Multi-agent Consensus Problem Research Articles

On the Existence of Stable Real nth-Order Transfer Functions With Desired Phase at n Frequencies

We consider the following question: Given n distinct non-negative frequencies {ω 1 , ω 2 , ... ω n }, does there always exist a stable real nth-order transfer function (TF) with a desired phase at these frequencies? For n even, we prove that the answer is yes and propose a numerical algorithm for obtaining such TFs. For n > 1 odd, we conjecture that the answer is no. These results are useful for designing lower-order output feedback compensators that solve the multi-agent consensus problem for high-order linear agent dynamics.

Resilient Randomized Quantized Consensus

We consider the problem of multiagent consensus where some agents are subject to faults/attacks and might make updates arbitrarily. The network consists of agents taking integer-valued (i.e., quantized) states under directed communication links. The goal of the healthy normal agents is to form consensus in their state values, which may be disturbed by the non-normal, malicious agents. We develop update schemes to be equipped by the normal agents whose interactions are asynchronous and subject to nonuniform and time-varying time delays. In particular, we employ a variant of the so-called mean subsequence reduced algorithms, which have been long studied in computer science, where each normal agent ignores extreme values from its neighbors. We solve the resilient quantized consensus problems in the presence of totally/locally bounded adversarial agents and provide necessary and sufficient conditions in terms of the connectivity notion of graph robustness. Furthermore, it will be shown that randomization is essential both in quantization and in the updating times when normal agents interact in an asynchronous manner. The results are examined through a numerical example.

Distributed Fault-Tolerant Consensus Protocol for Fuzzy Multi-Agent Systems

A distributed actuator fault-tolerant strategy for fuzzy multi-agent systems is investigated in this paper. The proposed strategy utilizes an adaptive methodology in designing the consensus control. Compared with well-known consensus analysis, this paper devotes to the fault effect in analyzing multi-agent consensus problem. We conducted a Lyapunov stability analysis to unfold the advantages of proposed method in the distributed fault-tolerant control. Simulation example is provided to demonstrate the effectiveness of the theoretical results.

Distributed real-time non-linear receding horizon control methodology for multi-agent consensus problems

This work investigates the consensus problem for multi-agent nonlinear systems through the real-time nonlinear receding horizon control methodology. A scheme is developed to reach the consensus for nonlinear multi-agent systems under fixed directed/undirected graph(s) without any linearization technique. The problem of consensus is converted into an optimization problem and is directly solved by the backwards sweep Riccati method to generate the control protocol which is a non-iterative algorithm. Stability analysis is conducted to provide convergence guarantees. An extension to the leader-following consensus problem of nonlinear systems is presented. Several examples are provided to validate the effectiveness of the presented scheme.

Leader-following consensus for discrete-time descriptor multi-agent systems with observer-based protocols

In this paper, the leader-following consensus problem of discrete-time descriptor multi-agent systems is considered. Each agent’s dynamics is modelled by a discrete-time linear descriptor system, and the interaction topology among the agents is assumed to be directed. To solve the multi-agent consensus problem, three different architectures of connecting observers and controllers are used to construct the consensus protocols. A kind of modified generalized algebraic Riccati equation is provided to design the protocol’s gain matrices. Based on graph theory, matrix theory and the Lyapunov method, some sufficient convergence conditions are established to guarantee the descriptor multi-agent system achieves consensus. Finally, a simulation example is provided to illustrate the obtained results.

Cyber-Security in Multi-Agent Consensus Problems

Cyber-Security in Multi-Agent Consensus Problems

The consensus problem in the behavioral approach

In this paper we investigate the multi-agent consensus problem in a broad context, by assuming both for the agents and for the distributed controllers higher order input–output dynamic models.The behavioral approach developed by Jan Willems seems to be the most appropriate set-up where to investigate this general problem.By making use of the behavioral approach, we will show that the consensus problem can be naturally rephrased as a special case of stabilization problem: the stabilization pertains only a part of the system variables (the outputs) and it is achieved through regular full interconnection of the agent models and of the controllers. It turns out that if the communication among agents is described by a weighted, undirected and connected graph, then a necessary and sufficient condition for the consensus problem to be solvable is that the output is stabilizable from the input in the agents model. In this respect, the theory here developed for higher-order input–output models naturally extends the results about consensus derived in the state-space approach.

Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer

In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.

Distributed optimal control for multi-agent systems with obstacle avoidance

In this paper, we investigate distributed optimal control of a multi-agent consensus problem in an obstacle-laden environment. A new optimal control protocol is proposed which can let the multi-agent system reach consensus as well as avoid obstacles with a reasonable control effort. The penalty function designed to achieve obstacle avoidance capability is constructed from an inverse optimal control perspective. The asymptotic stability and optimality of the consensus algorithm are proven. In addition, the control law of each agent only requires local information from the neighbors. Finally, simulations are presented to illustrate the effectiveness of the proposed methods.

Distributed observer-based consensus protocol for descriptor multi-agent systems

In this paper, the consensus problem of descriptor multi-agent systems is considered. Each agent’s dynamics is given in the general form of a continuous-time linear descriptor system, and the communication topology among the agents is assumed to be directed in fixed topology case and balanced in switching topology case, respectively. Three kinds of distributed observer-based consensus protocols are proposed to solve the descriptor multi-agent consensus problem. Multi-step algorithms are provided to design the gain matrices and coupling constants involved in the protocols. The design approach is based on the generalized Riccati equation, and Lyapunov stability theory. Some sufficient consensus conditions are established to guarantee that the descriptor multi-agent system achieves consensus under the directed fixed topology and balanced switching topology. Furthermore, the state variable feedback consensus problem and the observer-based consensus problem with a desired decay rate are discussed. Finally, a simulation example is provided to illustrate the obtained results.

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.

Distributed reduced‐order observer‐based approach to consensus problems for linear multi‐agent systems

In this study, the authors probe the multi-agent consensus problem with general linear dynamics via the distributed reduced-order observer-based protocols under directed switching topology. A new type reduced-order observer is adopted to modify the existed consensus protocols. Based on graph theory, Riccati equation and Lyapunov method, a multi-step algorithm is provided to design the gain matrices involved in the used protocols. The consensus stability problem is investigated by use of the piecewise Lyapunov functions incorporated with an average dwell time approach. It is shown that if the average dwell time is chosen sufficiently large and all directed switching topologies have a directed spanning tree, then the multi-agent system can achieve consensus via the author's modified protocols. Furthermore, as the special cases, the consensus conditions under fixed topology and balanced switching topology are obtained easily. To obtain a desired consensus decay rate, the related gain matrix design approach is provided. Finally, a simulation example is given to illustrate the effectiveness of their obtained results.

Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design

This paper considers the leader-following tracking problem of second-order nonlinear multi-agent systems with a reference leader. It is assumed that all following agents can only access the relative position information with its neighbors, the position and velocity information of the leader is only accessed by a subset of the following agents, and the leader׳s bounded reference input cannot be available by any following agents. To track the active leader, a distributed discontinuous observer-based consensus protocol is proposed for each following agent, whose observer is used to estimate the agent׳s unmeasured velocity. Under connected undirected interaction topology, the proposed protocol can be used to solve the second-order nonlinear multi-agent consensus problem. While the reference input of the leader is known, the proposed protocol can solve the consensus problem under a class of directed switching interaction topologies. Furthermore, to make the designed approach in fully distributed fashion, the distributed adaptive laws are provided to design the protocol coupling parameters. Finally, a numerical example is presented to illustrate our obtained result.

Coverage Control for Mobile Sensor Networks on a Circle

This paper investigates the coverage problem for mobile sensor networks on a circle. The goal is to minimize the largest distance from any point on the circle to its nearest sensor while preserving the mobile sensors' order. The coverage problem is translated into a multi-agent consensus problem by showing that the largest distance from any point to its nearest sensor is minimized if the counterclockwise distance between each sensor and its right neighbor reaches a consensus. Distributed control laws are also developed to drive the mobile agents to the optimal configuration with order preservation. Simulation results illustrate the effectiveness of the proposed control laws.

A distributed event‐triggered scheme for discrete‐time multi‐agent consensus with communication delays

This study mainly investigates the event-triggered data transmission in discrete-time multi-agent consensus problem with communication delays. A new distributed event-triggered scheme is proposed for the considered multi-agent network model. An action of the agent is triggered by an `event' which is a well-defined condition on the system state. For the proposed event-triggered protocol, the authors prove that the multi-agent network will achieve consensus asymptotically. Numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.

An observer-based consensus tracking control and application to event-triggered tracking

Leader–follower mechanism provides an important framework for multi-agent consensus problems. In this paper, a consensus tracking problem is investigated for a second-order multi-agent system with a self-active leader. The input (acceleration) to the leader is assumed to be time-varying and unavailable to followers. An observer-based consensus tracking control is designed on the basis of a novel distributed velocity estimation technique. The ultimate boundedness and the stability of the tracking error system are analyzed by virtue of an Input-State-Stability (ISS) Lyapunov function approach. Then, the dynamic consensus tracking control is applied to solve an event-triggered tracking problem. Finally, some numerical simulation results are presented to demonstrate the effectiveness of the proposed consensus tracking control.

On Weak-Invariance Principles for Nonlinear Switched Systems

In this technical note, we develop two weak-invariance principles for nonlinear switched systems. We first present a union weak-invariance principle for switched systems which includes as a special case the integral invariance principle. It is shown that the switched solution approaches the largest weakly invariant set of the combined zero loci of the output functions. Then, we extend the union weak-invariance principle to an intersection weak-invariance principle, which greatly reduces the convergence region. Unlike the existing results, in which the constructions of Lyapunov functions are inevitable, our principles do not require the existence of Lyapunov functions. Numerical examples are presented to demonstrate the feasibility of our principles, as well as applications to multi-agent consensus problems.

Discrete-time multi-agent consensus with quantization and communication delays

In this paper, discrete-time multi-agent consensus problem with quantization and communication delays is investigated. A new discrete-time multi-agent consensus model is considered in which each agent can only receive the delayed quantized information from its neighbors. In the presence of quantization and communication delays, it is shown that the multi-agent network can achieve consensus under the connectivity network topology. Simulation examples are also provided to demonstrate the correctness of the theoretical results.

Consensus of Multi-Agent Systems: A Relative-Input-Output Approach

This paper studies the multi-agent consensus problem of complex networks consisting of general homogeneous continuous linear time-invariant systems with controls under a time-invariant directional communication topology. A new approach based on relative-input-output is proposed to solve the problem. In contrast to a popular method where each agent is equipped with an observer, and hence involving heavy observer dynamics, the proposed approach is static and utilizes relative-input and relative-output eliminating the observers aforementioned, therefore is practically much simpler and easier to implement significantly reducing computational and communicational burdens and costs. Extension of the framework is then made to tackle a dual problem: consensus of distributed filtering without controls. Two numerical examples are provided to validate the proposed approach.

Consensus Control for Variable Multi-Agent Systems with Faults and Disturbances

This paper investigates multi-agent consensus problem with an active leader as well as external disturbances and some faults. The undirected networks with variable interconnection topology are taken into consideration. Distributed consensus control algorithm is proposed to analyze the disturbance rejection and fault sensitivity problem arising in the coordination control of multi-agent networks. With a proposed control scheme, we then present sufficient conditions under which all agents can reach consensus with the desired performance index. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.