Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

Neural networks-based iterative learning control consensus for periodically time-varying multi-agent systems

In this paper,the problem of adaptive iterative learning based consensus control for periodically time-varying multi-agent systems is studied,in which the dynamics of each follower are driven by nonlinearly parameterized terms with periodic disturbances.Neural networks and Fourier base expansions are introduced to describe the periodically time-varying dynamic terms.On this basis,an adaptive learning parameter with a positively convergent series term is constructed,and a distributed control protocol based on local signals between agents is designed to ensure accurate consensus of the closed-loop systems.Furthermore,consensus algorithm is generalized to solve the formation control problem.Finally,simulation experiments are implemented through MATLAB to demonstrate the effectiveness of the method used.

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

Hyperbolic Tangent Function-Based Protocols for Global/Semi-Global Finite-Time Consensus of Multi-Agent Systems

This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols.

Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems

Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as safety and liveness,there is still a lack of quantitative and uncertain property verifications for these systems.In uncertain environments,agents must make judicious decisions based on subjective epistemic.To verify epistemic and measurable properties in multi-agent systems,this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge(FCTLK).We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems.In addition,we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures,as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic(FCTL)formulas.Accordingly,we transform the FCTLK model checking problem into the FCTL model checking.This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads.Finally,we present correctness proofs and complexity analyses of the proposed algorithms.Additionally,we further illustrate the practical application of our approach through an example of a train control system.

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This paper investigates the robust cooperative output regulation problem for a class of heterogeneousuncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizingthe internal model approach and the adaptive control technique, a distributed adaptive internal model isconstructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed ofa distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggeringmechanism is proposed, in which each agent updates its control input at its own triggering time instants. It isshown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solvedwithout requiring either the global information associated with the communication topology or the bounds ofthe uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided toillustrate the effectiveness of the proposed control strategy.

Robust adaptive leaderless consensus of unknown non-minimum phase linear multi-agent systems subject to disturbances and/or unmodeled dynamics

This article investigates the problem of robust adaptive leaderless consensus for heterogeneous uncertain nonminimumphase linear multi-agent systems over directed communication graphs. Each agent is assumed tobe of unknown nominal dynamics and also subject to external disturbances and/or unmodeled dynamics. Anovel distributed robust adaptive control strategy is proposed. It is shown that the robust adaptive leaderlessconsensus problem is solved with the proposed control strategy under some sufficient conditions. Two examplesare provided to demonstrate the efficacy of the proposed control strategy.

Adaptive Event-Triggered Time-Varying Output Group Formation Containment Control of Heterogeneous Multiagent Systems

In this paper,a class of time-varying output group formation containment control problem of general linear hetero-geneous multiagent systems(MASs)is investigated under directed topology.The MAS is composed of a number of tracking leaders,formation leaders and followers,where two different types of leaders are used to provide reference trajectories for movement and to achieve certain formations,respectively.Firstly,compen-sators are designed whose states are estimations of tracking lead-ers,based on which,a controller is developed for each formation leader to accomplish the expected formation.Secondly,two event-triggered compensators are proposed for each follower to evalu-ate the state and formation information of the formation leaders in the same group,respectively.Subsequently,a control protocol is designed for each follower,utilizing the output information,to guide the output towards the convex hull generated by the forma-tion leaders within the group.Next,the triggering sequence in this paper is decomposed into two sequences,and the inter-event intervals of these two triggering conditions are provided to rule out the Zeno behavior.Finally,a numerical simulation is intro-duced to confirm the validity of the proposed results.

Robust Consensus Tracking Control of Uncertain Multi-Agent Systems With Local Disturbance Rejection

In this paper,a new distributed consensus tracking protocol incorporating local disturbance rejection is devised for a multi-agent system with heterogeneous dynamic uncertainties and disturbances over a directed graph.It is of two-degree-of-freedom nature.Specifically,a robust distributed controller is designed for consensus tracking,while a local disturbance estimator is designed for each agent without requiring the input channel information of disturbances.The condition for asymptotic disturbance rejection is derived.Moreover,even when the disturbance model is not exactly known,the developed method also provides good disturbance-rejection performance.Then,a robust stabilization condition with less conservativeness is derived for the whole multi-agent system.Further,a design algorithm is given.Finally,comparisons with the conventional one-degree-of-freedombased distributed disturbance-rejection method for mismatched disturbances and the distributed extended-state observer for matched disturbances validate the developed method.

Distributed Adaptive Output Consensus of Unknown Heterogeneous Non-Minimum Phase Multi-Agent Systems

This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs.The dynamics of followers are allowed to be non-minimum phase with unknown arbitrary individual relative degrees.This is contrary to many existing works on distributed adaptive control schemes where agent dynamics are required to be minimum phase and often of the same relative degree.A distributed adaptive pole placement control scheme is developed,which consists of a distributed observer and an adaptive pole placement control law.It is shown that under the proposed distributed adaptive control scheme,all signals in the closed-loop system are bounded and the outputs of all the followers track the output of the leader asymptotically.The effectiveness of the proposed scheme is demonstrated by one practical example and one numerical example.

Practical bipartite consensus for multi-agent systems:A barrier function-based adaptive sliding-mode control approach

This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller.

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 networked control multi-agent systems using a double-layer encryption scheme

This paper addresses the decentralized consensus problem for a system of multiple dynamic agents with remote controllers via networking,known as a networked control multi-agent system(NCMAS).It presents a challenging scenario where partial dynamic entities or remote control units are vulnerable to disclosure attacks,making them potentially malicious.To tackle this issue,we propose a secure decentralized control design approach employing a double-layer cryptographic strategy.This approach not only ensures that the input and output information of the benign entities remains protected from the malicious entities but also practically achieves consensus performance.The paper provides an explicit design,supported by theoretical proof and numerical verification,covering stability,steady-state error,and the prevention of computation overflow or underflow.

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.

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 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.

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.

Robust Leader-Following Output Regulation of Uncertain Multi-Agent Systems With Time-Varying Delay

In this paper, the robust analysis and design of leader-following output regulation for multi-agent systems described by general linear models is given in presence of timevarying delay and model uncertainty. To this aim, a new regulation protocol for the closed-loop multi-agent system under a directed graph is proposed. An important specification of the proposed protocol is to guarantee the leader-following output regulation for uncertain multi-agent systems with both stable and unstable agents. Since many signals can be approximated by a combination of the stationary and ramp signals, the presented results work for adequate variety of the leaders. The analysis and design conditions are presented in terms of certain matrix inequalities. The method proposed can be used for both stationary and ramp leaders. Simulation results are presented to show the effectiveness of the proposed method.

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with time varying delays are investigated. The idea of guaranteed cost con trol is introduced into consensus problems for high-dimensiona multi-agent systems with time-varying delays, where a cos function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality(LMI)sufficient conditions for guaranteed cost consensus and consensu alization are given. Moreover, a guaranteed cost upper bound o the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independen of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.