Leader-following Multi-agent Systems Research Articles

Distributed adaptive formation control for non‐identical non‐linear multi‐agents systems based on sliding mode

This study investigates the distributed control strategy for handling the time-invariant and time-varying formation tracking problem of a class of non-linear nonidentical leader-follower multi-agent systems with uncertainties and unknown external disturbances. Firstly, the neighbour-based distributed finite-time observers are proposed for the followers to estimate the position and velocity of the leader. Then, two novel distributed adaptive formation control algorithms based on the approximation capability of neural networks and sliding mode are developed. One can prove that, with the proposed observer and the control laws, all the followers will reach the desired time-invariant or time-varying formation tracking, and achieve the consistent velocity with the leader in spite of uncertainties and disturbances. Finally, illustrative simulation examples are given to verify the effectiveness of the obtained theoretical results.

Observer‐based formation tracking control for leader–follower multi‐agent systems

This study investigates the formation tracking control for second-order leader-follower multi-agent systems. To estimate the velocity and acceleration of the leader, distributed observers are constructed for each follower. Based on the observed states, the authors propose a novel distributed formation tracking control protocol and analyse two communication networks with and without communication delays. Then, they prove that each agent can follow the active leader closely and form the desired spatial pattern. Finally, simulation examples are provided to show the validity of the theoretical results.

Stochastic consensus of double-integrator leader-following multi-agent systems with measurement noises and time delays

ABSTRACTThis paper studies a leader-following consensus problem of continuous-time double-integrator multi-agent systems with measurement noises and time-varying communication delays under directed topology. By utilising the neighbour position and velocity information, which are delayed and disturbed by measurement noises whose intensities are considered a function related to the neighbour position and velocity of agents, a distributed consensus protocol is presented, sufficient conditions of the tracking consensus in the sense of mean square are derived. Finally, the effectiveness of the proposed consensus protocol is proved by some simulations.

Integrated design of fault estimation and fault-tolerant control for linear multi-agent systems using relative outputs

In this paper, the problem of fault estimation and fault-tolerant control is investigated for linear multi-agent systems with mismatched uncertainty. Different from the existing results, an integrated design method is proposed to solve the problem of bi-directional uncertainty which arises from the combination of fault estimation and control. In order to realize a distributed integrated design, spectral decomposition and coordinate transformation are introduced so that the leader-following multi-agent systems can be decoupled into independent observable subsystems. For this new subsystem, an unknown input observer and a fault-tolerant controller are constructed by only using the relative outputs, and an integrated design condition is given in terms of linear matrix inequality. Finally, two examples are utilized to illustrate the validity of this method.

Resilient adaptive optimal control of distributed multi‐agent systems using reinforcement learning

This study presents a unified resilient model-free reinforcement learning (RL) based distributed control protocol for leader-follower multi-agent systems. Although RL has been successfully used to learn optimal control protocols for multi-agent systems, the effects of adversarial inputs are ignored. It is shown in this study, however, that their adverse effects can propagate across the network and impact the learning outcome of other intact agents. To alleviate this problem, a unified RL-based distributed control frameworks is developed for both homogeneous and heterogeneous multi-agent systems to prevent corrupted sensory data from propagating across the network. To this end, only the leader communicates its actual sensory information and other agents estimate the leader' state using a distributed observer and communicate this estimation to their neighbours to achieve consensus on the leader state. The observer cannot be physically affected by any adversarial input. To further improve resiliency, distributed control protocols are designed to attenuate the effect of the adversarial inputs on the compromised agent itself. An off-policy RL algorithm is developed to learn the solutions of the game algebraic Riccati equations arising from solving the control problem. No knowledge of the agent's dynamics is required and it is shown that the proposed RL-based control protocol is resilient against adversarial inputs.

Leader-following fixed-time output feedback consensus for second-order multi-agent systems with input saturation

ABSTRACTThis paper investigates the leader-following fixed-time output feedback consensus problem for second-order multi-agent systems with input saturation. By combing fixed-time control technique and bi-limit homogeneous systems theory, a class of bounded fixed-time consensus protocols are developed for leader-following multi-agent systems. The protocol design is divided into two parts. First, when all the state information of the followers are measurable, a state feedback consensus protocol is designed to achieve fixed-time consensus. Then, when the velocity information is unmeasurable, an observer-based fixed-time consensus protocol is proposed. With the help of Lyapunov stability theorem and the property of a homogeneous function, it is theoretically shown that the states of all followers can track that of the leader in fixed-time in the presence of input saturation. Finally, numerical simulation is carried out to illustrate the effectiveness of theoretical results.

LQR Based Optimal Topology of Hybrid-Weighted Multiagent Systems

In this paper, the optimal topology structure is studied for hybrid-weighted leader-follower multiagent systems (MASs). The results are developed by taking advantage of linear quadratic regulator (LQR) theory. We show that the multiagent star composite structure is the optimal topology which can enable the MAS to achieve the bipartite consensus. In particular, we prove that the optimal topology corresponding to the multiagent system with the first-order static leader and the second-order dynamic leader is, respectively, a hybrid-weighted star composite structure and an unevenly hybrid-weighted star composite structure. The results of the paper indicate that, in addition to the necessary information communication between leader and followers, the information exchange among followers increases the control cost of the system.

Fault-tolerant Consensus of Leader-following Multi-agent Systems Based on Distributed Fault Estimation Observer

This paper is concerned with the fault-tolerant consensus control problem for leader-following multi-agent systems with actuator faults and external disturbance. Firstly, by employing the relative output estimation errors with respect to the corresponding neighbours and the leader, a distributed fault estimation observer is constructed for each follower and the established global estimation error system is proven to be asymptotically stable. Secondly, based on the obtained fault estimation, the active fault-tolerant consensus control protocol for each follower is proposed with the utilization of the relative output measurements rather than the state of the systems. Under this control protocol, the actuator faults can be compensated and the influence of disturbance can be eliminated as well. Moreover, it is worth noticing that the process of designing the fault estimation observer and the fault-tolerant controller is separated and their performances are considered simultaneously to simplify the design procedures. Finally, an illustrative example is presented to demonstrate the applicability and the effectiveness of the obtained results.

Distributed adaptive event-triggered protocol for tracking control of leader-following multi-agent systems

A novel adaptive event-triggered control protocol is developed to investigate the tracking control problem of multi-agent systems with general linear dynamics. By introducing the event-triggered control strategy, each agent can decide when to transfer its state to its neighbors at its own triggering instants, which can greatly reduce communication burden of agents. It is shown that the “Zeno phenomenon” does not occur by verifying that there exists a positive lower bound on the inter-event time intervals of agents under the proposed adaptive event-triggered control algorithm. Finally, an example is provided to testify the effectiveness of the obtained theoretical results.

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.

Resilient Autonomous Control of Distributed Multiagent Systems in Contested Environments.

An autonomous and resilient controller is proposed for leader-follower multiagent systems under uncertainties and cyber-physical attacks. The leader is assumed nonautonomous with a nonzero control input, which allows changing the team behavior or mission in response to the environmental changes. A resilient learning-based control protocol is presented to find optimal solutions to the synchronization problem in the presence of attacks and system dynamic uncertainties. An observer-based distributed H∞ controller is first designed to prevent propagating the effects of attacks on sensors and actuators throughout the network, as well as to attenuate the effect of these attacks on the compromised agent itself. Nonhomogeneous game algebraic Riccati equations are derived to solve the H∞ optimal synchronization problem and off-policy reinforcement learning (RL) is utilized to learn their solution without requiring any knowledge of the agent's dynamics. A trust-confidence-based distributed control protocol is then proposed to mitigate attacks that hijack the entire node and attacks on communication links. A confidence value is defined for each agent based solely on its local evidence. The proposed resilient RL algorithm employs the confidence value of each agent to indicate the trustworthiness of its own information and broadcast it to its neighbors to put weights on the data they receive from it during and after learning. If the confidence value of an agent is low, it employs a trust mechanism to identify compromised agents and remove the data it receives from them from the learning process. The simulation results are provided to show the effectiveness of the proposed approach.

Distributed neuro‐adaptive control protocols for non‐strict feedback non‐linear MASs with input saturation

This study develops distributed neuro-adaptive control protocols for synchronisation of leader–follower multi-agent systems (MASs) with non-linear dynamics in non-strict-feedback form. The communication graph is assumed to be directed, and the agents are considered heterogeneous. The leader's dynamics are also assumed non-linear, and the state derivative of the leader is unknown to its immediate followers. The well-known command filtered backstepping approach, presented for single-agent systems in the literature, is extended to the synchronisation of MASs with non-strict-feedback non-linear dynamics. This obviates the requirement of computing the n th-order derivatives of the local neighbourhood synchronisation error at the step n of the design. The number of adaptive tuning laws and consequently the complexity of the neuro-adaptive design is reduced by estimating only a positive scalar related to unknown non-linear dynamics of each agent. An auxiliary system is then introduced into the control design to compensate for the discrepancy between designed and saturated control signals. The proposed distributed control protocol guarantees that all signals in the closed-loop system are cooperatively semi-globally uniformly ultimately bounded, and the consensus error for all agents converge to a small neighbourhood of the origin. Finally, a simulation example demonstrates the effectiveness of the proposed control scheme.

Adaptive Fault-Tolerant Consensus for a Class of Uncertain Nonlinear Second-Order Multi-Agent Systems With Circuit Implementation

In this paper, a robust fault-tolerant consensus control strategy and its circuit implementation method are proposed for a class of nonlinear second-order leader-following multi-agent systems against multiple actuator faults and time-varying state/input-dependent system uncertainties. The faults of partial loss of actuator effectiveness and bias-actuators are considered without knowing eventual faulty information. The uncertainties are supposed to be structured and to satisfy integral quadratic constraints. The nonlinear dynamics of underlying systems are described by linear state-dependent functions based on the differential mean value theorem. By designing adaptive schemes and state-feedback control gains, a novel distributed control strategy is constructed to ensure the asymptotic consensus of agents in the presence of actuator faults, uncertainties, and nonlinear dynamics. The control strategy is further physically implemented based on the circuit theory. The efficiency of the developed control circuits is verified by a multiple coupled nonlinear forced pendulum system based on a circuit simulation software.

Group multiple lags consensus of fractional-order nonlinear leader-following multi-agent systems via adaptive control

In this paper, group multiple lags consensus of fractional-order leader-following multi-agent systems with nonlinear dynamics are investigated, in which two kinds of lag consensus are considered. One is said to be outergroup lag consensus, which means that different group leaders reach lag consensus. The other one is called innergroup lag consensus, that is to say, the followers will reach lag consensus with their own group leader. Based on Mittag–Leffler stability for fractional-order systems, algebraic graph theory, a class of novel control protocols is designed and the corresponding sufficient conditions are derived to guarantee the achievement of group multiple lags consensus. Furthermore, considering parametric uncertainties, an adaptive control technology is employed to solve the group multiple lags consensus for fractional order multi-agent systems, and the corresponding adaptive control protocols and sufficient conditions are proposed. Finally, numerical simulations are given to demonstrate the effectiveness of the obtained results.

Leader-Follower Consensus of Multiagent Systems With Time Delays Over Finite Fields.

This paper studies the leader-follower consensus of multiagent systems with time delays and switching topology over finite fields. First, an equivalent algebraic form is established for leader-follower multiagent systems with time delays over finite fields. Second, based on the algebraic form, a necessary and sufficient condition is presented for the finite-field leader-follower consensus with time delays. Third, the switching topology case is considered, and a new criterion is presented for the finite-field leader-follower consensus with time delays and switching topology. Finally, an example is worked out to illustrate the obtained results.

Leader-Follower Output Synchronization of Linear Heterogeneous Systems With Active Leader Using Reinforcement Learning.

This paper develops optimal control protocols for the distributed output synchronization problem of leader-follower multiagent systems with an active leader. Agents are assumed to be heterogeneous with different dynamics and dimensions. The desired trajectory is assumed to be preplanned and is generated by the leader. Other follower agents autonomously synchronize to the leader by interacting with each other using a communication network. The leader is assumed to be active in the sense that it has a nonzero control input so that it can act independently and update its control to keep the followers away from possible danger. A distributed observer is first designed to estimate the leader's state and generate the reference signal for each follower. Then, the output synchronization of leader-follower systems with an active leader is formulated as a distributed optimal tracking problem, and inhomogeneous algebraic Riccati equations (AREs) are derived to solve it. The resulting distributed optimal control protocols not only minimize the steady-state error but also optimize the transient response of the agents. An off-policy reinforcement learning algorithm is developed to solve the inhomogeneous AREs online in real time and without requiring any knowledge of the agents' dynamics. Finally, two simulation examples are conducted to illustrate the effectiveness of the proposed algorithm.

Leader-to-Formation Stability of Multiagent Systems: An Adaptive Optimal Control Approach

This note proposes a novel data-driven solution to the cooperative adaptive optimal control problem of leader-follower multiagent systems under switching network topology. The dynamics of all the followers are unknown, and the leader is modeled by a perturbed exosystem. Through the combination of adaptive dynamic programming and internal model principle, an approximate optimal controller is iteratively learned online using real-time input-state data. Rigorous stability analysis shows that the system in closed-loop with the developed control policy is leader-to-formation stable, with guaranteed robustness to unmeasurable leader disturbance. Numerical results illustrate the effectiveness of the proposed data-driven algorithm.

Distributed robust consensus control for nonlinear leader–follower multi-agent systems based on adaptive observer-based sliding mode

This paper investigates an adaptive observer-based consensus control strategy for general nonlinear multi-agent systems (MASs). The distributed control of leader–follower MASs is studied in the presence of unknown parts in the dynamical equations of the followers which may be due to model simplification, parameter uncertainties and/or external disturbances. In order to decrease the conservatism of robust analysis, the upper bound of unknown terms are considered as unknown positive constants and are obtained through the adaptation laws. Additionally, it is assumed that all the agents’ states are not directly measurable and nonlinear distributed observers are designed. Furthermore, the robust consensus is achieved via distributed adaptive observer-based sliding mode controllers. In this regard, a theorem is given and it is proved that the consensus error converges to zero. Finally, computer simulations are performed and the theoretical results are verified.

Distributed fault detection and isolation for leader–follower multi-agent systems with disturbances using observer techniques

For the purpose of fault detection and isolation for leader–follower multi-agent systems with disturbances, a sliding-mode observer is designed using local information and suitable auxiliary information received from neighbor agents. By means of the observer, each agent can estimate the overall state of follower agents even if they are not directly connected. Then, using the relative output estimations, a residual vector is developed to detect and isolate the fault occurring on any follower agent of the leader–follower multi-agent systems. By the end, numerical simulations are employed to verify the effectiveness of the theoretical results.

An adaptive control architecture for leader–follower multiagent systems with stochastic disturbances and sensor and actuator attacks

ABSTRACTIn this paper, we develop a novel distributed adaptive control architecture for addressing networked multiagent systems subject to stochastic exogenous disturbances with compromised sensor and actuators. Specifically, for a class of linear leader–follower multiagent systems, we develop a new structure of the neighbourhood synchronisation error for the control design protocol of each follower. The proposed control algorithm addresses time-varying multiplicative sensor attacks on the leader state measurements. In addition, the framework addresses time-varying multiplicative actuator attacks on the followers that do not have a communication link with the leader and additive actuator attacks on all follower agents in the network. The proposed adaptive controller guarantees uniform ultimate boundedness of the state tracking error for each agent in a mean-square sense.