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This paper considers a class of distributed aggregative games for first-order and second-order integrator-type multi-cluster systems, respectively. Two Nash equilibrium seeking algorithms are designed based on a distributed aggregation observer which is used to estimate the aggregations of the clusters. The convergence is proved by the input-to-state stable method. Moreover, the algorithms are applied to a class of location control problems, that is, distributed nonlinear placement problems for multi-cluster systems. Finally, some simulations are presented to illustrate the effectiveness of the designed algorithms. [ABSTRACT FROM AUTHOR]

In this article, a class of distributed quadratic games is considered over an undirected graph. The issue on the communication topology restriction is introduced and the players’ dynamics are with nonlinear dynamics and unknown time-varying perturbation. A distributed Nash equilibrium seeking algorithm is proposed based on a high-gain observer method, and the convergence is analyzed by the Lyapunov stability theory. It is shown that each player estimates the rival players’ states, and the errors between the players’ states and the Nash equilibrium are ultimately bounded by a small bound. Moreover, the presented algorithm is free of chattering phenomena because it is designed using the hyperbolic tangent function instead of the signum function to dominant the perturbation. The effectiveness of the proposed algorithm is validated via a simulation of the oligopoly game in which five firms produce the same products in a duopoly market structure. [ABSTRACT FROM AUTHOR]

This article investigates the distributed localization and circumnavigation problem for a group of agents using bearing measurements. In particular, there is one agent appointed as a pathfinder in the group that is responsible for measuring the relative bearing with respect to an uncertain target. We consider both persistent and intermittent measurement cases. The objective is to drive all the agents such that they first localize the given target and then circumnavigate it isometrically. First, for the persistent measurement case, a distributed control algorithm is developed by introducing a distributed observer. In terms of Lyapunov theorem, it is shown that the proposed control algorithm guarantees the achievement of the localization and circumnavigation objective. Next, we focus on the case of the intermittent bearing measurement. In particular, another feasible distributed control algorithm is designed. Based on the nonlinear contraction theory, it is demonstrated that the localization and circumnavigation objective can also be achieved. Simulation and experiment results verify the effectiveness of the proposed distributed control algorithms. [ABSTRACT FROM AUTHOR]

Summary: This article addresses a surveillance problem where the goal is to achieve a circular motion around a target by a non‐holonomic differentially driven mobile robot. The available information for the mobile robot includes its own position, velocity with respect to the inertial frame, and the bearing angle of the target in its body frame. Since the target position is unavailable, an estimator is first proposed to localize it. Then a two‐step controller is given to drive the mobile robot to move onto a circular trajectory with a desired radius around it. It is shown that the proposed algorithm guarantees the convergence of the estimation error to a small neighborhood of zero and the motion of the robot to a small neighborhood of a designed radius. The performance of the proposed algorithm is first verified by simulations. Then, several experiments on a differentially driven mobile robot, Pioneer 3‐DX, are presented to further validate the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the distributed resource allocation problem with nonsmooth local cost functions subject to the coupled equality and inequality constraints. In particular, each local cost function is expressed as the sum of a differentiable function and two nonsmooth functions. By using the operator splitting and primal–dual method, a continuous-time distributed proximal algorithm is developed, which can be applied to more general local cost functions that are convex but not necessarily smooth. In addition, the proposed algorithm is fully distributed in the sense that the gain parameter can be determined locally and does not require any global information of the network. By applying Lyapunov stability analysis and convex optimization theory, it is shown that the decision variables of all the agents converge to an optimal solution. Finally, a simulation example is carried out to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We consider a distributed consensus problem over a network, where at each time instant every node receives two pieces of information from disjoint neighboring sets: a weighted average of current states of neighbors from a primary network, and a weighted average of one-hop delayed states of neighbors from a secondary network. The proposed algorithm makes each node update its state to a weighted average of these individual averages. We show that convergence to consensus is guaranteed with non-trivial weights. We also present an explicit formula for the weights allocated to each piece of the information for the optimal rate of convergence, when the secondary network is the complement of the primary network. Finally numerical examples are given to explore the case when the neighbor sets of the agents do not cover the whole network. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for multi-agent systems. A distributed consensus algorithm is developed by constructing homogeneous pulse width modulators for agents in the network. In particular, a certain percentage of the sampling period named duty cycle is modulated according to some state difference with respect to the neighbors at each sampling instant. During each duty cycle, the amplitude of the pulse is fixed. The proposed pulse width modulation scheme enables all agents to sample asynchronously with arbitrarily large sampling periods. It provides an alternative digital implementation strategy for multi-agent systems. We show that consensus is achieved asymptotically under the proposed scheme. The results are compared with the self-triggered ternary controller. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a distributed cooperative tracking problem is studied for a group of non-identical second-order nonlinear systems with bounded external disturbances. The control goal is to drive the states of the followers to converge to those of a time-varying leader in the presence of only local information interactions from the leader to the followers and between the followers. We first propose a simple distributed control algorithm for the case when both the relative position and relative velocity measurements are available for feedback. It is shown that distributed cooperative tracking can be achieved if in the sensing topology the leader has directed paths to all followers. Then, the extension to the case when the velocity measurements are not available is studied. We consider two different scenarios, i.e., when the absolute position measurements and local communication between neighbors are available and only the relative position measurements are available. Distributed observers and distributed control inputs are designed to address these two scenarios. Numerical studies are carried out to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper, swarm tracking problems with group dispersion and cohesion behaviors are discussed for a group of Lagrange systems. The agent group is separated into two subgroups. One is called the leader group, whose members are encapsulated with the desired generalized coordinates and generalized coordinate derivatives. The other one, referred to as the follower group, is guided by the leader group. The objective is to guarantee distributed tracking of generalized coordinate derivatives for the followers and to drive the generalized coordinates of the followers close to the convex hull formed by those of the leaders. Both the case of constant leaders’ generalized coordinate derivatives and the case of time-varying leaders’ generalized coordinate derivatives are considered. The proposed control algorithms are shown to achieve velocity matching, connectivity maintenance and collision avoidance. In addition, the sum of the steady-state distances between the followers and the convex hull formed by the leaders is shown to be bounded and the bound is explicitly given. Simulation results are presented to validate the effectiveness of theoretical conclusions. [Copyright &y& Elsevier]

This brief studies distributed containment control for double-integrator dynamics in the presence of both stationary and dynamic leaders. In the case of stationary leaders, we propose a distributed containment control algorithm and study conditions on the network topology and the control gains to guarantee asymptotic containment control in any dimensional space. In the case of dynamic leaders, we study two cases: leaders with an identical velocity and leaders with nonidentical velocities. For the first case, we propose two distributed containment control algorithms to solve, respectively, asymptotic containment control under a switching directed network topology and finite-time containment control under a fixed directed network topology. In particular, asymptotic containment control can be achieved for any dimensional space if the network topology is fixed and for only the 1-D space if the network topology is switching. For the second case, we propose a distributed containment control algorithm under a fixed network topology where the communication patterns among the followers are undirected and derive conditions on the network topology and the control gains to guarantee asymptotic containment control for any dimensional space. Both simulation results and experimental results on a multi-robot platform are provided to validate some theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, time-domain (Lyapunov theorems) and frequency-domain (the Nyquist stability criterion) approaches are used to study leaderless and leader-following consensus algorithms with communication and input delays under a directed network topology. We consider both the first-order and second-order cases and present stability or boundedness conditions. Several interesting phenomena are analyzed and explained. Simulation results are presented to support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper develops a distributed primal–dual algorithm via an event-triggered mechanism to solve a class of convex optimization problems subject to local set constraints, coupled equality and inequality constraints. Different from some existing distributed algorithms with the diminishing step-sizes, our algorithm uses the constant step-sizes, and is shown to achieve an exact convergence to an optimal solution with an ergodic convergence rate of O (1 / k) for general convex objective functions, where k > 0 is the iteration number. Based on the event-triggered communication mechanism, the proposed algorithm can effectively reduce the communication cost without sacrificing the convergence rate. Finally, a numerical example is presented to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a simple but efficient framework is proposed to achieve finite-time decentralized formation tracking of multiple autonomous vehicles with the introduction of decentralized sliding mode estimators. First, we propose and study both first-order and second-order decentralized sliding mode estimators. In particular, we show that the proposed first-order decentralized sliding mode estimator can guarantee accurate position estimation in finite time and the proposed second-order decentralized sliding mode estimator can guarantee accurate position and velocity estimation in finite time. Then the decentralized sliding mode estimators are employed to achieve decentralized formation tracking of multiple autonomous vehicles. In particular, it is shown that formation tracking can be achieved for systems with both single-integrator kinematics and double-integrator dynamics in finite time. By using the decentralized sliding mode estimators, many formation tracking/flying scenarios can be easily decoupled into two subtasks, that is, decentralized sliding mode estimation and vehicle desired state tracking, without imposing a stringent condition on the information flow. Finally, several simulation results are presented as a proof of concept. [ABSTRACT FROM AUTHOR]

This paper studies the Nash equilibrium seeking problem for non-cooperative games subject to set and nonlinear inequality constraints. The cost function for each player and the constrained function are determined by all the players' decision variables. Each player is assigned a constrained set while all the players are subject to a coupling nonlinear inequality constraint. A continuous-time distributed seeking algorithm using local information interaction is proposed, where the players deliver/receive information unidirectionally over a directed network. In particular, a distributed observer is first introduced for each player to estimate all the others' decision variables. Then, by using these estimates, a seeking algorithm is synthesized with a projection operator. Based on the time-scale separation approach, it is shown that the proposed continuous-time distributed seeking algorithm guarantees the convergence of the strategy profile to an arbitrarily small neighborhood of the generalized Nash equilibrium satisfying a KKT condition. An illustrative example is finally presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Distributed optimization for uncertain nonlinear interconnected multi-agent systems is considered in this paper. The objective is to design distributed algorithms by using local information such that all the agents' outputs converge to the global optimal output. The problem is challenging due to unknown modeling uncertainties and nonlinear interconnections. First, a distributed algorithm composed of a distributed state observer and a distributed optimal output observer is presented for heterogeneous outputs. Next, it is shown that the objective can be achieved by employing solely a distributed optimal output observer if the agents' outputs are homogeneous. Finally, the algorithms' effectiveness is validated by an electrical power system composed of four-machine subsystems. [ABSTRACT FROM AUTHOR]