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This article aims at developing a scaling-function approach for distributed optimization of unbalanced multiagent networks under convex constraints. The distinguishing feature of the algorithm is that it does not employ agents’ out-degree information, nor does it require the estimation of the left eigenvector, corresponding to the zero eigenvalue, of the Laplacian matrix. Existing approaches for unbalanced networks either demand the knowledge on agents’ out-degrees, which is impractical in applications, where an agent might not be aware of the detection and employment of its information by other agents, or require every agent to be equipped with a network-sized estimator, causing an additional $n^2$ storage and communication cost with $n$ being the network size. The results exhibit an inherent connection between the selection of the scaling factor and the convergence property of the algorithm, among other known factors such as the network topology and the boundedness of the subgradients of the local objective functions. Numerical examples are provided to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

Due to the nonsymmetric property of the associated Laplacian matrix and the existence of uncertainties in the agent dynamics, the leaderless consensus problem of uncertain multiagent systems under general directed graphs is challenging. Motivated by the classical model reference adaptive control, in this article, we propose a simple yet efficient scheme, called the model reference adaptive consensus, by arranging each agent a reference output to track, where the output is generated by a linear reference model with the relative state measurements as input. We consider two typical agent dynamics, namely, the general linear dynamics with matching uncertainties and the second-order dynamics with extended matching uncertainties. Different linear reference models are designed for the above uncertain agent dynamics. For the first one, dynamical consensus is achieved under a fixed directed graph containing a directed spanning tree. For the latter one, position consensus is achieved under switching uniformly jointly connected graphs. In the proposed algorithms, only the relative states are interacted among the agents and there is no requirement on the communication of virtual signals. [ABSTRACT FROM AUTHOR]

This article studies a distributed average tracking (DAT) problem, in which a collection of agents work collaboratively, subject to local communication, to track the average of a set of reference signals, each of which is available to a single agent. Our primary objective is to seek a design methodology for DAT under possibly weight-unbalanced directed networks—the most general and thus most challenging case from the network topology perspective, which has few results in the literature. For this purpose, we propose a distributed algorithm based on a chain of two integrators that are coupled with a distributed estimator. It is found that the convergence depends on not only the network topology but also the deviations among the reference signal accelerations. Another primary interest of this article stems from the dynamics perspective—a point perceived as a main source of control design difficulty for multiagent systems. Indeed, we devise a nonlinear algorithm that is capable of achieving DAT under weight-unbalanced directed networks for agents subject to high-order integrator dynamics. The results show that the convergence to the vicinity of the average of the reference signals is guaranteed as long as the signals’ states and control inputs are all bounded. Both algorithms are robust to initialization errors, i.e., DAT is insured even if the agents are not correctly initialized, enabling the potential applications in a wider spectrum of application domains. [ABSTRACT FROM AUTHOR]

This paper addresses distributed average tracking of physical second-order agents with heterogeneous unknown nonlinear dynamics, where there is no constraint on input signals and there is no need for correct initialization. The unknown nonlinear terms in agents’ dynamics are heterogeneous, satisfying a Lipschitz-like condition that will be defined later and is more general than the Lipschitz condition. In the proposed algorithm, a control input and a filter are designed for each agent. Each agent's filter has two outputs and the idea is that the first output estimates the average of the input signals, and the second output estimates the average of the input velocities asymptotically. In parallel, each agent's position and velocity are driven to track, respectively, the first and the second outputs. Having an unknown term in agents’ dynamics necessitates designing the filters for agents. Since the nonlinear terms in agents’ dynamics can be unbounded and the input signals are arbitrary, novel time-varying gains are employed in agents’ filters and control inputs to overcome these unboundedness effects. Finally, the results are improved to achieve the distributed average tracking for a group of double-integrator agents, where there is no constraint on input signals and the filter is not required anymore. Numerical simulations are also presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to a distributed consensus problem for second-order multiagent systems with nonconvex velocity and control input constraints. A distributed control algorithm is introduced using local information. It is shown that consensus can be achieved as long as the union of the communication graphs has directed spanning trees among each time interval of certain bounded length in the presence of arbitrarily bounded communication delays. Finally, a numerical example is included to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, we study the consensus problem for second-order multi-agent systems with heterogeneous unknown inertias and control gains under a general directed graph. Unlike the existing consensus algorithms for second-order multi-agent systems in which all agents are assumed to have common unit inertias or share common control gains, we allow the inertias and the control gains to be heterogeneous and time-varying for each agent. We propose fully distributed consensus algorithms over a general directed graph when there exist, respectively, absolute velocity damping and relative velocity damping. Novel integral-type Lyapunov functions are proposed to study the consensus convergence. Moreover, the adaptive $\sigma$- modification schemes for the gain adaptation are proposed, which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence. Furthermore, we show that one proposed algorithm also works for consensus of agents with intrinsic Lipschitz nonlinear dynamics. The control gains are varying and updated by distributed adaptive laws. As a result, the proposed algorithms require no global information and thus can be implemented in a fully distributed manner. [ABSTRACT FROM AUTHOR]

This technical note introduces a non-quadratic function that is defined in terms of multiple Laplacian quadratics, called the function of composite Laplacian quadratics. The function is mainly used for control synthesis and analysis of multi-agent systems. Some important properties of the function are studied. In particular, the one-level-set dissipation property is established, and the gradient of the function is derived. The function is further applied to solve the consensus problem of linear differential inclusions (LDIs). Finally, a numerical example is given to verify the validity of the derived results. [ABSTRACT FROM AUTHOR]

This technical note studies finite-time consensus problem for a team of networked nonlinear agents with unknown Lipschitz terms under communication constraints, where each agent has a limited sensing range. Because the induced interaction graph is typically state-dependent and dynamic, we propose a distributed nonlinear consensus algorithm that is capable of preserving the initial interaction patterns. By using tools from nonsmooth analysis, sufficient conditions are obtained such that finite-time consensus can be reached. An upper bound of the convergence time is derived via a two-step analysis. The validity of the theoretical result is shown by one simulation example. [ABSTRACT FROM AUTHOR]

This technical note addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this technical note, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied. [ABSTRACT FROM AUTHOR]