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This article studies the tracking control problem of networked multiagent systems under both multiple networks and event-triggered mechanisms. Multiple networks are to connect multiple agents and reference systems with decentralized controllers to guarantee their information transmission, whereas the event-triggered mechanisms are to reduce the information transmission via the networks. In this article, each agent has a network to communicate with its controller and reference system, and all networks are independent and asynchronous and have local event-triggered mechanisms, which are based on local measurements and determine whether the local measurements need to be transmitted via the corresponding network. To address this scenario, we first implement the emulation-based approach to develop a novel hybrid model for the tracking control of networked multiagent systems. Next, sufficient conditions are derived and decentralized event-triggered mechanisms are designed to guarantee the desired tracking performance. Furthermore, the proposed approach is applied to derive novel results for the event-triggered observer design problem of networked multiagent systems. Finally, two numerical examples are presented to illustrate the validity of the developed results. [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 paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are not required to be strongly connected at any time, the gradients of the local objective functions are not required to be bounded when their independent variables tend to infinity, and the constraint sets are not required to be bounded. For continuous-time multiagent systems, a distributed continuous algorithm is first introduced where the stepsizes and the convex constraint sets are both nonuniform. It is shown that all agents reach a consensus while minimizing the team objective function even when the constraint sets are unbounded. After that, the obtained results are extended to discrete-time multiagent systems and then the case where each agent remains in a corresponding convex constraint set is studied. To ensure all agents to remain in a bounded region, a switching mechanism is introduced in the algorithms. It is shown that the distributed optimization problems can be solved, even though the discretization of the algorithms might deviate the convergence of the agents from the minimum of the objective functions. [ABSTRACT FROM AUTHOR]

This note is devoted to the distributed optimization problem of multi-agent systems with nonconvex velocity constraints, nonuniform position constraints, and nonuniform stepsizes. Two distributed constrained algorithms with nonconvex velocity constraints and nonuniform stepsizes are proposed in the absence and the presence of nonuniform position constraints by introducing a switching mechanism to guarantee all agents’ position states to remain in a bounded region. The algorithm gains need not to be predesigned and can be selected by each agent using its own and neighbors’ information. By a model transformation, the original nonlinear time-varying system is converted into a linear time-varying one with a nonlinear error term. Based on the properties of stochastic matrices, it is shown that the optimization problem can be solved as long as the communication topologies are jointly strongly connected and balanced. One numerical example is given to show the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this technical note, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information. The gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors' information. It is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval. The analysis approach is based on multiple novel model transformations, proper control parameter selections, boundedness analysis of state-dependent stochastic matrices1, exploitation of the convexity of stochastic matrices, and the joint connectivity of the communication graphs. Numerical examples are included to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for continuous-time multi-agent systems with single-integrator dynamics. The objective is for multiple agents to cooperatively optimize a team objective function formed by a sum of local objective functions with only local interaction and information while explicitly taking into account nonuniform gradient gains, finite-time convergence, and a common convex constraint set. First, a distributed nonsmooth algorithm is introduced for a special class of convex objective functions that have a quadratic-like form. It is shown that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Second, a distributed algorithm is presented for general differentiable convex objective functions, in which the interaction gains of each agent can be self-adjusted based on local states. A corresponding condition is then given to guarantee that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Third, a distributed optimization algorithm with state-dependent gradient gains is given for general differentiable convex objective functions. It is shown that the distributed continuous-time optimization problem can be solved even though the gradient gains are not identical. Fourth, a distributed tracking algorithm combined with a distributed estimation algorithm is given for general differentiable convex objective functions. It is shown that all agents reach a consensus while minimizing the team objective function in finite time. Fifth, as an extension of the previous results, a distributed constrained optimization algorithm with nonuniform gradient gains and a distributed constrained finite-time optimization algorithm are given. It is shown that both algorithms can be used to solve a distributed continuous-time optimization problem with a common convex constraint set. Numerical examples are included to illustrate the obtained theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. The objective is to minimize the sum of local time-varying cost functions, each of which is known to only an individual agent, through local interaction. Here, the optimal point is time varying and creates an optimal trajectory. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. In both cases, a centralized approach is first introduced to solve the optimization problem. Then, this problem is solved in a distributed manner and a discontinuous algorithm based on the signum function is proposed in each case. In the case of single-integrator (respectively, double-integrator) dynamics, each agent relies only on its own position and the relative positions (respectively, positions and velocities) between itself and its neighbors. A gain adaption scheme is introduced in both algorithms to eliminate certain global information requirement. To relax the restricted assumption imposed on feasible cost functions, an estimator based algorithm using the signum function is proposed, where each agent uses dynamic average tracking as a tool to estimate the centralized control input. As a tradeoff, the estimator-based algorithm necessitates communication between neighbors. Then, in the case of double-integrator dynamics, the proposed algorithms are further extended. Two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. To account for interagent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics. It is shown that the center of the agents tracks the optimal trajectory, the connectivity of the agents is maintained, and interagent collision is avoided. [ABSTRACT FROM AUTHOR]

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]

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors’ velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

In this note, a constrained consensus problem is studied for multi-agent systems in unbalanced networks in the presence of communication delays. Here each agent needs to lie in a closed convex constraint set while reaching a consensus. The communication graphs are directed, dynamically changing, and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length. The analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary. To tackle the loss of symmetry caused by unbalanced graphs and communication delays, a novel approach is proposed. The idea is to estimate the distance from each agent to the intersection set of all agents' constraint sets based on the properties of the projection on convex sets so as to show consensus convergence by contradiction. It is shown that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system. It is also shown that the communication delays do not affect the consensus stability and constrained consensus is reached even if the communication delays are arbitrarily bounded. Finally, a numerical example is included to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This note studies the distributed containment control problem for a group of autonomous vehicles modeled by double-integrator dynamics with multiple dynamic leaders. The objective is to drive the followers into the convex hull spanned by the dynamic leaders under the constraints that the velocities and the accelerations of both the leaders and the followers are not available, the leaders are neighbors of only a subset of the followers, and the followers have only local interaction. Two containment control algorithms via only position measurements of the agents are proposed. Theoretical analysis shows that the followers will move into the convex hull spanned by the dynamic leaders if the network topology among the followers is undirected, for each follower there exists at least one leader that has a directed path to the follower, and the parameters in the algorithm are properly chosen. Numerical results are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this note, we study a distributed coordinated tracking problem for multiple networked Euler–Lagrange systems. The objective is for a team of followers modeled by full-actuated Euler–Lagrange equations to track a dynamic leader whose vector of generalized coordinates is time varying under the constraints that the leader is a neighbor of only a subset of the followers and the followers have only local interaction. We consider two cases: i) The leader has a constant vector of generalized coordinate derivatives, and ii) The leader has a varying vector of generalized coordinate derivatives. In the first case, we propose a distributed continuous estimator and an adaptive control law to account for parametric uncertainties. In the second case, we propose a model-independent sliding mode control algorithm. Simulation results on multiple networked two-link revolute joint arms are provided to show the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

In this article, a distributed constrained optimization problem is studied with nonconvex input constraints, nonuniform convex state constraints, and nonuniform step sizes for single-integrator multiagent systems. Due to the existence of nonconvex input constraints, the edge weights between agents are equivalently multiplied with different time-varying scaling factors, and thus, the real interaction relationship cannot be kept balanced, even if the original communication graphs are kept balanced. Due to the existence of nonuniform convex state constraints and nonuniform step sizes, the system contains strong nonlinearities, which are coupled with the unbalance of the real interaction relationship, making existing analysis approaches hard to apply in this article. The main idea of the analysis approach is to fully explore the angles between the vectors from the agent states to their own projections on the intersection set of the convex state constraint sets so as to show that the distances from the agents to the intersection set diminish to zero as time evolves. By combining the analysis approaches in this article and our previous works, all agents are proved to converge to a common point and simultaneously solve the given optimization problem as long as the union of the communication graphs is strongly connected and balanced among each time interval of certain length. Numerical examples are given to show the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This note further studies the previously proposed consensus protocol for linear multi-agent systems with communication noises. Each agent is allowed to have its own time-varying gain to attenuate the effect of communication noises. Therefore, the common assumption that all agents have the same noise-attenuation gain is not necessary. It has been proved that if all noise-attenuation gains are infinitesimal of the same order, then the mean square leader-following consensus can be reached. Furthermore, the convergence rate of the multi-agent system has been investigated. If the noise-attenuation gains belong to a class of functions which are bounded above and below by t^-\beta $(\beta\in(0,1))$ asymptotically, then the second-moment of the relative state between each follower agent and the leader agent is characterized by a function bounded above by t^-\beta asymptotically. [ABSTRACT FROM PUBLISHER]

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 note addresses the adaptive consensus problem of first-order and second-order linearly parameterized multi-agent systems with unknown identical control directions. First, we propose a new Nussbaum-type function based on which a key lemma is established. The lemma plays an important role in analyzing the consensus of the closed-loop multi-agent systems. Second, the Nussbaum-type function is used to design adaptive control laws for first-order and second-order linearly parameterized multi-agent systems so that each agent seeks for the unknown control direction adaptively and cooperatively. Then, under the assumption that the interconnection topology is undirected and connected, it is proved that the first-order and second-order multi-agent systems can achieve consensus by choosing proper design parameters. Two simulation examples are given to illustrate the effectiveness of the proposed control laws. [ABSTRACT FROM AUTHOR]

This article addresses the problem of cooperative adaptive containment control for multiagent systems, which specifies the objective of jointly achieving containment control and accurate adaptive learning/identification of unknown system parameters. We consider a class of linear uncertain multiagent systems with multiple leaders subject to bounded unmeasurable inputs and multiple followers subject to unknown system dynamics. A novel cooperative adaptive containment control architecture is proposed, which consists of a discontinuous nonlinear state-feedback control law and a filter-based cooperative adaptation law. This new control architecture is compelling in the sense that exponential convergence of both containment tracking errors to zero and adaptation parameters to their true values can be achieved simultaneously under a mild cooperative finite-time excitation condition. This condition significantly relaxes existing ones (e.g., persistent excitation and finite-time excitation) for parameter identification in adaptive control systems. Effectiveness of the proposed approach has been demonstrated through both rigorous analysis and a case study. [ABSTRACT FROM AUTHOR]

This paper studies the distributed time-varying convex optimization problem for a class of nonlinear multiagent systems. An auxiliary system is first designed to estimate the global optimal state and its high-order derivatives by means of a distributed algorithm. Relying on this auxiliary system, the solution of the distributed time-varying convex optimization problem is converted into that of a tracking problem for a class of nonlinear systems. A tracking control scheme is then proposed based on the back-stepping strategy. Simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This technical note addresses the distributed specified-time consensus protocol design problem for multiagent systems with general linear dynamics over directed graphs. By using motion planning approaches, a novel class of distributed consensus protocols are developed. With a prespecified settling time, the proposed protocols solve the consensus problem of linear multiagent systems over directed graphs containing a directed spanning tree. In particular, the settling time can be offline prespecified, according to task requirements. Compared with the existing results for multiagent systems, to our best knowledge, this is the first time specified-time consensus problems are raised and solved for general linear multiagent systems over directed graphs. Extensions to the specified-time formation flying are further studied for multiple satellites described by Hill equations. [ABSTRACT FROM AUTHOR]

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch–Kuhn–Tucker condition. By using tools from nonsmooth analysis and set-valued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

We study synchronization of coupled linear systems over networks with weak connectivity and nonuniform time-varying delays. We focus on the case where the internal dynamics are time-varying but nonexpansive (stable dynamics with a quadratic Lyapunov function). Both uniformly jointly connected and infinitely jointly connected communication topologies are considered. A new concept of quadratic synchronization is introduced. We first show that global asymptotic quadratic synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns out that the existence of a uniform time interval for the jointly connected communication topology is not necessary and quadratic synchronization can be achieved when the time-varying nonuniform delays are arbitrarily bounded. Simulation results are provided to validate 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]

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]