Lyapunov-Based Output Containment Control of Heterogeneous Multi-Agent Systems With Markovian Switching Topologies and Distributed Delays

This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.

Distributed optimization for discrete-time multiagent systems with nonconvex control input constraints and switching topologies

This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies.We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point,while their control inputs are constrained in their own nonconvex region.It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term.Based on the dynamic transformation technique,the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term.By utilizing the nonnegative matrix theory,it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected.Finally,a numerical simulation example is used to demonstrate the acquired theoretical results.

Time-varying formation for general linear multi-agent systems via distributed event-triggered control under switching topologies

This paper investigates the time-varying formation problem for general linear multi-agent systems using distributed event-triggered control strategy.Different from the previous works,to achieve the desired time-varying formation,a distributed control scheme is designed in an event-triggered way,in which for each agent the controller is triggered only at its own event times.The interaction topology among agents is assumed to be switching.The common Lyapunov function as well as Riccati inequality is applied to solve the time-varying formation problem.Moreover,the Zeno behavior of triggering time sequences can be excluded for each agent.Finally,a simulation example is presented to illustrate the effectiveness of the theoretical results.

Extended consensus analysis of multi-agent systems with switching topologies

Theoretical analysis of consensus for networked multi-agent systems with switching topologies was conducted.Supposing that information-exchange topologies of networked system are dynamic,a modified linear protocol is proffered which is more practical than existing ones.The definition of trajectory consensus is given and a new consensus protocol is exhibited such that multi-agent system achieves trajectory consensus.In addition,a formation control strategy is designed.A common Lyapunov function is proposed to analyze the consensus convergence of networked multi-agent systems with switching topologies.Simulations are provided to demonstrate the effectiveness of the theoretical results.

Stability of General Linear Dynamic Multi-Agent Systems under Switching Topologies with Positive Real Eigenvlues

The time-varying network topology can significantly affect the stability of multi-agent systems.This paper examines the stability of leader-follower multi-agent systems with general linear dynamics and switching network topologies,which have applications in the platooning of connected vehicles.The switching interaction topology is modeled as a class of directed graphs in order to describe the information exchange between multi-agent systems,where the eigenvalues of every associated matrix are required to be positive real.The Hurwitz criterion and the Riccati inequality are used to design a distributed control law and estimate the convergence speed of the closed-loop system.A sufficient condition is provided for the stability of multi-agent systems under switching topologies.A common Lyapunov function is formulated to prove closed-loop stability for the directed network with switching topologies.The result is applied to a typical cyber-physical system—that is,a connected vehicle platoon—which illustrates the effectiveness of the proposed method.

Consensus of multiple autonomous underwater vehicles with double independent Markovian switching topologies and timevarying delays

A new method in which the consensus algorithm is used to solve the coordinate control problems of leaderless multiple autonomous underwater vehicles（multi-AUVs） with double independent Markovian switching communication topologies and time-varying delays among the underwater sensors is investigated.This is accomplished by first dividing the communication topology into two different switching parts,i.e.,velocity and position,to reduce the data capacity per data package sent between the multi-AUVs in the ocean.Then,the state feedback linearization is used to simplify and rewrite the complex nonlinear and coupled mathematical model of the AUVs into a double-integrator dynamic model.Consequently,coordinate control of the multi-AUVs is regarded as an approximating consensus problem with various time-varying delays and velocity and position topologies.Considering these factors,sufficient conditions of consensus control are proposed and analyzed and the stability of the multi-AUVs is proven by Lyapunov-Krasovskii theorem.Finally,simulation results that validate the theoretical results are presented.

Limited-Budget Consensus Design and Analysis for Multiagent Systems With Switching Topologies and Intermittent Communications

This paper investigates limited-budget consensus design and analysis problems of general high-order multiagent systems with intermittent communications and switching topologies.The main contribution of this paper is that the tradeoff design between the energy consumption and the consensus performance can be realized while achieving leaderless or leaderfollowing consensus,under constraints of limited budgets and intermittent communications.Firstly,a new intermittent limitedbudget consensus control protocol with a practical trade-off design index is proposed,where the total budget of the whole multiagent system is limited.Then,leaderless limited-budget consensus design and analysis criteria are derived,in which the matrix variables of linear matrix inequalities are determined according to the total budget and the practical trade-off design parameters.Meanwhile,an explicit formulation of the consensus function is derived to describe the consensus state trajectory of the whole system.Moreover,a new two-stage transformation strategy is utilized for leader-following cases,by which the dynamics decomposition of leaderless and leader-following cases can be converted into a unified framework,and sufficient conditions of the leader-following limited-budget consensus design and analysis are determined via those of the leaderless cases.Finally,numerical simulations are given to illustrate theoretical results.

Multi-agent consensus with time-varying delays and switching topologies

The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and processes its own state information with time-varying self-delay respectively. The state time-delay feedback is introduced into the existing consensus protocol to begenerate an improved protocol. Then a sufficient condition is derived which can make the system with time-varying self-delays achieve the consensus. On this basis, a specific form of consensus equilibrium influenced by the initial states of agents, time-delays and state feedback intensity is figured out. In addition, the multi-agent consensus is considered with time-varying topologies. Finally, simulations are presented to il ustrate the validity of theoretical results.

Consensus algorithm for multiple quadrotor systems under fixed and switching topologies

The distributed leadless consensus problem for multiple quadrotor systems under fixed and switching topologies is investigated. The objective is to design protocols achieving consensus for networked quadrotors＇ positions and attitudes. Because the model of a quadrotor is a strong high-order nonlinear coupling system, the approach of feedback linearization is employed to transform the model into a group of four linear subsystems among which there is no coupling. Then, a consensus algorithm is proposed which consists of a local feedback controller and interactions from the finite neighbors under fixed undirected topologies. Especially, the problem of choosing the parameters in the consensus algo-rithm is also addressed, enlightened by the results of the robust control theory. Furthermore, it is proved that the proposed algo-rithm also guarantees the consensus under undirected switching topologies. Simulation results show the effectiveness of the pro- posed algorithm.

Event-Triggered Fixed-Time Consensus of Second-Order Nonlinear Multi-Agent Systems with Delay and Switching Topologies

To address fixed-time consensus problems of a class of leader-follower second-order nonlinear multi-agent systems with uncertain external disturbances,the event-triggered fixed-time consensus protocol is proposed.First,the virtual velocity is designed based on the backstepping control method to achieve the system consensus and the bound on convergence time only depending on the system parameters.Second,an event-triggered mechanism is presented to solve the problem of frequent communication between agents,and triggered condition based on state information is given for each follower.It is available to save communication resources,and the Zeno behaviors are excluded.Then,the delay and switching topologies of the system are also discussed.Next,the system stabilization is analyzed by Lyapunov stability theory.Finally,simulation results demonstrate the validity of the presented method.

Time-Varying Formation-Containment Tracking Control for Unmanned Aerial Vehicle Swarm Systems with Switching Topologies and a Non-Cooperative Target

This paper studies the time-varying formation-containment tracking control problems for unmanned aerial vehicle(UAV)swarm systems with switching topologies and a non-cooperative target,where the UAV swarm systems consist of one tracking-leader,several formation-leaders,and followers.The formation-leaders are required to accomplish a predefined time-varying formation and track the desired trajectory of the tracking-leader,and the states of the followers should converge to the convex hull spanned by those of the formation-leaders.First,a formation-containment tracking protocol is proposed with the neighboring relative information,and the feasibility condition for formation-containment tracking and the algebraic Riccati equation are given.Then,the stability of the control system with the designed control protocol is proved by constructing a reasonable Lyapunov function.Finally,the simulation examples are applied to verify the effectiveness of the theoretical results.The simulation results show that both the formation tracking error and the containment error are convergent,so the system can complete the formation containment tracking control well.In the actual battlefield,combat UAVs need to chase and attack hostile UAVs,but sometimes when multiple UAVs work together for military interception,formationcontainment tracking control will occur.

Cooperative Target Tracking of Multiple Autonomous Surface Vehicles Under Switching Interaction Topologies

This paper is concerned with the cooperative target tracking of multiple autonomous surface vehicles(ASVs)under switching interaction topologies.For the target to be tracked,only its position can be measured/received by some of the ASVs,and its velocity is unavailable to all the ASVs.A distributed extended state observer taking into consideration switching topologies is designed to integrally estimate unknown target dynamics and neighboring ASVs'dynamics.Accordingly,a novel kinematic controller is designed,which takes full advantage of known information and avoids the approximation of some virtual control vectors.Moreover,a disturbance observer is presented to estimate unknown time-varying environmental disturbance.Furthermore,a distributed dynamic controller is designed to regulate the involved ASVs to cooperatively track the target.It enables each ASV to adjust its forces and moments according to the received information from its neighbors.The effectiveness of the derived results is demonstrated through cooperative target tracking performance analysis for a tracking system composed of five interacting ASVs.

Cooperative output feedback consensus control of second-order nonlinear multi-agent systems under Markovian switching topologies

This paper deals with the leader-following consensus problem for a class of second-order nonlinear multi-agent systems by output feedback.The communication topology is characterized by a Markovian switching graph.Firstly,an input-driven observer is introduced to estimate the consensus error of each follower agent.Then,a cooperative nonlinear control law is constructed using the relative output information between neighboring agents by employing the backstepping methodology,which achievesleader-following consensusin mean square sense.Compared with the existing results,the nonlinear functions are required to satisfy polynomial growth condition rather than globally Lipschitz growth or Lipschitz-like growth condition.A numerical example is given to illustrate the theoretical results.

Consensus Problem of Heterogeneous Multi-agent Systems with Time Delay under Fixed and Switching Topologies

Consensus problem is investigated for heterogeneous multi-agent systems composed of first-order agents and second-order agents in this paper. Leader-following consensus protocol is adopted to solve consensus problem of heterogeneous multi-agent systems with time-varying communication and input delays. By constructing Lyapunov-Krasovkii functional, sufficient consensus conditions in linear matrix inequality(LMI) form are obtained for the system under fixed interconnection topology. Moreover, consensus conditions are also obtained for the heterogeneous systems under switching topologies with time delays. Simulation examples are given to illustrate effectiveness of the results.

Robust leaderless time-varying formation control for unmanned aerial vehicle swarm system with Lipschitz nonlinear dynamics and directed switching topologies

This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.

Consensus control of multi-manipulator systems based on disturbance observer under Markov switching topologies

In this paper,to solve the consensus control problem of multi-manipulator systems under Markov switching topologies,we propose a distributed consensus control strategy based on disturbance observer.In multi-manipulator systems,external disturbance described by heterogeneous exogenous systems is considered,and all communication topologies are directed.First,a disturbance observer is presented to suppress the influence of unknown external disturbance,and the equivalent compensation is introduced into the control protocol in multi-manipulator systems.Then,a novel control protocol based on neighbor information is designed,which guarantees that multi-manipulator systems reach consensus under Markov switching topologies.Finally,two simulation examples verify the validity of the theoretical result.

Leader-following consensus of multi-agent systems with switching topologies and time-delays

This paper investigates the leader-following consensus problem of multi-agent systems where the leader is static and the controlling effect of each follower depends on its own state. The control protocols are proposed for two cases： i） for network with switching topologies and undirected information flow; ii） for network with directed information flow and communication time-delays. With the aid of several tools from algebraic graph, matrix theory and stability the- ory, the sufficient conditions guaranteeing leader-following consensus are obtained by constructing appropriate Lyapunov functions. Simulations are presented to demonstrate the effectiveness of our theoretical results.

Robust Consensus Tracking of Heterogeneous Multi-Agent Systems Under Switching Topologies

This paper considers a robust consensus tracking problem of heterogeneous multi-agent systems with time-varying interconnection topologies. Based on common Lyapunov function and internal model techniques, both state and output feedback control laws are derived to solve this problem.The proposed design is robust by admitting some parameter uncertainties in the multi-agent system.

Passivity-based consensus for linear multi-agent systems under switching topologies

This paper studies the passivity-based consensus analysis and synthesis problems for a class of stochastic multi-agent systems with switching topologies. Based on Lyapunov methods, stochastic theory, and graph theory, new different storage Lyapunov functions are proposed to derive sufficient conditions on mean-square exponential consensus and stochastic passivity for multi-agent systems under two different switching cases, respectively. By designing passive time-varying consensus protocols, the solvability conditions for the passivity-based consensus protocol synthesis problem, i.e., passification, are derived based on linearization techniques. Numerical simulations are provided to illustrate the effectiveness of the proposed methods.

Multiple Unmanned Underwater Vehicles Consensus Control with Unmeasurable Velocity Information and Environmental Disturbances Under Switching Directed Topologies

A consensus algorithm proposed in the paper is applied to tackle remarkable problems of unmeasurable velocities,the environmental disturbances, and the limited communication environment for the multiple unmanned underwater vehicles(multi-UUVs). Firstly, for a complex nonlinear and coupled model of the unmanned underwater vehicle(UUV), a technique of feedback linearization is developed to transform the nonlinear UUV model into a secondorder integral UUV model. Secondly, to address the problem of the unavailable velocity information and environmental disturbances for the multi-UUVs system, we design a distributed extended state observer(DESO) to estimate the unmeasurable velocities and environmental disturbances using the relative position information. Finally,we propose a protocol based on the estimation information from the DESO and demonstrate that the multi-UUVs system with the switching directed topologies under the protocol can reach consensus asymptotically. The theoretical result proposed in the literature is verified by one numerical example.