Consensus Control Problem Research Articles

Cooperative Nearest-Neighbor Control of Multi-Agent Systems: Consensus and Formation Control Problems

This letter studies the problem of cooperative nearest-neighbor control of multi-agent systems where each agent can only realize a finite set of control points. Under the assumption that the underlying graph representing the communication network between agents is connected and the interior of the convex hull of all finite actions of each agent contains the zero element, consensus or distance-based formation problems can practically be stabilized by means of nearest-neighbor control approach combined with the well-known consensus control or distributed formation control laws, respectively. Furthermore, we provide the convergence bound for each corresponding error vector which can be computed based on the information of individual agent’s finite control points. Finally, we show Monte Carlo numerical simulations that confirm our analysis.

Predefined-Time Consensus of Nonlinear Multi-Agent Input Delay/Dynamic Event-Triggered Under Switching Topology

The consensus control problem of multi-agent systems (MASs) is studied. Firstly, a predefined-time consensus control algorithm is proposed for nonlinear uncertain systems with the input delay and switching topology. Then, the problem of resource consumption is considered, a dynamic event-triggered predefined-time consensus control algorithm is presented by introducing internal dynamic variables, which can make the MASs achieve consensus in the preset time. The correctness of the algorithm is proved by algebraic graph theory and Lyapunov theory, and there is no Zeno behavior. Simulation comparison experiments verify the effectiveness and superiority of the proposed algorithm. Compared with the finite-time control algorithm, the convergence time of this algorithm is independent of the initial state. The upper bound of the system convergence time can be set by selecting a time parameter. Compared with the fixed-time control algorithm, the convergence time of this algorithm is independent of the controller parameters, only related to a single parameter, the setting is simple, and the estimated convergence time is less conservative. Compared with the static triggering mechanism, the dynamic triggering mechanism can avoid a large number of triggering.

Dynamic Event-Triggered Communication-Based Adaptive Consensus Tracking of Uncertain Nonlinear Multiagent Systems in Pure-Feedback Form

This study is aimed at investigating a dynamic event-triggered communication-based adaptive distributed consensus control problem for a class of uncertain pure-feedback nonlinear multiagent systems with limited communication resources. The nonaffine nonlinear functions of multiagent systems are assumed to be unknown and heterogeneous, and intermittent inter-agent communication is considered to occur within a directed network. A novel adaptive distributed dynamic surface control strategy using neural networks is developed to manage non-differentiable virtual control laws associated with the intermittent communication between agents with uncertain nonaffine nonlinear parts. The key contribution of this research is the derivation of dynamic event-triggering conditions using distributed tracking errors to efficiently adjust inter-event times, while ensuring the consensus tracking performance and robustness against unexpected external disturbances. Compared with the existing static event-triggered communication approach, the proposed controller can alleviate the communication burden among agents. Using technical lemmas, it is shown that all signals of the considered system are semiglobally uniformly ultimately bounded, and Zeno behavior is strictly excluded. Comparative simulation results illustrate the effectiveness of the proposed dynamic event-triggered control approach.

Seeking Velocity-Free Consensus for Multi-Agent Systems With Nonuniform Communication and Measurement Delays

This paper addresses the consensus control problem of nonuniform delayed multi-agent systems without velocity measurements, and further obtains an explicit expression for the delay margin condition (critical time delay). Firstly, the passivity-based control technique is introduced to design the nominal consensus controller, which can enhance the robustness of the system by injecting additional relative damping. Then, the system states and the virtual state of the damping term are incrementally generalized into a third-order equation. Based on the frequency domain method, this equation was transformed into a high-order polynomial. Thus, the consensus conditions of the delayed multi-agent system are obtained according to the monotonicity of the polynomial. In detail, the conditions are presented in the form of an upper bound on the time delays and inequality sets of controller parameters. Finally, the effectiveness of the proposed controller and its corresponding consensus conditions are verified by designing the numerical simulation experiments.

Consensus of Matrix-Weighted Hybrid Multiagent Systems.

As we all know, heterogeneity is a very important feature of multiagent systems (MASs). In this article, we examine the consensus control problems of matrix-weighted hybrid MASs, which contain discrete-time and continuous-time dynamic agents. Under fixed and switched undirected networks, three consensus algorithms are proposed for matrix-weighted hybrid MASs. In the three consensus algorithms, the sampled data control method is utilized in the continuous-time subsystem to analyze the convergence of different dynamic agents in the matrix-weighted interaction mode. For the symmetric matrix-weighted fixed and switched multiagent networks, when the sampling period meets certain conditions, the consensus criteria are established via the matrix theory, Lyapunov stability theory, and analysis theory. Moreover, asymmetric matrix-weighted fixed multiagent networks which can be applied to some scenarios with scaled and rotated updates constraints are considered, and consensus criteria are also obtained when the sampling period meets certain conditions. Finally, a few simulation examples are supplied to validate the correctness of the obtained theoretical results.

H2 suboptimal leader-follower consensus control of multi-agent systems

In this paper, we investigate the distributed H2 suboptimal leader-follower consensus control problem for linear multi-agent systems using dynamic output feedback. By considering an autonomous leader, a number of followers, and an associated H2 cost functional, we aim to design a distributed protocol to ensure that the leader-follower consensus is achieved while the associated H2 cost is smaller than an a priori given upper bound. To this end, we first show that the H2 suboptimal leader-follower consensus control problem can be equivalently derived as the H2 suboptimal control problem of a set of independent systems. Based on this, we then present a design method for computing a distributed protocol. The computation of the feedback gains involves two Riccati inequalities whose dimension matches the state dimension of the agents. A simulation example is provided to demonstrate the performance of the proposed protocol.

Reliable Leader-Following Consensus of Discrete- Time Semi-Markovian Jump Multi-Agent Systems

This paper is concerned with the leader-following reliable consensus control problem of a class of discrete-time semi-Markovian jump multi-agent systems. Two stochastic jump processes are employed to characterize the changes of system parameters and actuator faults. The abrupt changes of the agent parameters are described by a discrete semi-Markovian process. Another discrete Markovian jump process represents the actuator faults which stochastically occur and change during the operation of the subsystem. Firstly, sufficient conditions for guaranteeing the leader-following consensus are derived. Secondly, a non-fragile distributed reliable consensus control protocol is presented for the underlying system with additive norm bounded gain perturbations. Thirdly, the proposed approach of distributed consensus controller is extended to the scenario which system parameters are uncertain and fault transition probability matrix is confined to a polytope composed of multiple vertices. Finally, two examples are provided to illustrate the efficacy of the presented results.

Reinforcement-learning-based fixed-time attitude consensus control for multiple spacecraft systems with model uncertainties

In this study, the problem of fixed-time attitude consensus control was investigated for multiple spacecraft systems with model uncertainties. First, a distributed fixed-time adaptive observer is proposed for estimating the states of the leader. Subsequently, on the basis of the observation errors, transformed error dynamics are described and they are used to combine the unknown nonlinear terms of a spacecraft system. By using the non-singular fast terminal sliding mode technique and a reinforcement learning optimization algorithm, we implemented a neural-network-based fixed-time control strategy to achieve optimal attitude consensus control. The stability of the system and the fixed-time convergence of the tracking error are demonstrated by using the Lyapunov theory. Furthermore, the effectiveness and superiority of the control strategy are shown through numerical simulations.

Fault-tolerant consensus control of multi-agent systems under actuator/sensor faults and channel noises: A distributed anti-attack strategy

This study investigates the fault-tolerant consensus control problem of multi-agent systems subject to simultaneous actuator/sensor faults and channel noises in physical hierarchy and hostile connectivity-mixed attacks in cyber hierarchy. Actuator/sensor faults are remodeled into unified abrupt-type and incipient-type characteristics, and connectivity-mixed attacks are established with connectivity-maintained and connectivity-paralyzed topologies by a switching and nonoverlapping version. Normalization and estimation-based observer is devised to recollect unknown state and fault observations, and distributed anti-attack fault-tolerant consensus strategy is also developed to achieve the tolerance to faults, resilience to attacks and robustness to noises, respectively, with the novel incorporated sensor fault and output channel noise estimation as well as neighboring output information. Criteria of executing leader-following consensus of multi-agent systems under cyber-physical threats are derived with attack frequency and activation rate technologies. Effectiveness and improvements of the proposed fault-tolerant consensus algorithm are validated on two case studies: 1) multi-machine power system synchronization and 2) multi-aircraft system coordination.

Distributed consensus tracking control based on state and disturbance observations for mixed-order multi-agent mechanical systems

In this paper, we study the cooperative consensus control problem of mixed-order (also called hybrid-order) multi-agent mechanical systems (MMSs) under the condition of unmeasurable state, unknown disturbance and constrained control input. Here, the controlled mixed-order MMSs are consisted of the mechanical agents having heterogeneous nonlinear dynamics and even non-identical orders, which means that the agents can be of different types and their states to be synchronized can be not exactly the same. In order to achieve the ultimate synchronization of all mixed-order followers, we present a novel distributed adaptive tracking control protocol based on the state and disturbance observations. Wherein, a distributed state observer is used to estimate the followers’ and their neighbors’ unmeasurable states. And, a novel estimated-state-based disturbance observer (DOB) is proposed to reduce the effect of unknown lumped disturbance for the mixed-order MMSs. The proposed control protocol and observers are fully distributed and can be calculated for each follower locally. Lyapunov theory is used for proving the stability of the proposed control algorithm and the convergence of the cooperative tracking errors. A practical cooperative longitudinal landing control example of unmanned aerial vehicles (UAVs) is given to illustrate the effectiveness of the presented control protocol.

Iterative learning based consensus control for distributed parameter type multi-agent differential inclusion systems with time-delay

This paper investigates consensus control problem for a class of distributed parameter type multi-agent differential inclusion systems with state time-delay by utilizing iterative learning control (ILC). Unlike most ILC literature of nonlinear distributed parameter systems that require an identical virtual leader, the virtual leader is iteratively varying in this work and can be described by any follower agent. Both P -type closed-loop and D -type open-loop ILC are proposed for the distributed parameter type multi-agent differential inclusion systems, which enable the output trajectories of each agent to achieve consensus in the sense of W 1 , 2 norm as the iteration number increases. Meanwhile, consensus control theorems for these protocols are established by using Steiner-type selector, Green's formulas and some technical inequalities. Finally, numerical simulations testify the validity of the proposed methods.

Intermittent Cluster Consensus Control of Multiagent Systems From a Static/Dynamic Output Approach

This article is concerned with the cluster consensus control problem for multiagent linear systems with a directed communication topology, where only relative output measurements of neighboring agents are available to each agent. Motivated by the pinning control technique, both static and dynamic intermittent output control strategies are proposed. Using Lyapunov functions, sufficient conditions are developed to ensure cluster consensus with existence-guaranteed control parameters. Both periodic and nonperiodic operations of intermittent controllers are investigated. Finally, the effectiveness of the theoretical results is demonstrated by a simulation example.

Distributed adaptive fault-tolerant consensus control for multi-agent systems with event-triggered communication

ABSTRACT In this paper, the distributed fault-tolerant consensus control problem is studied for multi-agent systems with event-triggered communication. Unknown time-varying actuator faults including partial loss of effectiveness and bias are taken into consideration. For the sake of fault compensations, a novel distributed event-triggered control law is put forward via the adaptive fault-tolerant technique in the leaderless network. Then, two event-triggered mechanisms are constructed, and a positive function introduced therein is greatly useful for scheduling the information transmission as well as excluding the Zeno behavior. Under the proposed protocol, the consensus errors are proved to converge to zero asymptotically in a scalable and fully distributed way. Furthermore, the results obtained in the leaderless network are extended to the leader-following case. Finally, simulation examples are conducted to confirm the validity of the presented results.

Robust consensus control of nonlinear multi‐agent systems based on convergence rate estimation

AbstractConvergence rate is an important performance criterion for consensus control of multi‐agent systems (MASs). It has been an important and difficult problem to accelerate the convergence rate of MASs. In this article, a robust consensus control scheme based on the convergence rate estimation for a nonlinear high‐order MAS is proposed to accelerate the convergence rate as well as improve the control performance of the MAS. In the proposed control scheme, a novel convergence rate indicator (CRI) is defined to measure the influence of the model nonlinearity, the state couplings within a single agent and among multiple agents in the MAS on convergence rate. Then, a distributed consensus controller with a CRI‐based additive term is designed by the backstepping technique with disturbance observers to enhance the robustness of the closed‐loop system. Furthermore, from a theoretical perspective, the robustness and the stability of the MAS are proved. Finally, the consensus control problem of the multi‐agent control system composed of five single‐link robot arms is simulated to validate the effectiveness of the proposed controller. Simulation results illustrate that the proposed consensus control approach with CRI has better performance than conventional backstepping consensus control techniques of the MAS in the same conditions.

Adaptive consensus control of second-order nonlinear multi-agent systems with event-dependent intermittent communications

This article deals with the adaptive consensus control problem for second-order nonlinear multi-agent systems under intermittent communications. The main contribution is that a novel event-dependent intermittent communication scheme is proposed, where the work time and the rest time can be changed according to the current states. This event-dependent intermittent communication is named Sun’s intermittent communication scheme. In this communication scheme, by dividing the nonnegative real region into three subregions, the work time and the rest time are decided by the events, which are produced by the pre-given subregions and a Lyapunov function. Then by developing a distributed adaptive protocol based on state estimates of neighboring agents, the overall consensus is achieved under the event-dependent intermittent communication. Compared with the existing related schemes, the proposed scheme can tolerate a larger intermittent rate. Finally, a simulation example is developed to verify the proposed approach.

Distributed Finite-Time Consensus Control of Multiagent Systems With Fully Intermittent Communication via Dynamic Event-Triggered Strategy

Taking into account the multi-agent systems (MASs) with the single-order integrator dynamics and the directed internal topology, this brief is devoted to investigating the finite-time consensus (FTC) control problem based on the event-triggered strategy (ETS). A novel dynamic and state-dependent ETS is designed by using an adaptive and dynamic variable for each agent. Based on the triggered states, a discontinuous FTC control strategy is proposed and the tools from the non-smooth analysis theory are adapted to analyze the stability. Moreover, under the developed protocol, consensus can be realized after a finite transient time while avoiding the continuous information transmissions among agents. Finally, the effectiveness corroboration of the theoretical results are provided by the numerical simulation.

Fuzzy Adaptive Finite-Time Consensus Control for High-Order Nonlinear Multiagent Systems Based on Event-Triggered

This article studies the fuzzy adaptive finite-time consensus control problem for high-order nonlinear multiagent systems with unknown nonlinear dynamics. In control design,fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and under the frameworks of adaptive backstepping recursive design and finite-time stability theory, an adaptive fuzzy finite-time consensus control method is developed. To save communication resources and reduce the numbers of controller execution times, a dynamic event-triggered mechanism with a relative threshold is established. Subsequently, an event-triggered-based finite-time fuzzy adaptive control scheme is formulated. Furthermore, by constructing novel integral-type Lyapunov functions and adding a power integrator technique, the finite-time stability of the closed-loop system and the convergence of consensus tracking errors are proved. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed adaptive event-triggered consensus control method.

Adaptive Discontinuous Control for Fixed-Time Consensus of Nonlinear Multi-Agent Systems

This paper mainly focuses on the fixed-time consensus (FXC) control problem for nonlinear multi-agent systems (MASs). For the cases of leader-following and leaderless, two adaptive discontinuous protocols are designed, respectively, to realize our control goals. Common adaptive control protocols always significantly increase the dimension of the considered system model, while the protocols presented here only require two adaptive update laws and are therefore simpler to apply in the engineering control. Moreover, no additional conditions are required to ensure that the system can achieve FXC successfully, except for some necessary assumptions. Simulation examples also illustrate that these two protocols are effective.

On consensus control of nonlinear multiagent systems satisfying incremental quadratic constraints

In this paper, we investigate the problem of leaderless consensus control for the multiagent systems whose nonlinear dynamics satisfying incremental quadratic constraints. A distributed dynamic consensus protocol, decided by communication among neighboring agents, is presented to render nonlinear agent consensus with appropriate coupling weights. Next, an observer-based distributed protocol is considered to ensure consensus of nonlinear system without knowing full state information. Further, extensions to consensus strategies with nonlinear dynamics for the leader-following fashion are also addressed. By comparison to the traditional nonlinear consensus control methodologies, the proposed approach generalizes the Lipschitz nonlinearity as well as the combined nonlinearity of one-sided Lipschitz condition and quadratic inner-boundness condition towards a more generalized type of nonlinearity, which shows us a less conservative result in the Lyapunov proof. Finally, the numerical simulations for six agents are illustrated to show the feasibility and performance of the proposed control protocol with or without the presence of the observer.

Distributed consensus control of nonlinear multi‐agent systems with sensor uncertainty

AbstractThis article focuses on the distributed consensus control problem for nonlinear multi‐agent systems subject to sensor uncertainty. To be specific, we study nonlinear multi‐agent systems of lower or upper triangular structure with unknown growth rate and sensor uncertainty. A new time‐varying gain approach is proposed to construct observers as well as distributed output‐feedback controllers. By selecting suitable design parameters, the leader‐follower consensus of nonlinear multi‐agent systems is achieved. Different from the existing results, a time‐varying function in a logarithmic form is introduced to deal with unknown growth rate. Moreover, a monotonically increasing time‐varying function is constructed to cope with uncertain sensor sensitivity. Two simulation examples are provided to demonstrate the effectiveness of the proposed distributed consensus control algorithms.