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.

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.

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.

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.

A PI+R Control Scheme Based on Multi-Agent Systems for Economic Dispatch in Isolated BESSs

Battery energy storage systems(BESSs)are widely used in smart grids.However,power consumed by inner impedance and the capacity degradation of each battery unit become particularly severe,which has resulted in an increase in operating costs.The general economic dispatch(ED)algorithm based on marginal cost(MC)consensus is usually a proportional(P)controller,which encounters the defects of slow convergence speed and low control accuracy.In order to solve the distributed ED problem of the isolated BESS network with excellent dynamic and steady-state performance,we attempt to design a proportional integral(PI)controller with a reset mechanism(PI+R)to asymptotically promote MC consensus and total power mismatch towards 0 in this paper.To be frank,the integral term in the PI controller is reset to 0 at an appropriate time when the proportional term undergoes a zero crossing,which accelerates convergence,improves control accuracy,and avoids overshoot.The eigenvalues of the system under a PI+R controller is well analyzed,ensuring the regularity of the system and enabling the reset mechanism.To ensure supply and demand balance within the isolated BESSs,a centralized reset mechanism is introduced,so that the controller is distributed in a flow set and centralized in a jump set.To cope with Zeno behavior and input delay,a dwell time that the system resides in a flow set is given.Based on this,the system with input delays can be reduced to a time-delay free system.Considering the capacity limitation of the battery,a modified MC scheme with PI+R controller is designed.The correctness of the designed scheme is verified through relevant simulations.

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 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.

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.

Connectivity-maintaining Consensus of Multi-agent Systems With Communication Management Based on Predictive Control Strategy

This paper studies the connectivity-maintaining consensus of multi-agent systems.Considering the impact of the sensing ranges of agents for connectivity and communication energy consumption,a novel communication management strategy is proposed for multi-agent systems so that the connectivity of the system can be maintained and the communication energy can be saved.In this paper,communication management means a strategy about how the sensing ranges of agents are adjusted in the process of reaching consensus.The proposed communication management in this paper is not coupled with controller but only imposes a constraint for controller,so there is more freedom to develop an appropriate control strategy for achieving consensus.For the multi-agent systems with this novel communication management,a predictive control based strategy is developed for achieving consensus.Simulation results indicate the effectiveness and advantages of our scheme.

Tracking Control of Multi-Agent Systems Using a Networked Predictive PID Tracking Scheme

With the rapid development of network technology and control technology,a networked multi-agent control system is a key direction of modern industrial control systems,such as industrial Internet systems.This paper studies the tracking control problem of networked multi-agent systems with communication constraints,where each agent has no information on the dynamics of other agents except their outputs.A networked predictive proportional integral derivative(PPID)tracking scheme is proposed to achieve the desired tracking performance,compensate actively for communication delays,and simplify implementation in a distributed manner.This scheme combines the past,present and predictive information of neighbour agents to form a tracking error signal for each agent,and applies the proportional,integral,and derivative of the agent tracking error signal to control each individual agent.The criteria of the stability and output tracking consensus of multi-agent systems with the networked PPID tracking scheme are derived through detailed analysis on the closed-loop systems.The effectiveness of the networked PPID tracking scheme is illustrated via an example.

Fixed-time group consensus of second-order multi-agent systems based on event-triggered control

The problem of fixed-time group consensus for second-order multi-agent systems with disturbances is investigated.For cooperative-competitive network,two different control protocols,fixed-time group consensus and fixed-time eventtriggered group consensus,are designed.It is demonstrated that there is no Zeno behavior under the designed eventtriggered control.Meanwhile,it is proved that for an arbitrary initial state of the system,group consensus within the settling time could be obtained under the proposed control protocols by using matrix analysis and graph theory.Finally,a series of numerical examples are propounded to illustrate the performance of the proposed control protocol.

2-D distributed pose estimation of multi-agent systems using bearing measurements

This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and positions,while the followers can measure the relative bearings or(angular and linear)velocities in their unknown local coordinate frames.For the orientation estimation,the local relative bearings are used to obtain the relative orientations among the agents,based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation.For the position estimation,the local relative bearings are used to obtain the position constraints among the agents,and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints.Both the orientation and position estimation errors converge to zero asymptotically.A simulation example is given to verify the theoretical results.