Distributed control for output-constrained nonlinear multi-agent systems with completely unknown non-identical control directions

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol.     

Consensus control via iterative learning for distributed parameter models multi-agent systems with time-delay

Most of the available results of iterative learning control (ILC) are that solve the consensus problem of lumped parameter models multi-agent systems. This paper considers the consensus control problem of distributed parameter models multi-agent systems with time-delay. By using the knowledge between neighboring agents, considering time-delay problem in the multi-agent systems, a distributed P-type iterative learning control protocol is proposed. The consensus error between any two agents in the sense of L² norm can converge to zero after enough iterations based on proposed ILC law. And then we extend these conclusions to Lipschitz nonlinear case. Finally, the simulation result shows the effectiveness of the control method.     

Consensus of linear multi-agent systems based on full-order observer

This paper considers distributed consensus problem of multi-agent systems consisting of general linear dynamics with a time-invariant communication topology. A distributed full-order observer type consensus protocol based on relative output measurements of neighbor agents is proposed. It is found that the consensus problem of linear multi-agent systems with a directed communication topology having a spanning tree can be solved if and only if all subsystems are asymptotically stable. Some necessary and sufficient conditions are obtained for ensuring consensus in multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and linear control theory. Finally, simulation example is given to illustrate the effectiveness of the theoretical results.     

Leader-following fixed-time quantized consensus of multi-agent systems via impulsive control

In this paper, we mainly tend to consider distributed leader-following fixed-time quantized consensus problem of nonlinear multi-agent systems via impulsive control. An appropriate quantized criterion and some novel control protocols are proposed in order to solve the problem. The protocols proposed integrates the two control strategies from the point of view of reducing communication costs and constraints, which are quantized control and impulsive control. The fixed-time quantized consensus of multi-agent is analyzed in terms of algebraic graph theory, Lyapunov theory and comparison system theory, average impulsive interval. The results show that if some sufficient conditions are met, the fixed-time consensus of multi-agent systems can be guaranteed under impulsive control with quantized relative state measurements. In addition, compared with finite-time consensus, the settling-time of fixed-time quantized consensus does not depend on the initial conditions of each agent but on the parameters of the protocol. Finally, numerical simulations are exploited to illustrate the effectiveness and performance to support our theoretical analysis.     

Distributed control of cluster lag consensus for first-order multi-agent systems on QUAD vector fields

This paper addresses the problem of cluster lag consensus for first-order multi-agent systems which can be formulated as moving agents in a capacity-limited network. A distributed control protocol is developed based on local information, and the robustness of the protocol is analyzed by using tools of Frobenius norm, Lyapunov functional and matrix theory. It is shown that when the root agents of the clusters are influenced by the active leader and the intra-coupling among agents is stronger enough, the multi-agent system will reach cluster lag consensus. Moreover, cluster lag consensus for multi-agent systems with a time-varying communication topology and heterogeneous multi-agent systems with a directed topology are studied. Finally, the effectiveness of the proposed protocol is demonstrated by some numerical simulations.     

Adaptive synchronization of multi-agent systems via variable impulsive control

This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.     

Distributed data driven control for multi-agent consensus with unknown system dynamics

This study investigates the consensus tracking problem for unknown multi-agent systems (MASs) with time-varying communication topology by using the methods of data-driven control and model predictive control. Under the proposed distributed iterative protocol, sufficient conditions for reducing tracking error are analyzed for both time invariable and time varying desired trajectories. The main feature of the proposed protocol is that the dynamics of the multi-agent systems are not required to be known and only local input-output data are utilized for each agent. Numerical simulations are presented to illustrate the effectiveness of the derived consensus conditions.     

Distributed optimal consensus protocol for high-order integrator-type multi-agent systems

Optimal consensus control of high-order multi-agent systems (MASs) modeled by multiple integrator-type dynamics is studied. A fully distributed optimal control protocol that achieves the specific consensus behavior is designed for MASs with linear dynamics, where topology-dependent conditions are removed. Further, a distributed consensus protocol for high-order nonlinear MASs with one-sided Lipschitz continuity is presented using the optimization approach, and the optimal solution can be obtained by solving a standard algebraic Riccati equation. Some numerical examples are finally provided to illustrate the effectiveness of the presented approaches.     

Distributed fixed-time control of high-order multi-agent systems with non-holonomic constraints

In this paper, a protocol is proposed for fixed-time consensus of the high-order chained-form multi-agent systems subject to non-holonomic constraints. By employing the backstepping structure and a power integrator, the distributed fixed-time protocol is designed to guarantee that system states reach consensus before a fixed time. The fixed settling time can be calculated explicitly, and it is independent of initial conditions. The proposed protocol is applied to multi-agent wheeled mobile robots to support the theoretical result.     

Event-triggered group consensus for multi-agent systems subject to input saturation

This paper investigates group consensus for leaderless multi-agent systems with non-identical dynamics. The consensus protocol is put forward in the form of the distributed event-triggered control subject to saturation, which depends on information from neighboring agents at event-triggered instants. In order to exclude the Zeno behavior and save resources, the given event-triggered condition is detected only at discrete sampling times, where the sampling intervals can be variable. Based on the graph theory, Lyapunov–Krasovskii functional method and by adopting the free-weighting matrix technique, some sufficient group consensus criteria in terms of linear matrix inequalities are derived. Furthermore, optimization problems aiming at maximizing the event-triggered parameter and the consensus region are proposed. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Distributed secure consensus control of nonlinear multi-agent systems under sensor and actuator attacks

In this paper, we focus on an output secure consensus control issue for nonlinear multi-agent systems (MASs) under sensor and actuator attacks. Followers in an MAS are in strict-feedback form with unknown control directions and unknown dead-zone input, where both sensors and nonlinear characteristics of dead-zone in actuators are paralyzed by malicious attacks. To deal with sensor attacks, uncertain dynamics in individual follower are separated by a separation theorem, and estimation parameters are introduced for compensating and mitigating the influence from adversaries. The influence from actuator attacks are treated as a total displacement in a dead-zone nonlinearity, and an upper bound, as well as its estimation, is introduced for this displacement. The dead-zone nonlinearity, sensor attacks and unknown control gains are gathered together regarded as composite unknown control directions, and Nussbaum functions are utilized to address the issue of unknown control directions. A distributed secure consensus control strategy is thus developed recursively for each follower in the framework of surface control method. Theoretically, the stability of the closed-loop MAS is analyzed, and it is proved that the MAS achieves output consensus in spite of nonlinear dynamics and malicious attacks. Finally, theoretical results are verified via a numerical example and a group of electromechanical systems.     

Sliding-mode consensus algorithms for disturbed second-order multi-agent systems

In this paper, both leaderless and leader-follower consensus problems for a class of disturbed second-order multi-agent systems are studied. Based on integral sliding-mode control, sliding-mode consensus protocols are proposed for leaderless and leader-follower multi-agent systems with disturbances, respectively. Firstly, for leaderless second-order multi-agent systems, a sliding-mode consensus protocol is proposed to make the agents achieve asymptotic consensus. Secondly, for leader-follower second-order multi-agent systems, a finite-time sliding-mode consensus protocol is designed to make the agents achieve consensus in finite time. Both kinds of consensus protocols inherit the anti-disturbance performance and robustness of sliding-mode control and require less communication information. Finally, two numerical simulations are given for leaderless and leader-follower second-order multi-agent systems to validate the efficiency of the proposed consensus protocols.     

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Distributed formation control of double-integrator fractional-order multi-agent systems with relative damping and nonuniform time-delays

In this paper, distributed formation control problems are studied for double-integrator fractional-order multi-agent systems (DIFOMASs) with relative damping and nonuniform time-delays. The required state deviations of a group of multi-agent systems are achieved through a local state information interaction, which means that this group of multi-agent systems achieves formation control. In the context of this paper, the dynamic model is first established and the formation control protocol is designed for distributed formation control of DIFOMASs with relative damping under symmetric time-delays and asymmetric time-delays. Then, some sufficient conditions for achieving distributed formation control of DIFOMASs are acquired with the help of graph theory, matrix theory, stability theory and frequency-domain theory. In the end, two simulation examples are performed to verify the efficacy of our proposed method.     

Finite-time consensus of linear multi-agent system via distributed event-triggered strategy

In this paper, we mainly investigate the finite-time consensus problem of general linear multi-agent systems. The paper proposed a suitable event-triggered control strategy. The strategy has some desirable properties including: distributed, independent, and asynchronous. It is theoretical demonstrated that the multi-agent system can achieve consensus in a certain time regardless of the initial condition under this event-triggered control scheme. In addition, without finding singular triggering problem, we prove the feasibility of this proposed event-triggered control protocol. Finally, we put forward some simulation graphs for the sake of showing the availability of our conclusions.     

Leader-following successive lag consensus of nonlinear multi-agent systems via observer-based event-triggered control

This article investigates the leader-following successive lag consensus (SLC) for nonlinear multi-agent systems (NMASs) via the observer-based event-triggered control (OBETC), in which two scenarios including constant consensus delay and time-varying consensus delay are considered. Since the system states might not be directly available in actual scenes, the state estimation method is utilized for followers to track their full information. Based on the relative state, a class of distributed event-triggered control protocols is constructed, where the event-triggered strategy is introduced such that each follower can determine the broadcasting time to its neighbors. Obviously, these designed control protocols considerably lessen the expense over communication networks and the frequency of protocol updates. Furthermore, with the aid of the Lyapunov function method, a series of sufficient conditions for guaranteeing the leader-following SLC of NMASs is obtained. Meanwhile, it is proved that no Zeno behavior is exhibited. Finally, several numerical examples are given to illustrate the validity of our theoretical results.     

Adaptive bipartite output consensus for heterogeneous multi-agent systems with quantized information: A fixed-time approach

This paper researches the output consensus problem of heterogeneous linear multi-agent systems with cooperative and antagonistic interactions. Two fixed-time state compensator control approaches, one static dynamic and the other distributed adaptive dynamic, are considered for heterogeneous systems subject to logarithmic quantization. Then, a fixed-time output regulation control protocol is constructed to cope with the problem of bipartite output consensus and adaptive fixed-time output consensus of heterogeneous systems which is fully distributed without any global information. Besides, the fully distributed adaptive algorithm is employed to calculate the system matrix of leader and it’s also effectively eliminated the harmful chattering. Finally, two simulations are carried out to testify the feasibility of theoretical results.     

Formation consensus for discrete-time heterogeneous multi-agent systems with link failures and actuator/sensor faults

In this paper, a distributed control protocol is presented for discrete-time heterogeneous multi-agent systems in order to achieve formation consensus against link failures and actuator/sensor faults under fixed and switching topologies. A model equivalent method is proposed to deal with the heterogeneous system consists of arbitrary order systems with different parameters. Based on graph theory and Lyapunov theory, stability conditions to solve formation consensus problem are developed for the underlying heterogeneous systems with communication link failures. In order to tolerate actuator/sensor faults, a distributed adaptive controller is proposed based on fault compensation. The desired control is designed by linear matrix inequality approach together with cone complementarity linearisation algorithm. After applying the new control scheme to heterogeneous systems under the directed topologies with link failures and faults, the resulting closed-loop heterogeneous system is validated to be stable. The effectiveness of the new formation consensus control strategy and its robustness are verified by simulations.     

Aperiodically intermittent output feedback consensus control for second-order leader-following multi-agent systems based on observer

This study examines the leader-following consensus problem of a class of second-order nonlinear multi-agent systems, where the velocity information is supposed to be unmeasurable. Under the setting, this paper presents a novel aperiodically intermittent output feedback control protocol such that all followers reach consensus with the leader, in which a distributed state observer is built for each follower to observe the velocity state. Based on the Lyapunov stability theory and some matrix analysis techniques, a couple of sufficient conditions for the leader-following consensus of the nonlinear multi-agent system under study are obtained even though the velocity state is unavailable. Finally, the effectiveness of the theoretical results is verified by numerical simulation.     

Distributed disturbance observer based consensus control for linear multi-agent systems with mismatched disturbances

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws.