Second-order Consensus Problem Research Articles

Byzantine-Resilient Second-Order Consensus in Networked Systems.

This article studies the second-order consensus problem in networked systems containing the so-called Byzantine misbehaving nodes when only an upper bound on either the local or the total number of misbehaving nodes is known. The existing results on this subject are limited to malicious/faulty model of misbehavior. Moreover, existing results consider consensus among normal nodes in only one of the two states, with the other state converging to either zero or a predefined value. In this article, a distributed control algorithm capable of withstanding both locally bounded and totally bounded Byzantine misbehavior is proposed. When employing the proposed algorithm, the normal nodes use a combination of the two relative state values obtained from their neighboring nodes to decide which neighbors should be ignored. By introducing an underlying virtual network, conditions on the robustness of the communication network topology for consensus on both states are established. Numerical simulation results are presented to illustrate the effectiveness of the proposed control algorithm.

Event-Triggered Sliding Mode Neural Network Controller Design for Heterogeneous Multi-Agent Systems

A class of heterogeneous second-order multi-agent consensus problems is studied, in which an event-triggered method is used to improve the feasibility of the control protocol. The sliding mode control method is used to achieve the robustness of the system. A special type of general radial basis function neural network is applied to estimate the uncertainties. The event-triggered mechanism is introduced to reduce the update frequency of the controller and the communication frequency among the agents. Zeno behavior is avoided by ensuring a lower bound between two adjacent trigger instants. Finally, the simulation results are provided to demonstrate that the time evolution of consensus errors eventually approaches zero. The consensus of multi-agent systems is achieved.

Three-dimensional impact-angle-constrained cooperative guidance strategy against maneuvering target

In order to improve the multiple-missile cooperative attack capability and penetration capability, this paper investigates two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target for controllable thrust missiles. First, a three-dimensional nonlinear guidance model is established that does not assume small missile lead angles in the guidance process. Second, in the line-of-sight (LOS) direction of the cluster cooperative guidance strategy, the proposed guidance algorithm transforms the simultaneous attack problem into a second-order multiagent consensus problem, which effectively solves the practical problem of low guidance precision provoked by the time-to-go estimation. Then, by combining second-order sliding mode control (SMC) and nonsingular terminal SMC theory, the guidance algorithms in the normal and lateral directions to the LOS are designed, respectively, so that the multi-missile can accurately attack a maneuvering target while satisfying the impact angle constraints. Finally, by utilizing the second-order multiagent consensus tracking control in the leader-following cooperative guidance strategy, a novel leader-following time consistency algorithm is investigated to ensure that the leader and followers can attack the maneuvering target simultaneously. Moreover, the stability of the investigated guidance algorithms is proved mathematically. The effectiveness and superiority of the proposed cooperative guidance strategies are verified by numerical simulations.

Bipartite Consensus for Second-Order Multiagent Systems With Matrix-Weighted Signed Network

The second-order scalar-weighted consensus problem of multiagent systems has been well explored. However, in some practical antagonistic interaction networks, the interdependencies of multidimensional states of the agents must be described by matrix coupling. In order to highlight the influence of matrix coupling in the antagonistic interaction network, we investigate the second-order matrix-weighted bipartite consensus problem on undirected structurally balanced signed networks. Under the proposed bipartite consensus protocol, an algebraic condition is obtained for achieving second-order bipartite consensus via utilizing matrix-valued Gauge transformation and stability theory. Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus. Besides, because of the existence of negative (positive) semidefinite connections, the matrix-weighted network may have clustering phenomena, which means that matrix weights play a critical role in achieving consensus. An algebraic graph condition for admitting cluster bipartite consensus is provided. By designing matrix weights in practical scenarios, the required number of clusters can be obtained. Finally, the theoretical results are verified by five simulation examples.

Second-Order Consensus for Multi-Agent Systems With Various Intelligent Levels via Intermittent Sampled-Data Control

This brief is concerned with the second-order consensus problem of multi-agent systems (MASs) over directed communication topologies. Due to engineering applications, agents in the network may have nonidentical intelligent degrees in practical scenarios. A novel intermittent sampled-data control protocol with different intelligent levels is proposed. Necessary and sufficient conditions are derived to guarantee the desired consensus under the protocol. Nevertheless, since the velocity states of real agents may not be measured, a novel protocol only utilizing past sampled position data with distinct intelligent levels is presented, under which the conditions of realizing consensus can be attained via similar analysis. Finally, the asymptotic consensus of MASs can be verified by some numerical simulations. The states of agents with the same intelligent level can be validated to converge to the common value as well.

Second-order consensus of multiagent systems with matrix-weighted network

This paper studies second-order consensus problem on the matrix-weighted undirected network, which is a generalization of second-order scalar-weighted network. The matrix coupling can describe the interdependencies of multi-dimensional states among agents. To highlight the influence of matrix coupling, we analyze the double integral model in matrix-weighted multiagent system network. A sufficient and necessary algebraic condition based on coupling strength, matrix theory and Lyapunov stability theory is established to achieve second-order consensus. With aid of the established property, a fairly straightforward algebraic graph condition is obtained, which ensures that the matrix-weighted multiagent system achieves second-order consensus. Moreover, owing to the existence of positive semi-definite connections, the clustering phenomena naturally exists, which shows that matrix coupling plays an important role in the convergence of the matrix-weighted multiagent system network. And an algebraic graph condition for finding all clusters is offered, which can guarantee the desired number of clusters via designing matrix-weights in practical applications. Finally, four simulation examples are given to illustrate the effectiveness of the obtained results.

Second-order bipartite consensus for networked robotic systems with quantized-data interactions and time-varying transmission delays

This paper investigates the second-order bipartite consensus (BC) problems for networked robotic systems (NRSs) subject to model uncertainties and external disturbances over signed directed graphs. We have newly presented two classes of hierarchical control algorithms (HCAs) to solve the BC problems for NRSs in a more practical and challenging case of quantized-data interactions (QDIs) and time-varying transmission delays (TVTDs). By using Hurwitz criterion and Lyapunov stability argument, several sufficient conditions on control parameters are obtained and the BC performance of the regulated system is analyzed. Three examples validate the presented theoretical findings.

Second-Order Consensus of Hybrid Multi-Agent Systems With Unknown Disturbances Via Sliding Mode Control

In this paper, we consider the second-order consensus problem of hybrid multi-agent systems with unknown disturbances by using sliding mode control under the leader-follower network. First, the hybrid multi-agent system model with disturbances and nonlinear term is proposed, which is composed of continuous-time dynamic agents and discrete-time dynamic agents. Second, the definition of the second-order consensus of hybrid multi-agent system is given. Then, we assume that the interaction among all agents happens in sampling time and each continuous-time dynamic agent can observe its own states in real time. Based on the equivalent approaching law and the states information among agents, the sliding mode control protocols are designed to achieve the second-order consensus of the hybrid multi-agent system. Some sufficient conditions are given for solving the second-order consensus under the sliding mode control protocols. Finally, some simulations are also given to illustrate the validity of the proposed method.

A Game-theoretical Approach for a Finite-time Consensus of Second-order Multi-agent System

The second-order consensus problem depends on not only the topology condition but also the coupling strength of the relative positions and velocities between neighboring agents. This paper seeks to solve the finite-time consensus problem of second-order multi-agent systems by games with special structures. Potential game and weakly acyclic game were applied for modeling the second-order consensus problem with different topologies. Furthermore, this paper introduces the event-triggered asynchronous cellular learning automata algorithm for optimizing the decision making process of the agents, which facilitates a convergence with the Nash equilibrium. Finally, numerical examples illustrate the effectiveness of the models.

Second-order consensus of discrete-time multi-agent systems in directed networks with nonlinear dynamics via impulsive protocols

Abstract In this paper, we discuss the second-order consensus problem of discrete-time multi-agent systems with fixed and switching topology. Impulsive protocols are introduced for such multi-agent systems with nonlinear dynamics. The consensus problem of multi-agent systems is analyzed by algebraic graph theory and matrix theory, where a connection of impulsive control methods and network topologies is established. Our main results indicate that the second-order consensus of multi-agent systems can be achieved if the graphs of the topology are balanced and strongly connected under suitable conditions. Numerical simulations are presented to support the theoretical results.

Consensus of second-order delayed nonlinear multi-agent systems via node-based distributed adaptive completely intermittent protocols

The paper discusses second-order consensus problem of nonlinear multi-agent systems with time delay and intermittent communications. Basing on local intermittent information among the agents, an effective control protocol is proposed by node-based distributed adaptive intermittent information, which a time-varying coupling weight to each node in the communication, some novel criteria are derived in matrix inequalities form by resorting to the generalized Halanay inequality. It is proved that second-order consensus can be reached if the measure of communication is larger than a threshold value under the strongly connected and balanced topology. Moreover, consensus problem is also considered for second-order non-delayed nonlinear multi-agent systems. Finally, a simulation example is presented to illustrate the theoretical results.

Consensus of nonlinear second-order multi-agent systems with mixed time-delays and intermittent communications

The paper investigates second-order consensus problem of nonlinear multi-agent systems with mixed time-delays and intermittent communications, where the mixed time-delays are composed of discrete and distributed delays, and each agent is assumed to obtain the relatively completely intermittent information of neighboring agents due to communication constraints. A new kind of distributed control protocol is designed based on the adaptive intermittent control ideas, some novel criteria are derived in matrix inequalities form by resorting to the generalized Halanay inequality. It is proved that second-order consensus can be reached if communication duration is larger than a threshold value under the strongly connected and balanced topology, and the relationship between the delays and communication duration over each control period is sought out. Finally, two simulation examples are provided to illustrate the effectiveness of the obtained theoretical results.

Second-order consensus in time-delayed networks based on periodic edge-event driven control

The second-order consensus problems in multi-agent systems with undirected topologies and time-invariant delays are considered in this paper. The time-delay robustness of a consensus protocol based on periodic edge-event driven control is investigated, and the studied protocol can largely reduce the communication and controller-updating costs. The relationship between time delays and event-detecting period is characterized. By Lyapunov methods, it is shown that the protocol can solve state consensus problems when the interaction topology is connected, and the system does not exhibit Zeno behavior. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.

Distributed quantised consensus in groups of agents with acceleration‐like inputs: a reference model‐based scheme

This study investigates the second-order consensus problem in directed networks where the agents are governed by sampled-data dynamics with acceleration-like inputs. A distributed reference model-based approach is adopted to avoid using the global information of eigenvalues of the Laplacian matrix associated with the communication graph. First, the consensus via real-valued communication is studied and it is shown that the consensus can be achieved under the adopted protocol with appropriate parameters. Next, the quantisation effects in system performances are discussed based on the obtained parameter conditions, it is proved that the quantised consensus can be achieved under the proposed protocols. Two numerical examples are provided to illustrate the theoretical results.

Second-Order Consensus of Networked Thrust-Propelled Vehicles on Directed Graphs

This technical note addresses the second-order consensus problem of multiple underactuated thrust-propelled vehicles (TPVs) on directed graphs containing a directed spanning tree. We propose an adaptive control approach to resolve this problem, and the proposed controller does not rely on the commonly used backstepping methodology and the exact knowledge of the mass properties of the TPVs. In addition, the resultant complexity is reduced and the requirement on the interaction graph is relaxed. Using an input-output analysis, we show that the proposed controller realizes second-order consensus of the TPVs, i.e., the position and velocity consensus errors between the TPVs converge to zero, and moreover the velocities of the TPVs converge to the weighted average of their initial values. The performance of the proposed control approach is shown by a numerical simulation.

Second-order consensus for heterogeneous multi-agent systems in the cooperation–competition network: A hybrid adaptive and pinning control approach

In this paper, a second-order consensus problem is investigated for the heterogeneous agents in the cooperation–competition network, with the parameters of the agents’ dynamics being uncertain. By introducing an exosystem, a hybrid adaptive and pinning control strategy is firstly proposed to ensure that all the agents follow a desired trajectory which is a function of the exosystem state. Several effective sufficient conditions are obtained by applying algebraic graph theory and the Barbalat lemma. Besides, the switching topologies between the competition agents are also considered. With the help of the Barbalat-like lemma, it is found that second-order consensus problem of the heterogeneous agents can be solved even when the competition sub-network is dynamic. Finally, simulation results are presented to validate the effectiveness of the theoretical analysis.

Second-order consensus in multi-agent systems with directed topologies and communication constraints

The paper investigates second-order consensus problem for multi-agent systems with nonlinear dynamic and directed topologies, where each agent can only communicate with its neighbors on some disconnected time intervals. A novel intermittent consensus protocol is designed by its own and the neighbor's relative local information. Based on the Lyapunov stability theory and the intermittent control method, some novel and simple criteria are derived for consensus of multi-agent systems under a fixed strongly connected topology, it is proved that consensus can be reached if the general algebraic connectivity and the measure of communication are larger than the corresponding threshold values, respectively. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.

Fast second-order consensus via predictive mechanisms

In this paper, we discuss second-order consensus problems for multi-agent systems with dynamic agents and fixed topologies. A new second-order consensus protocol incorporating the predictive mechanism is proposed and a convergence analysis related to the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network is provided. We establish a direct connection between the eigenvalues of the Laplacian matrix and parameters of the proposed second-order consensus model, and we compute a lower bound for the sum of parameters. It is proved under general conditions related to the second-order consensus protocol and the network topology that the asymptotic consensus is achieved and the convergence speed is increased via designing a state predictor. Finally, simulation results are provided to verify the effectiveness of the proposed protocol and the analytical claims.

Consensus of second-order multi-agent systems with nonlinear dynamics and time delay

This paper aims at investigating the second-order consensus problem of the multi-agent systems with nonlinear dynamics. Since it is more difficult to obtain the velocity information compared with the position information in practical application, a very simple sufficient condition for updating the coupling gain of the velocity information exchange between each agent is firstly derived to achieve asymptotic consensus. Furthermore, communication delay of each agent is considered for velocity information exchange. The velocity signal from a virtual leader is introduced to reach the second-order consensus. All the above fundamental consensus criteria are guaranteed base on algebraic graph theory, matrix theory, and Lyapunov stability method. Two simulation examples are provided to demonstrate the effectiveness of the analytical results. The results obtained in this paper can be easily applied to various cases, which can facilitate practical designs for the second-order consensus.

Second-Order Consensus of Leader-Following Multi-Agent Systems with Jointly Connected Topologies and Time-Varying Delays

In this paper, we discuss, respectively, second-order leader-following consensus problems with and without time-varying communication delays. Lyapunov theorems and matrix approach are employed to prove that all the leader-following agents will achieve second-order consensus if the velocity communication topology between the leader and each following agent is connected and the position communication topologies of all the leader-following agents are jointly connected. Several simulation results are presented to support the effectiveness of our theoretical results.