Relay switched, scalable topology control for mobile robot networks based on motion synchronization

A mobile robot network is said to be easily scalable to any number of robots if its performance is kept almost fixed after these robots are added or some fail in the network. An interaction dynamics model based on motion synchronization is first established. Considering the mobility of mobile robot networks, we propose a relay switched, distributed topology control for the scalable network to drive neMy added robots to the most suitable positions with more neighbors as well as self-heal the blank positions of failed robots, and give a metric of the topology structure for evaluating the performance of network topologies. Then, we prove the stability of motion synchronization with the individual control based on Lyapunov exponent. Finally, the results of simulations have demonstrated the validity of the proposed modeling and control methods.

Consensus tracking protocol and formation control of multi-agent systems with switching topology

Consensus tracking control problems for single-integrator dynamics of multi-agent systems with switching topology are investigated. In order to design effective consensus tracking protocols for a more general class of networks, which are aimed at ensuring that the concerned states of agents converge to a constant or time-varying reference state, new consensus tracking protocols with a constant and time-varying reference state are proposed, respectively. Particularly, by contrast with spanning tree, an improved condition of switching interaction topology is presented. And then, convergence analysis of two consensus tracking protocols is provided by Lyapunov stability theory. Moreover, consensus tracking protocol with a time-varying reference state is extended to achieve the fbrmation control. By introducing formation structure set, each agent can gain its individual desired trajectory. Finally, several simulations are worked out to illustrate the effectiveness of theoretical results. The test results show that the states of agents can converge to a desired constant or time-varying reference state. In addition, by selecting appropriate structure set, agents can maintain the expected formation under random switching interaction topologies.

Consensus of high-order dynamic multi-agent systems with switching topology and time-varying delays

This paper studies the consensus problems for a group of agents with switching topology and time-varying communication delays, where the dynamics of agents is modeled as a high-order integrator. A linear distributed consensus protocol is proposed, which only depends on the agent＇s own information and its neighbors＇ partial information. By introducing a decomposition of the state vector and performing a state space transformation, the closed-loop dynamics of the multi-agent system is converted into two decoupled subsystems. Based on the decoupled subsystems, some sufficient conditions for the convergence to consensus are established, which provide the upper bounds on the admissible communication delays. Also, the explicit expression of the consensus state is derived. Moreover, the results on the consensus seeking of the group of high-order agents have been extended to a network of agents with dynamics modeled as a completely controllable linear time-invariant system. It is proved that the convergence to consensus of this network is equivalent to that of the group of high-order agents. Finally, some numerical examples are given to demonstrate the effectiveness of the main results.

Consensus problem of second-order multi-agent systems with time-varying communication delay and switching topology

Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality （LMI） are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader＇s states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.

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.

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.

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.

Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction

Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique, nonlinear consensus protocols are presented. We prove that a group of agents can reach a β-consensus, the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents. Moreover, we derive the conditions to guarantee that all the agents reach a β-consensus on a desired group decision value. Finally, a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed. Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.

Coordinated Control of Multi-Agent Systems with a Varying-Velocity Leader and Input Saturation

In this paper,we investigate a leader-following tracking problem for multi-agent systems with boundedinputs.We propose a distributed bounded protocol for each follower to track a leader whose states may not be completelymeasured.We theoretically prove that each agent can follow the leader with estimable track errors.Finally,somenumerical simulations are presented to illustrate our theoretical results.

Agreement coordination for second-order multi-agent systems with disturbances

This paper is devoted to the study of consensus problems for the second-order multi-agent systems with external disturbances, switching topology and commanication time-delay. Firstly, we perform a model transformation and separate the agreement states from the disagreement states. Secondly, according to this system, we derive a sufficient condition for consensus problem without disturbances by using the Lyapunov-based approach. Furthermore, we give a design criterion in terms of bilinear matrix inequality for the control protocol in the presence of disturbances. Finally, numerical simulations are provided to show the effectiveness of our strategies.

Consensus of multi-vehicle cooperative attack with stochastic multi-hop time-varying delay and actuator fault

A consensus-distributed fault-tolerant(CDFT)control law is proposed for a class of leader-following multi-vehicle cooperative attack(MVCA)systems in this paper.In particular,the switching communication topologies,stochastic multi-hop timevarying delays,and actuator faults are considered,which may lead to system performance degradation or on certain occasions even cause system instability.Firstly,the estimator of actuator faults for the following vehicle is designed to identify the actuator faults under a fixed topology.Then the CDFT control protocol and trajectory following error are derived by the relevant content of Lyapunov stability theory,the graph theory,and the matrix theory.The CDFT control protocol is proposed in the same manner,where a more realistic scenario is considered,in which the maximum trajectory following error and information on the switching topologies during the cooperative attack are available.Finally,numerical simulation are carried out to indicate that the proposed distributed fault-tolerant(DFT)control law is effective.

Quantized Formation Control of Heterogeneous Nonlinear Multi-Agent Systems with Switching Topology

This paper studies the formation control problem for the second-order heterogeneous nonlinear multi-agent systems(MASs)with switching topology and quantized control inputs.Compared with formation control under the fixed topology,under the switching topology inherent nonlinear dynamics of the agent and the connectivity change of the communication topology are considered.Moreover,to avoid the chattering phenomenon caused by unknown input disturbances,the hysteretic quantizers are incorporated to quantize the input signals.By using the Lyapunov stability theory and leader-follower formation approach,the proposed formation control scheme ensures that all signals of the MASs are semi-globally uniformly ultimately bounded(SGUUB).Finally,the efficiency of the theoretical results is proved by a simulation example.

A chattering free consensus controller for multiple Lur'e systems with a non-autonomous leader and directed switching topology

Achieving asymptotical cooperative goal for multi-agent systems(MASs)with non-autonomous leaders(i.e.,leaders with nonzero inputs)is a critical but challenging issue.Traditional approach is to use discontinuous controllers which may cause chattering phenomenon in practical applications.How to achieve the asymptotical goal via a chattering free cooperative controller remains to be open so far.In this paper,an adaptive continuous controller is designed to achieve zero error consensus tracking in multiple Lur’e systems with a non-autonomous leader under directed switching topology.Firstly,an unknown input observer(UIO)based on relative outputs is given to estimate the relative full states.Then an adaptive continuous controller is designed by introducing a decay function which remains positive into the term that plays the role of eliminating the impacts of leader’s nonzero inputs.Secondly,by using multiple Lyapunov functions(MLFs)technique,it is proven that zero error consensus tracking can be achieved if the average dwell time(ADT)is greater than a positive threshold.Finally,theoretical result is verified by performing simulations on Chua’s circuits.Compared with existing work,the proposed controller can not only achieve asymptotical consensus,but also is chattering free.

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.