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In this article, we investigate a novel reinforcement-learning (RL)-based scheme to address the optimal leader–follower consensus issue for constrained-input continuous-time multiagent systems. First, as for input-constrained problems, the fundamental smooth assumption is not satisfied for the value function. To deal with this problem, we employ the method of vanishing viscosity solutions to relax this smooth assumption to a continuity assumption for the value function, which broadens the scope of RL applications. Second, the control cost functions take a more general form which guarantees the continuity of the optimal control policy instead of the specific integrand form used in previous input-constrained RL-based schemes. Based on these results, we introduce a novel identifier–critic–actor structure to extend the conventional critic–actor RL framework into a distributed model-free one, where the learning of the identifier, critic, and actor is online and simultaneous. We provide the simulation examples to validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Relative states between neighbors are ubiquitous in large-scale systems, and the relative state saturations need to be considered when designing controllers based on this relative state information. This article investigates the consensus control of the delayed multiagent systems under the relative state saturations. By means of an incidence matrix, the consensus under the relative state saturations is transformed into the stability of edge dynamics operating on constrained sets. To enable the edge states to stay within the constrained sets, a novel nonlinear protocol is designed by embedding an elaborate saturation function. Sufficient conditions are identified, under which not only consensus is achieved but also relative state saturations do not occur. Moreover, this analytical result can address the consensus problem while preserving connectivity, within the limited communication range framework. Simulations illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the consensus tracking of exponentially unstable multiagent systems with time-varying input delay. The truncated predictor feedback approach is utilized for designing delay-dependent state and output feedback protocols. And the explicit conditions that can realize consensus tracking are established in terms of parametric Lyapunov equations and scalar inequalities. Besides, the protocol design algorithms under the maximum allowable delay and the maximum convergence rate are, respectively, provided. Compared with the existing results, the salient characteristic of the current results is to reveal the quantitative relationship among the time delay, unstable plant, network topologies, and the convergence rate. Specifically, for achieving the consensus tracking, the synchronization force from network connectivity needs to dominate the anti-synchronization force from unstable open-loop poles and input delays; the maximum allowable input delay is inversely proportional to the sum of the unstable open-loop poles; the convergence rate becomes smaller as the input delay bounds or/and the sum of the unstable poles in plant increase. Numerical simulations confirm the effectiveness of the proposed theoretical design. [ABSTRACT FROM AUTHOR]

Containment control is an important issue in the consensus problem of multiagent systems (MASs). This article presents an output-based containment control strategy for a class of nonaffine nonlinear MASs with uncertainies and directed topology. With the help of differential homeomorphism transform and the idea of active disturbance rejection control (ADRC), a nonaffine nonlinear MAS is transformed into an affine one with uncertainties. Two filters with extended states in each follower are designed with the idea of extended state observer to reconstruct the states of the transformed MAS. Then, uncertainties of the MAS are compensated with the help of the estimations of the extended states. Moreover, the derivative of the virtual control signal in the backstepping technique is replaced by a tracking differentiator (TD), overcoming the so-called “explosion of complexity” problem. By means of Lyapunov theory, the containment errors of the followers are proven to converge to a small neighborhood around the origin via an appropriate choice of parameters. Simulation examples are provided to demonstrate the proposed control strategy. [ABSTRACT FROM AUTHOR]

This article considers integral sliding-mode control (ISMC) for multiagent systems with matched disturbances through adaptive dynamic programming (ADP) method. A distributed disturbance observer (DDO) is designed for each agent to generate the disturbance estimation. Using the disturbance estimation, an ISMC scheme is proposed to reject the input disturbance and obtain the equivalent local neighbor consensus sliding-mode dynamics. Then, a discount performance function is designed for each agent, and ADP technique is utilized to address the optimal consensus control for the equivalent sliding-mode dynamics online. Based on the gradient descent algorithm, we propose the adaptive weight tuning laws for the critic-actor neural networks (NNs) to carry out the ADP method. Furthermore, the local neighbor consensus errors and the weight estimation errors for the critic-actor NNs are proved to be uniformly ultimately bounded (UUB). Finally, the practical example is applied to validate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

Consensus control of multiagent systems (MASs) has applications in various domains. As MASs work in networked environments, their security control becomes critically desirable in response to various cyberattacks, such as denial of service (DoS). Efforts have been made in the development of both time- and event-triggered consensus control of MASs. However, there is a lack of precise calculation of control input during the attacking periods. To address this issue, a distributed secure consensus control with event triggering is developed for linear leader-following MASs under DoS attacks. It is designed with a dual-terminal event-triggered mechanism, which schedules information transmission through two triggered functions for each follower: one on the measurement channel (sensor-to-controller) and the other on the control channel (controller-to-actuator). To deal with DoS attacks, the combined states in the triggered functions are replaced by their estimations from an observer. Sufficient conditions are established for the duration and frequency of DoS attacks. To remove continuous monitoring of the measurement errors, a self-triggered secure control scheme is further developed, which combines the system states and other information at past triggered instants. Theoretical analysis shows that the followers in MASs under DoS attacks are able to track the leader and meanwhile the Zeno behavior is excluded. Case studies are conducted to demonstrate the effectiveness of our distributed secure consensus control of MASs. [ABSTRACT FROM AUTHOR]

Within the multiagent systems framework, the relative states between neighbors can be acquired by some on-board sensors, and then the relative state saturations inevitably occur due to the limited sensing capabilities. This paper investigates the consensus problem of nonlinear multiagent systems subject to the relative state saturations. Utilizing the incidence matrix and the edge Laplacian, the consensus problem of nonlinear multiagent systems with the relative state saturations can be cast into the stabilization problem of edge dynamics operating on the constrained set. Three types of protocols, namely continuous, intermittent, and adaptive state feedback protocols are, respectively, proposed for achieving the constrained consensus, and meanwhile yielding consensus values. A consensus analysis is provided by virtue of state saturation theory, switched system theory, adaptive theory, and Lyapunov stability theory. Output feedback protocol is also designed. Finally, the obtained results are applied to connectivity preservation for first-order nonlinear multiagent systems, despite the presence of limited communication range and input constraints. The theoretical results are validated by two simulation examples. [ABSTRACT FROM AUTHOR]

The relative state between neighbors represents the difference of two connected agents’ states, and it possesses specific physical meanings in practice. Under this background, the saturation constraints in the relative state inevitably occur. This article studies the consensus problems under the relative state saturation constraints. Novel adaptive proportional–integral (PI) protocols are designed to solve the constrained consensus problem. Specifically, the adaptive coupling weights and the saturation functions are embedded into the proposed protocols, and the former can render the protocols independent of any global topology graph information, while the latter can confine the relative state to stay in its constrained set. Sufficient conditions are identified under which the constrained consensus can be achieved. Considering that the solution matrix is required to be diagonally dominant, an iterative learning-based heuristic algorithm is proposed to seek the diagonally dominant positive-definite solution matrix. For the special case that the input matrix is row full rank, more stringent saturation functions are constructed, and it not only achieves the constrained consensus but also realizes the nonovershoot and shorter settling time associated with edge states. Besides, this result can be applied to preserve connectivity of the communication network. The theoretical analyses are validated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses an adaptive event-triggered consensus control problem for a class of second-order nonlinear multiagent systems (MASs) in an undirected communication topology. A novel adaptive distributed event-triggered consensus control scheme is presented for the MAS with unknown functions based on the definition of an auxiliary state, and the coefficient of the triggered function can be regulated adaptively with dependence on the auxiliary state error to ensure not only the control performance but also the efficiency of the network interactions. Furthermore, two self-triggered algorithms are developed for two cases, known functions and unknown ones, by the current state and information at the previous event time instant instead of the requirement for continuous monitoring auxiliary state errors. In theory, the stability of the resulting closed-loop system is rigorously investigated, and it is proven that all signals in the closed-loop system are bounded and the Zeno behavior is ruled out. Finally, two simulation examples, both real-time and numerical ones, are provided to verify the theoretical claims. [ABSTRACT FROM AUTHOR]

Cyber security of microgrids attracts increasing attention since the relatively open communication network of the microgrids is vulnerable to hacker attacks. This study proposes a real‐time distributed economic dispatch scheme for the grid‐connected microgrid against the cyberattacks. Firstly, a virtual leader agent is placed at the point of common coupling to measure the real‐time power tracking error for achieving the power supply–demand balance, and then the optimal solution of the economic dispatch model is solved by the consensus algorithm of the multi‐agent system theory. Subsequently, a set of detection algorithms is designed for each generator to determine whether its neighbouring generators suffer from the cyberattacks. The attacked generator is gradually marginalised from the communication network through updating the weight in the communication adjacency matrix based on its reputation value, thereby the impact of the attacked generator on the whole system is reduced greatly. Finally, the numerical simulations are carried out to verify the effectiveness of the proposed cyberattack‐resilient distributed economic dispatch scheme. [ABSTRACT FROM AUTHOR]

This paper investigates leaderless consensus and leader-following consensus of multiagent systems with Lipschitz nonlinearity and input delay. For such systems, the observer-based truncated prediction feedback protocols are designed via dropping the distributed term and remaining the exponential term of the solution of the system equation over the delay period. Using Lyapunov–Krasovskii functional approach, two sufficient criteria are, respectively, established for achieving leaderless and leader-following consensus. The observer and controller gains are then obtained by means of an iterative linear matrix inequality procedure. A numerical simulation verifies the effectiveness of the proposed control design approach. [ABSTRACT FROM AUTHOR]

Within the framework of multiagent systems, relative information can be directly acquired by vehicle-mounted sensors and the relative information constraints inevitably occur due to limited sensing capabilities. This paper investigates observer-based consensus of nonlinear multiagent systems subject to relative state estimate constraints. Each agent’s state is constructed via a state observer, and the relative state estimate is assumed to be confined into a hypercube. In virtue of the edge Laplacian, the consensus problem of nonlinear multiagent systems under this constraint is converted into the stabilization problem of edge dynamics operating on the constrained set. Observer-based intermittent protocol and adaptive protocol are, respectively, designed for achieving consensus. A convergence analysis is provided with the help of state saturation theory, switched system theory and adaptive theory. Finally, the results on consensus with relate state estimate constraints are applied into the consensus problem while preserving the connectedness, and are validated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates finite-horizon optimal consensus control problem for unknown multiagent systems with state delays. It is well known that optimal consensus control is the solutions to the coupled Hamilton–Jacobi–Bellman (HJB) equations. An off-policy reinforcement learning (RL) algorithm is developed to learn the two-stage optimal consensus solutions to the coupled time-varying HJB equations using the measurable state data instead of the knowledge of the state-delayed system dynamics. Subsequently, for each agent, a single critic neural network (NN) is utilized to approximate the time-varying cost function and help to calculate optimal consensus control policy. Based on the method of weighted residuals, adaptive weight update laws for the critic NNs are proposed. Finally, the simulation results are provided to illustrate the effectiveness of the proposed off-policy RL method. [ABSTRACT FROM AUTHOR]

This paper is concerned with data-driven distributed optimal consensus control for unknown multiagent systems (MASs) with input delays. The input-delayed MAS model is first converted into a delay-free form using a model reduction method. By establishing an equivalent relationship on the predesigned performance indices of the two MASs, optimal consensus control of input-delayed MAS can be fully transformed to that of delay-free MAS. Based on the coupled Hamilton–Jacobi equations and Bellman’s optimality principle, optimal consensus control policies are derived for the transformed delay-free MAS. Then a policy iteration algorithm based on distributed asynchronous update mechanism is proposed to learn the coupled Hamilton–Jacobi–Bellman equations online. To perform the proposed data-driven adaptive dynamic programming algorithm, we adopt the measured data-based critic-actor neural networks to approximate the value functions and the control policies, respectively. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of distributed optimal consensus control for a continuous-time heterogeneous linear multiagent system subject to time varying input delays. First, by discretization and model transformation, the continuous-time input-delayed system is converted into a discrete-time delay-free system. Two delicate performance index functions are defined for these two systems. It is shown that the performance index functions are equivalent and the optimal consensus control problem of the input-delayed system can be cast into that of the delay-free system. Second, by virtue of the Hamilton–Jacobi–Bellman (HJB) equations, an optimal control policy for each agent is designed based on the delay-free system and a novel value iteration algorithm is proposed to learn the solutions to the HJB equations online. The proposed adaptive dynamic programming algorithm is implemented on the basis of a critic-action neural network (NN) structure. Third, it is proved that local consensus errors of the two systems and weight estimation errors of the critic-action NNs are uniformly ultimately bounded while the approximated control policies converge to their target values. Finally, two simulation examples are presented to illustrate the effectiveness of the developed method. [ABSTRACT FROM PUBLISHER]

This study is devoted to the consensus protocols design for a set of fractional‐order heterogeneous agents, which is composed of two kinds of agents differed by their dynamics and the fractional‐order α satisfies 0 < α < 2. Distributed state feedback consensus protocols are constructed for the two kinds of agents, respectively. Based on the Kronecker product technique and the fractional‐order stability theory, sufficient conditions are derived to ensure the consensus of heterogeneous multi‐agent systems in terms of linear matrix inequalities (LMIs). These can be solved numerically by LMI toolbox in Matlab. Finally, a simulation example is employed to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]