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.

Team-based fixed-time containment control for multi-agent systems with disturbances

We investigate the fixed-time containment control(FCC)problem of multi-agent systems(MASs)under discontinuous communication.A saturation function is used in the controller to achieve the containment control in MASs.One difference from using a symbolic function is that it avoids the differential calculation process for discontinuous functions,which further ensures the continuity of the control input.Considering the discontinuous communication,a dynamic variable is constructed,which is always non-negative between any two communications of the agent.Based on the designed variable,the dynamic event-triggered algorithm is proposed to achieve FCC,which can effectively reduce controller updating.In addition,we further design a new event-triggered algorithm to achieve FCC,called the team-trigger mechanism,which combines the self-triggering technique with the proposed dynamic event trigger mechanism.It has faster convergence than the proposed dynamic event triggering technique and achieves the tradeoff between communication cost,convergence time and number of triggers in MASs.Finally,Zeno behavior is excluded and the validity of the proposed theory is confirmed by simulation.

Group-Consensus of Hierarchical Containment Control for Linear Multi-Agent Systems

The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection and maintenance. Therefore, this paper is concerned with an extensional containment control issue, hierarchical containment control. It aims to enable a multitude of followers achieving a novel cooperation in the convex hull shaped by multiple leaders. Firstly, by constructing the three-layer topology, large-scale networks are decoupled. Then,under the condition of directed spanning group-tree, a class of dynamic hierarchical containment control protocol is designed such that the novel group-consensus behavior in the convex hull can be realized. Moreover, the definitions of coupling strength coefficients and the group-consensus parameter in the proposed dynamic hierarchical control protocol enhance the adjustability of systems. Compared with the existing containment control strategy, the proposed hierarchical containment control strategy improves dynamic control performance. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed hierarchical control protocol.

Containment Control of Fractional Order Multi-Agent Systems With Time Delays

In complex environments, many distributed multiagent systems are described with the fractional-order dynamics.In this paper, containment control of fractional-order multiagent systems with multiple leader agents are studied. Firstly,the collaborative control of fractional-order multi-agent systems(FOMAS) with multiple leaders is analyzed in a directed network without delays. Then, by using Laplace transform and frequency domain theorem, containment consensus of networked FOMAS with time delays is investigated in an undirected network, and a critical value of delays is obtained to ensure the containment consensus of FOMAS. Finally, numerical simulations are shown to verify the results.

Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems:An Output Regulation Approach

In this paper,we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks.A distributed dynamic observer based on the leaders’measurable output was designed to estimate a convex combination of the leaders’states.First,for the case of followers with identical state dimensions,distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders’convex hull within the output regulation framework.Subsequently,we extended theoretical results to the case where followers have nonidentical state dimensions.By establishing virtual errors between the dynamic observer and followers,a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem.Finally,two numerical simulations verified the effectiveness of the designed schemes.

Containment control for heterogeneous nonlinear multi-agent systems under distributed event-triggered schemes

We study the contain men t cont rol problem for high-order het erogeneous nonlinear multi-age nt systems under distributed event-triggered schemes.To achieve the containment control objective and reduce communication consumption among agents,a distributed event-triggered control scheme is proposed by applying the backstepping method,Lyapunov functional approach,and neural networks.Then,the results are extended to the self-triggered control case to avoid continuous monitoring of state errors.The developed protocols and triggered rules ensure that the output for each follower converges to the convex hull spanned by multi-leader signals within a bounded error.In addition,no agent exhibits Zeno behavior.Two numerical simulations are finally presen ted to verify the correctness of the obtained results.

Containment Control of Multi-Agent Systems with Stochastic Multiplicative Noises

This paper investigates the containment problem of continuous-time multi-agent systems with multiplicative noises,where the first-order and second-order multi-agent systems are studied respectively.Based on stochastic analysis tools,algebraic graph theory,and Lyapunov function method,the containment protocols based the relative states measurement with multiplicative noises are developed to guarantee the mean square and almost sure containment.Moreover,the sufficient conditions and necessary conditions related to the control gains are derived for achieving mean square and almost sure containment.It is also shown that multiplicative noises may works positively for the almost sure containment of the first-order multi-agent systems.Simulation examples are also introduced to illustrate the effectiveness of the theoretical results.

Adaptive distributed observer design for containment control of heterogeneous discrete-time swarm systems

This paper develops both adaptive distributed dynamic state feedback control law and adaptive distributed measurement output feedback control law for heterogeneous discrete-time swarm systems with multiple leaders.The convex hull formed by the leaders and the system matrix of leaders is estimated via an adaptive distributed containment observer.Such estimations will feed the followers so that every follower can update the system matrix of the corresponding adaptive distributed containment observer and the system state of their neighbors.The followers cooperate with each other to achieve leader-follower consensus and thus solve the containment control problem over the network.Numerical results demonstrate the effectiveness and computational feasibility of the proposed control laws.

Sampled data based containment control of second-order multi-agent systems under intermittent communications

This paper studies the sampled data based containment control problem of second-order multi-agent systems with intermittent communications,where velocity measurements for each agent are unavailable.A novel controller for second-order containment is put forward via intermittent sampled position data measurement.Several necessary and sufficient conditions are derived to achieve intermittent sampled containment control by means of analyzing the relationship among control gains,eigenvalues of the Laplacian matrix,the sampling period,and the communication width.Finally,several simulation examples are used to testify the correctness and effectiveness of the theoretical results.

Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises

A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples.

HYBRID CONTROL APPROACH FOR CONTAINER CRANES

A hybrid control approach is proposed to achieve the desired performance. Firstly a robust input shaper is designed to reduce the transient vibration and residual vibration of the container efficiently. Then a simple fuzzy logic controller is designed to eliminate the residual vibration completely in order to guarantee the positioning precision. Such a hybrid approach is simple in structure and readily realizable. Simulation results verify the fine performance of this hybrid control approach. It can achieve perfect elimination of residual vibration and concise positioning of the container load, and it is robust to parameter variations （mainly for cable length） and external disturbances.

Semi-Global Consensus Problems of Discrete-Time Multi-Agent Systems in the Presence of Input Constraints

This paper studies the consensus problems of the discrete-time multi-agent systems (MASs) in the presence of input saturation constraints over directed communication networks.Two kinds of consensus problems,of the leaderless consensus problem with no leader agent and the containment control problem with multiple leader agents,are investigated in this paper.Low gain feedback consensus algorithms based on the improved discretetime parametric algebraic Riccati equation (ARE) are proposed to solve the consensus problems.For the MAS without any leader,the trajectories of all agents converge together when the communication networks contain a directed spanning tree.For the MAS with multiple leaders,the trajectories of all follower agents converge to the convex hull spanned by the leader agents when there is at least one leader agent which is trackable for each follower agent.Simulation examples are provided to verify the theoretical results.