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This article considers the distributed time-varying optimal resource allocation problem with time-varying quadratic cost functions and a time-varying coupled equality constraint for multiagent systems. The objective is to design a distributed algorithm for agents with single-integrator dynamics to cooperatively satisfy the coupled equality constraint and minimize the sum of all local cost functions. Here, both the coupled equality constraint and cost functions depend explicitly on time. The cost functions are in quadratic form and may have nonidentical time-varying Hessians. To solve the problem in a distributed manner, an estimator based on the distributed average tracking method is first developed for each agent to estimate certain global information. By leveraging the estimated global information and an adaptive gain scheme, a distributed continuous-time algorithm is proposed, which ensures the agents to find and track the time-varying optimal trajectories with vanishing errors. We illustrate the applicability of the proposed method in the optimal hose transportation problem using multiple quadrotors. [ABSTRACT FROM AUTHOR]

This brief addresses distributed continuous-time optimization problems with time-varying objective functions. The goal is for multiple agents to cooperatively minimize the sum of local time-varying objective functions with only local interaction and information while explicitly taking into account distributed adaptive gain design. Here, the optimal point is time varying and creates an optimal trajectory. First, for the unconstrained case, a distributed nonsmooth algorithm coupled with a state-dependent gain is proposed. It is shown that the interaction gain for each agent can be computed according to the variation of the Hessian and gradient information of the convex local objective functions so that the algorithm can solve the time-varying optimization problem without imposing a bound on any information about the local objective functions. Second, for the case where there exist common time-varying linear equality constraints, an extended algorithm is presented, where local Lagrangian functions are introduced to address the equality constraints. The asymptotic convergence of both algorithms to the optimal solution is proved. Numerical simulations are presented to illustrate the theoretical results. In addition, the one proposed algorithm is experimentally implemented and validated on a multi-Crazyflie platform. [ABSTRACT FROM AUTHOR]

In this paper, the containment problem with nonconvex velocity constraints is studied for second-order discrete-time multiagent systems. A distributed projection-based algorithm is proposed for all followers to be gathered in the convex area formed by multiple stationary leaders. It is revealed that the algorithm can solve the velocity-constrained containment problem with communication delays and switching networks provided that each follower has at least a directed path from some leaders to itself in the union of graphs. The main analysis approaches include model transformation techniques, Lyapunov function, and convexity analysis. A simulation example is also included to elucidate the obtained result. [ABSTRACT FROM AUTHOR]

"Robust prescribed-time consensus of multi-agent systems with actuator saturation and actuator faults" by J. Zhou et al. investigates the prescribed-time leader-following consensus problem of multi-agent system with actuator saturation. In "Robust fault-tolerant consensus control for nonlinear multi-agent systems with prescribed transient and steady-state performance" by Y. Jiang et al., the finite-time consensus tracking problem for second-order nonlinear multi-agent systems subject to the actuator bias fault is investigated. "Finite-time leader-follower consensus control of multiagent systems with mismatched disturbances" by L. Gu et al. studies the robust finite-time leader-follower output consensus problems for second-order multi-agent systems with mismatched disturbances. [Extracted from the article]

This paper studies a containment problem with communication delays and switching topologies. A nonlinear projection containment control algorithm for followers with single-integrator discrete-time dynamics is proposed. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to show the nonincreasing monotonicity of the largest distance from the agents to the convex hull. It is shown that the nonlinear projection containment control algorithm is robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to show the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper studies containment control with communication delays and switching topologies. Firstly, a containment control algorithm for first‐order discrete‐time followers is proposed. Then, it is extended to handle double‐integrator dynamics. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to verify the nonincreasing monotonicity of the largest distance from the followers to the convex hull. It is shown that both algorithms are robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents both algorithms and experimental results to solve a distributed rendezvous problem with shortest distance to convex regions. In a multiagent network, each agent is assigned to a certain convex region and has information about only its own region. All these regions might not have an intersection. Through local interaction with their neighbors, multiple agents collectively rendezvous at an optimal location that is a priori unknown to each agent and has the shortest total squared distance to these regions. First, a distributed time-varying algorithm is introduced, where a corresponding condition is given to guarantee that all agents rendezvous at the optimal location asymptotically for bounded convex regions. Then a distributed tracking algorithm combined with a distributed estimation algorithm is proposed. It is first shown that for general possibly unbounded convex regions, all agents rendezvous in finite time and then collectively slide to the optimal location asymptotically. Then it is shown that for convex regions with certain projection compressibility, all agents collectively rendezvous at the optimal location in finite time, even when the regions are time varying. The algorithms are experimentally implemented on multiple ground robots to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consensus problem of general linear dynamic multiagent systems with stochastic sampling. In this paper, the sampling intervals randomly switch between two different values. The communication topology between agents is fixed and directed. Full- and reduced-order observers are designed based on neighbor agents’ relative output information. The algorithms to construct such observers are also provided. By using the estimated states of the agents, the observer-based consensus protocol with stochastic sampling are presented. Sufficient conditions to ensure consensus in mean square are derived by using Lyapunov stability theory. Finally, simulations are given to examine the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper characterizes a unified consensus region for multi-agent systems, where there exist fixed physical connections with information exchange. The notions of synchronization region in complex networks and consensus region in multi-agent systems can be explained under this unified framework. The effect of the coupling terms on the consensus regions in different situations is analyzed specifically. Furthermore, necessary and sufficient conditions for consensus of agents under both distributed state feedback and observer-based output feedback control are established. On the basis of a parameter-dependent Lyapunov function, a 2-step controller design procedure is proposed, which can reduce the conservativeness to some extent in comparison with the conventional direct Lyapunov method. In addition, for the case with disturbance, the robustness of the system is investigated. Finally, some numerical examples are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses distributed average tracking for a group of physical double-integrator agents under an undirected graph with reduced requirement on velocity measurements. The idea is that multiple agents track the average of multiple time-varying input signals, each of which is available to only one agent, under local interaction with neighbors. We consider two cases. First, a distributed algorithm and filter are proposed, where each agent needs its own and neighbors’ filter outputs obtained through communication besides its local relative positions and its input signal, input velocity and input acceleration. Here, the requirement for either absolute or relative velocity measurements is removed. The algorithm is robust to initialization errors and can deal with a wide class of input signals with bounded deviations in input signals, input velocities, and input accelerations. Second, a distributed algorithm and filter are proposed to remove the requirement for communication. Here, each agent needs to measure the relative positions between itself and its neighbors and its own velocity. However, the requirement for relative velocity measurements between the agent and its neighbors is removed. The algorithm is robust to initialization errors and can deal with the case, where the input signals, input velocities and input accelerations are all bounded. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed H ∞ constrained consensus problem for multi-agent systems. The objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired H ∞ performance index in the presence of external disturbances. A nonlinear distributed algorithm is adopted to solve this constrained consensus problem. To measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set, a nonlinear function is constructed as the H ∞ output function. By analyzing the convexity of the convex set, a sufficient condition is given to solve the constrained consensus problem with the desired H ∞ performance. Finally, a numerical simulation example is provided to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be achieved, a sliding mode control based approach is developed to merge the proposed control Lyapunov and barrier functions/functionals. Based on the sliding surface functional, a feedback control law is established to investigate the stabilization and safety objectives simultaneously. In particular, the properties of the sliding surface functional are analyzed, and further how to construct the sliding surface functional is discussed. Finally, the proposed approaches are illustrated via two numerical examples from the connected cruise control problem of automotive systems and the synchronization problem of multi-agent systems. [ABSTRACT FROM AUTHOR]

In this paper, the event-triggered consensus problem is studied for multi-agent systems with general linear dynamics under a general directed graph. Based on state feedback, we propose a decentralized event-triggered consensus controller (ETCC) for each agent to achieve consensus, without requiring continuous communication among agents. Each agent only needs to monitor its own state continuously to determine when to trigger an event and broadcast its states to its out-neighbors. The agent updates its controller when it broadcasts its states to its out-neighbors or receives new information from its in-neighbors. The ETCC can be implemented in multiple steps. it is proved that under the proposed ETCC there is no Zeno behavior exhibited. To relax the requirement of continuous monitoring of each agent’s own states, we further propose a self-triggered consensus controller (STCC). Simulation results are given to illustrate the theoretical analysis and show the advantages of the event-triggered and self-triggered controllers proposed in this paper. [ABSTRACT FROM AUTHOR]

A wide range of multi-agent coordination problems including reference tracking and disturbance rejection requirements can be formulated as distributed output regulation problem. The general framework captures typical tasks such as output synchronization, leader-following, formation keeping, and many more. We present a distributed regulator for groups of identical and non-identical linear agents subject to global external signals affecting all agents as well as local external signals affecting individual agents. Both signal types comprise references and disturbances. The main contribution is a novel coupling among the agents based on their transient state components, or estimates thereof in the output feedback case. The transient synchronization improves the cooperative behavior in transient phases and guarantees a desired decay rate of the synchronization error, which leads to a cooperative reaction on local disturbances acting on individual agents. [ABSTRACT FROM AUTHOR]

In this paper, we study a distributed optimization problem using a subgradient projection algorithm for multi-agent systems subject to nonidentical constraints and communication delays under local communication. Here the agents capable of communicating with their local neighbors are constrained to remain in possibly different closed convex sets and optimize a global objective function composed of a sum of local objective functions, each of which is known to only one agent. First, we consider the case of fixed graphs and show that distributed optimization might not be achieved on general strongly connected directed graphs. Instead, the agents optimize a weighted sum of the local objective functions. Then we consider the case of switching graphs and show that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the directed graphs is strongly connected among each time interval of a certain bounded length. Furthermore, we consider the case of communication delays, where the delays are mutually independent. It is shown that the distributed optimization problem can be solved by introducing additional delays to the subgradient projection algorithm and the communication delays can be arbitrarily bounded. Finally, numerical examples are included to show the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the containment control problem for multi-agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and time varying. Based on the relative states of neighboring agents, a distributed static continuous controller is designed, under which the containment error is uniformly ultimately bounded and the upper bound of the containment error can be made arbitrarily small, if the subgraph associated with the followers is undirected and, for each follower, there exists at least one leader that has a directed path to that follower. It is noted that the design of the static controller requires the knowledge of the eigenvalues of the Laplacian matrix and the upper bounds of the leaders' control inputs. In order to remove these requirements, a distributed adaptive continuous controller is further proposed, which can be designed and implemented by each follower in a fully distributed fashion. Extensions to the case where only local output information is available and to the case of multi-agent systems with matching uncertainties are also discussed. [ABSTRACT FROM AUTHOR]

SUMMARY Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi-agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi-agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low-dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi-step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi-agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The objective of this paper is to analyze the finite-time convergence of a nonlinear but continuous consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis are more challenging than those under the well-studied consensus algorithms for known linear systems. For this purpose, we propose a novel comparison based tool. By using this tool, it is shown that the proposed nonlinear consensus algorithm can guarantee finite-time convergence if the directed switching interaction graph has a directed spanning tree at each time interval. Specifically, the finite-time convergence is shown by comparing the closed-loop system under the proposed consensus algorithm with some well-designed closed-loop system whose stability properties are easier to obtain. Moreover, the stability and the finite-time convergence of the closed-loop system using the proposed consensus algorithm under a (general) directed switching interaction graph can even be guaranteed by the stability and the finite-time convergence of some well-designed nonlinear closed-loop system under some special directed switching interaction graph. This provides a stimulating example for the potential applications of the proposed comparison based tool in the stability analysis of linear/nonlinear closed-loop systems by making use of known results in linear/nonlinear systems. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses the design of distributed control gains for consensus in multi-agent systems with second-order nonlinear dynamics. First, an effective distributed adaptive gain-design strategy is proposed based only on local information of the network structure. Then, a leader–follower consensus problem in multi-agent systems with updated control gains is studied. A distributed adaptive law is then proposed for each follower based on local information of neighboring agents and the leader if this follower is an informed agent. Furthermore, a distributed leader–follower consensus problem in multi-agent systems with unknown nonlinear dynamics is investigated by combining the variable structure approach and the adaptive method. Finally, simulation examples are given to illustrate the theoretical analysis. [Copyright &y& Elsevier]

Abstract: This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics for both the cases without and with a leader whose control input might be nonzero and time varying. For the case without a leader, based on the relative output information of neighboring agents, two types of distributed adaptive dynamic consensus protocols are proposed, namely, the edge-based adaptive protocol which assigns a time-varying coupling weight to each edge in the communication graph and the node-based adaptive protocol which uses a time-varying coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for all undirected connected communication graphs. It is shown that the edge-based adaptive consensus protocol is applicable to arbitrary switching connected graphs. For the case where there exists a leader whose control input is possibly nonzero and bounded, a distributed continuous adaptive protocol is designed to guarantee the ultimate boundedness of the consensus error with respect to any communication graph which contains a directed spanning tree with the leader as the root and whose subgraph associated with the followers is undirected, requiring neither global information of the communication graph nor the upper bound of the leader’s control input. A distributed discontinuous protocol is also discussed as a special case. Simulation examples are finally given to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper, we study the distributed coordination for second-order multi-agent systems with intrinsic nonlinear dynamics under an undirected graph that characterizes the interaction among the agents or followers. Both the leaderless consensus problem and the coordinated tracking problem with a dynamic leader are considered. By introducing a distributed filter for each agent or follower, the proposed control algorithms use only relative position measurements in the absence of communication. In the special case without the intrinsic nonlinear dynamics, i.e., for multi-agent systems with double-integrator dynamics, we further derive a necessary and sufficient condition for the leaderless consensus problem under a general directed graph. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms. [Copyright &y& Elsevier]

Abstract: This paper deals with the distributed discrete-time coordinated tracking problem for multi-agent systems with Markovian switching topologies. In the multi-agent team, only some of the agents can obtain the leader’s state directly. The leader’s state considered is time varying. We present necessary and sufficient conditions for boundedness of the tracking error system and show the ultimate bound of the tracking errors. A linear matrix inequality approach is developed to determine the allowable sampling period and the feasible control gain. A simulation example is given to illustrate the effectiveness of the results. [Copyright &y& Elsevier]

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]