammer, and the sufficient and necessary conditions for Nash equilibrium (NE) strategy of the game are obtained under the linear constraints. Furthermore, the relationship between the NE solution and the global optimal solution of the corresponding quadratic programming is presented. In addition, a special analysis case is developed based on the continuous game framework in which each player has a continuum of strategies. Finally, we show that the performance can be improved based on our game theoretic framework, which is verified by numerical investigations.

Inspired by the interesting findings regarding the hierarchy and coordination of pigeons in Nagy et al. [Nature, 2010], we revisit the discrete-time leader-follower consensus problem with switching topologies. The purpose of this work is to investigate the impact of hierarchical topologies and followers' self-loops on the convergence performance of leader-follower consensus, including the convergence rate and robustness to switching topologies. We first study the fixed topology case, and show that the followers converge to the leader's state in finite time if and only if each follower has no self-loops and the topology is hierarchical. However, we show via counterexample, that leader-follower consensus may not be achieved when some followers have no self-loops and the topology is switching; even if each interaction graph has a spanning tree rooted at the leader. With the aid of binary relation theory, we further develop a new approach to present a novel sufficient condition for leader-follower consensus with switching topologies and with some followers having no self-loops. We prove that when no followers have self-loops and the same hierarchical organization is kept under the swit

Signed digraphs with both positive and negative weighted edges are widely applied to explain cooperative and competitive interactions arising from various social, biological, and physical systems. This article formulates and solves the asynchronous tracking control problem of multiagent systems with input uncertainties on switching signed digraphs. In the interaction setting, we assume that the leader moves at a time-varying acceleration that cannot be measured by the followers accurately, and further suppose that each agent receives its neighbors’ states information at certain instants determined by its own clock, which is not necessary to be synchronized with those of other agents. Using dynamically changing spanning subdigraphs of signed digraphs to describe graphically asynchronous interactions, the asynchronous tracking problem is equivalently transformed into a convergence problem of products of general substochastic matrices (PGSSM), in which the matrix elements are not necessarily non-negative and the row sums are less than or equal to 1. With the help of the matrix analysis technique and the composition of binary relations, we propose a new and original method to deal with the convergence problem of PGSSM, and further establish a spanning tree condition for asynchronous tracking control. Finally, the validity of the theoretical findings is verified through several numerical examples.

In this contribution, we propose and investigate the containment control issue for general linear multiagent systems (MASs) under the asynchronous setting, where the network topology is not subjected to any structural restrictions and the roles of the leaders and the followers are entirely determined by the network topology. It is assumed that the interaction time instants of each agent, at which this agent interacts with its neighbors, are independent of the other agents' and can be unevenly distributed. An asynchronous distributed algorithm is proposed to implement the control strategy of linear MASs. The non-negative matrix theory and the composition of binary relations are utilized to handle the asynchronous containment control issue. It is shown that the leaders in each closed and strongly connected component of the network topology will reach a common state and the followers will gradually enter the dynamic convex hull constructed by the leaders. Moreover, it is also proved that the system matrix can be strictly unstable, and the upper bound of the system matrix's spectral radius is explicitly stated. Finally, two simulation examples are also provided to verify the efficacy of our theoretical results.

In this paper, we investigate the optimal dynamic social-aware peer selection with spectrum-power trading to maximize the average sum energy efficiency (EE) of cellular users (CUs) for uplink transmission for an orthogonal frequency division multiple access (OFDMA) cellular network with deviceto- device (D2D) communications. Different from the previous studies, which mostly focus on how to exploit social ties in human social networks to construct the permutation of all the feasible peers, we consider dynamic peer selection with social awareness-aided spectrum-power trading in D2D overlaying communications. Specifically, the amount of transmit power from the D2D transmitters to relay the CUs for uplink transmission is determined by their social trust levels. Likewise, the D2D transmitters can gain the corresponding amount of spectrum from the CUs for D2D pair link communications which can be regarded as the compensation of the power consumption for relaying CUs. We formulate the dynamic peer selection problems with social awareness-aided spectrum-power trading in cooperative D2D communications into the infinite-horizon time-average renewal-reward problems subject to time average constraints on a collection of penalty processes. And the Lyapunov optimization concepts based drift-plus-penalty (DPP) algorithms are proposed to solve them. Simulation results demonstrate the effectiveness of the proposed dynamic peer selection algorithms. And further performance comparison indicates that the proposed dynamic peer selection algorithms not only maximize the average EE of CUs but also guarantee higher privacy protection.