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Most of the existing studies on controllability have only focused on networks with non‐negative weighted interactions/edges among agents. In fact, there are both positive and negative weighted interactions in a network, where positive/negative weight implies cooperative/antagonistic interaction. The controllability of leader‐based multi‐agent systems described by directed/undirected signed graphs is respectively considered for fixed topology and switching topology. A quantitative characterization of controllability is given based on the influence pattern of leaders and some algebraic and graphical features of controllability are established according to consensus protocols. Moreover, it is proved that all follower agents can be steered to the desired configuration under structurally balanced conditions. Specially, a simultaneously structurally balanced signed multiagent network can be controllable on switching topology even though each subnetwork is uncontrollable. Finally, several numerical examples and simulation results are given. [ABSTRACT FROM AUTHOR]

In this article, the problems of inverse-optimal consensus control (IOCC) for single-integral dynamics in Caputo continuous-time and Grunwald–Letnikov (G-L) discrete-time fractional-order multiagent systems (FOMASs) are investigated. For continuous-time FOMASs, by virtue of the variational method, the optimal solution under the constraint of the global performance index function is presented, and then the optimal state-feedback gain matrix (OSFGM) is derived through the Laplace transform and the inverse transform of fractional order. For discrete-time FOMASs, the OSFGM based on the algebraic Riccati equation (ARE) is computed, then it is shown that the OSFGM is a (asymmetric) Laplace matrix which has a zero eigenvalue and the corresponding network structure is a complete graph. Moreover, we rigorously prove that consensus can be achieved under the optimal state-feedback gain matrices. Finally, two simulation examples are shown to check the validity of the proposed theorems. [ABSTRACT FROM AUTHOR]

A consensus control issue is studied for general second-order multiagent systems via Q-learning method in this article. A novel second-order type with discrete-time dynamics is investigated to solve the corresponding consensus issues. Under fixed directed topology, in order to achieve general second-order consensus for the systems, a model-free Q-learning method is proposed, which can derive the coupling gains matrix without any information from the system dynamics. Moreover, applying the obtained coupling gains matrix, this general second-order multiagent systems can achieve consensus. Then, for undirected graphs, a similar corollary is obtained for this system to achieve general second-order consensus by means of the Q-learning method. Finally, the correctness of the new method is confirmed by several simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for directed positive multiagent systems with nonlinear control input. The directed topology is supposed to be strongly connected. For the case of sector input nonlinearities, the non-negative global consensus conditions are presented by using a novel analysis method which directly considers the nonlinear input, and the feedback matrices are obtained with convex optimization method by solving the quadratic matrix inequalities subject to non-negative constraints. For the case of saturation-type sector input nonlinearities, the global consensus and local consensus results are analyzed, respectively. With the properties of Metzler matrix, the non-negative consensus results are further extended to the strongly connected and balanced positive multiagent systems subject to (saturation-type) sector input nonlinearities and parameter uncertainties. The results are simplified, and the feedback matrices can be given by solving iterative linear matrix inequality with non-negative constraints. Two simulation examples and a practical electrical circuit model are finally carried out to verify the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper considers both semi-global and global containment control for a second-order multi-agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi-global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, M-matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the leader-following consensus of second-order multi-agent systems with nonlinear dynamics and time delay by employing periodically intermittent pinning control. All member agents and the virtual leader share the same nonlinear dynamics relating to the velocity and delayed velocity information. Based on Lyapunov stability theory, we obtain a novel criterion that is independent of the time delay and control width to guarantee the second-order consensus of multi-agent systems with time delay and periodically intermittent controllers. Numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays on undirected networks, in which both a single time-delay and multiple time-delays are addressed. It is established that the switching controllability of discrete-time multi-agent systems is only determined by the information from the leaders to the followers, and the discrete-time multi-agent systems are controllable even if each of its subsystems is uncontrollable. For the special case of fixed topology, an equivalent augmented system without time-delays is proposed to analyze the controllability of multi-agent systems via PBH rank test. Some numerical examples are provided to demonstrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]