Robust cooperative output regulation of heterogeneous uncertain linear multi-agent systems by intermittent communication

In this paper, we study the robust cooperative output regulation problem of heterogeneous linear multi-agent systems with system uncertainties and directed communication topology. A robust distributed event-triggered control scheme is proposed based on the internal model principle. To avoid continuous monitoring of measurement errors for the event-triggering condition, a novel self-triggered control scheme is further proposed. Moreover, by introducing a fixed timer in the triggering mechanisms, Zeno behavior can be excluded for each agent. An example is finally provided to demonstrate the effectiveness of the proposed self-triggered control scheme.     

Iterative learning control for fractional-order multi-agent systems

In this paper, we apply iterative learning control to both linear and nonlinear fractional-order multi-agent systems to solve consensus tacking problem. Both fixed and iteration-varying communicating graphs are addressed in this paper. For linear systems, a PD^α-type update law with initial state learning mechanism is introduced by virtue of the memory property of fractional-order derivative. For nonlinear systems, a D^α-type update law with forgetting factor and initial state learning is designed. Sufficient conditions for both linear and nonlinear systems are established to guarantee all agents achieving the asymptotic output consensus. Simulation examples are provided to verify the proposed schemes.     

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.     

Global adaptive fuzzy consensus control of nonlinear multi-agent systems via distributed event-triggered communication

This paper investigates globally bounded consensus of leader-following multi-agent systems with unknown nonlinear dynamics and external disturbance via adaptive event-triggered fuzzy control. Different from existing works where filtering and backstepping techniques are applied to design controllers and event-triggered conditions, a matrix inequality is established to obtain the feedback gain matrix and event-triggered functions. To save communication resources, a new distributed event-triggered controller with fully discontinuous communication among following agents is designed. Meanwhile, a strictly positive minimum of inter-event time is provided to exclude Zeno behavior. Furthermore, to achieve globally bounded leader-following consensus, an adaptive fuzzy approximator and a parameter estimator are designed to approximate the unknown nonlinear dynamics and parameters, respectively. Finally, the effectiveness of the proposed method is validated via a simulation example.     

Event-triggered leader-following consensus of multi-agent systems under semi-Markov switching topology with partially unknown rates

An event-triggered leader-following consensus problem for multi-agent systems with nonlinear dynamics was investigated in this study. The interaction topologies among the agents that we considered are randomly switched ones, governed by a semi-Markov process with partially unknown rates. By building the state error model between the leader and followers, the consensus problem is first converted into a stability problem. Moreover, an event-triggered transmission scheme based on sampling data was proposed to reduce communication redundancy. The consensus controller and event-triggered parameters can be designed effectively. By constructing a Lyapunov–Krasovskii functional (LKF) with a triple integral, the sufficient conditions required to guarantee the event-triggered consensus can be reached with respect to the linear matrix inequalities (LMIs). Ultimately, the validity of the theoretical results is demonstrated by a numerical example.     

Event-triggered robust distributed nonlinear model predictive control using contraction theory

In this paper, we study the cooperation problem over a group of discrete-time nonlinear dynamically decoupled multi-agent systems (MAS). A distributed model predictive control (DMPC) scheme is proposed in the event-triggered context. Agents cooperate through a coupled cost function subject to input constraints. From the practical perspective, the additive disturbances are taken into account in the controller design. Using the contraction theory in the framework of Riemannian manifolds, a novel constraint is constructed in the DMPC optimization problem to provide the capability of disturbance rejection. Moreover, the event-triggered mechanism is introduced for saving computational and communicational resources. The event-triggering condition is developed by checking the Riemannian distance between the actual and optimal state trajectories. The stability of the closed-loop system and recursive feasibility of the DMPC scheme, thereafter, are rigorously analyzed. In particular, the stability analysis is built upon the contraction theory, which distinguishes this work from the existing results using the conventional Lyapunov theory. It is shown that the recursive feasibility is guaranteed if the additive disturbances are bounded and the event-triggering condition is properly designed. The numerical simulation results demonstrate the effectiveness of the proposed algorithm.     

Consensus of multi-Agent systems with one-Sided lipschitz nonlinearity via nonidentical double event-Triggered control subject to deception attacks

As for the multi-agent systems (MASs) with time-varying switching subject to deception attacks, the leader-following consensus problem is studied in this article. The one-sided Lipschitz (OSL) condition is utilized for the nonlinear functions, which makes the results more general and relaxed than those obtained by Lipschitz condition. The nonidentical double event-triggering mechanisms (ETMs) are adopted for only a fraction of agents, and each agent transmits the data according to its own necessity. Semi-Markov process modeling with time-varying switching probability is adopted for switching topology and deception attacks occurring in transmission channel are considered. By using the cumulative distribution function (CDF) and the linear matrix inequality (LMI) technology, sufficient conditions for MASs to achieve consensus in mean square are obtained. An effective algorithm is presented to obtain the event-based control gains. The merits of the proposed control scheme are demonstrated via a simulation example.     

Finite-time consensus for the second-order leader-following nonlinear multi-agent system with event-triggered communication

This study discusses the finite-time consensus for the second-order leader-following nonlinear multi-agent system with event-triggered communication. An event-triggered control protocol is established to achieve finite-time consensus, which can effectively avoid the Zeno behavior. Due to the unevenness of an event-triggered controller and the occurrence of the event-triggered condition, it is more challenging to analyze the event-triggered finite-time consensus. Based on the knowledge of graph theory, all agents can achieve finite-time consensus via the proposed event-triggered control protocol. Different from homogeneity, a Lyapunov function is constructed to obtain the settling time. Finally, a simulation example illustrates the validity of the main results.     

Event-triggered tracking control for couple-group multi-agent systems

This paper mainly investigates the event-triggered tracking control for couple-group multi-agent systems in a disturbance environment, where the topology of the agents is switching. Consensus protocol is designed for the case that some agents reach a consistent value, while the other agents reach another consistent value. Then, event-triggered control laws are designed to reduce the frequency of individual actuation updating for discrete-time agent dynamics. Moreover, by applying the Lyapunov function method, a sufficient condition of couple-group consensus is established in terms of a matrix inequality when the communication topology is switching. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.     

Leaderless and leader-following consensus of linear multi-agent systems with distributed event-triggered estimators

This paper considers the event-triggered leaderless and leader-following consensus problems for linear multi-agent systems. By introducing event-triggered estimators, two novel control schemes are proposed. Different from the existing event-triggered controllers, which rely on the Fiedler eigenvalue of Laplacian matrix, the developed controllers only use the information from neighboring agents. Meanwhile, the adaptive trigger parameters are designed in the event-triggered mechanisms to improve the self-regulation ability of the event-triggered estimators. In addition, the leaderless consensus and the leader-following consensus can be achieved under the corresponding control protocols. Finally, two simulation examples are given to illustrate the validity of the proposed control protocols.     

Event-triggered control of interconnected nonlinear systems subjected to cyber-attacks and time-varying coupling

This paper addresses the problem of efficient control of nonlinear distributed networked control systems in the presence of stochastic deception attacks and time-varying coupling strength. A strategy combining model-based and event-triggered control to reduce the number of transmissions over a network thereby, saving network resources is proposed. In this strategy, a plant model at the controller end is used to estimate the state of each subsystem. Further, the control law between the two adjacent triggering instants changes in accordance with dynamics of the plant model. The nonlinearities present in each subsystem are approximated via neural network. The neural network weights and feedback signal are updated only when the event-triggering condition at the sensor end is violated. Also, a lower bound on the inter-event time is computed to avoid the occurrence of Zeno phenomena. Finally, the efficacy of the proposed methodology are verified through simulation examples.     

Multi-lagged-input iterative dynamic linearization based data-driven adaptive iterative learning control

This article presents a multi-lagged-input based data-driven adaptive iterative learning control (M-DDAILC) method for nonlinear multiple-input-multiple-output (MIMO) systems by virtue of multi-lagged-input iterative dynamic linearization (IDL). The original nonlinear and non-affine MIMO system is equivalently transformed into a linear input-output incremental counterpart without loss of dynamics. The proposed learning law utilizes the desired trajectory to cancel the influence from iteration-by-iteration variations, as well as additional multi-lagged inputs to improve control performance. The developed iterative estimation law is more effective and also makes estimation of the unknown parameters easier because the dynamics for each parameter to represent are decreased by dividing the system into multiple components in the multi-lagged-input IDL formulation. Moreover, the proposed M-DDAILC does not need an explicit and accurate model. It is proved to be iteratively convergent with rigorous analysis. Both a numerical example and a practical application to a permanent magnet linear motor are provided to verify the validity and applicability of the proposed method.     

Event-triggered control for multi-agent systems with randomly occurring nonlinear dynamics and time-varying delay

The paper investigates the consensus problem for multi-agent systems with randomly occurring nonlinear dynamics and time-varying delay. A novel event-triggered scheme has been proposed, which can lead to a significant reduction in information communication in a network. By utilizing stochastic analysis and properties of the Kronecker product, consensus criteria are derived in the form of linear matrix inequalities, which can be readily solved using the standard numerical software. Finally, an illustrative example is used to show the effectiveness of the event-triggered scheme.     

Event-triggered control for active vehicle suspension systems with network-induced delays

This paper presents a novel event-triggered H_∞ static output-feedback control for active vehicle suspension systems with network-induced delays. The proposed control schema introduces an event-triggering mechanism in the suspension system such that the communication resources can be significantly saved. By applying some improved slack inequalities and an augmented Lyapunov–Krasovskii functional (LKF), a new design condition expressed in the form of linear matrix inequalities (LMIs) is developed to derive the desired event-triggered controller. The obtained algorithm is then employed to solve the static output-feedback control gain. Compared with the traditional sampled-data H_∞ control scheme, the proposed controller is able to provide an enhanced disturbance attenuation level while saving the control cost. Finally, comparative simulation results are provided to show the performance of the proposed event-triggered controller.     

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.     

Event-triggered fully distributed asymptotic consensus for leaderless multiple Euler-Lagrange systems

In this paper, the fully distributed consensus for a class of multiple Euler-Lagrange systems is investigated, where the protocol is designed under the event-triggered control framework and the dynamics of Euler-Lagrange systems are heterogeneous. Since only local information interactions at triggered instants can be used and the Euler-Lagrange systems are of relatively complex dynamics, it is challenging to achieve asymptotic consensus without using any global information (such as the Laplacian matrix information). By skillfully integrating the adaptive control, distributed control and event-triggered control techniques, a novel protocol is proposed for the investigated multiple Euler-Lagrange systems. It is proven that the asymptotic consensus can be achieved by the developed protocol. By a numerical example, the effectiveness of the developed protocol is illustrated.     

Observer-based boundary control of semi-linear parabolic PDEs with non-collocated distributed event-triggered observation

This paper deals with the problem of boundary control for a class of semi-linear parabolic partial differential equations (PDEs) with non-collocated distributed event-triggered observation. A semi-linear Luenberger PDE observer with an output error based event-triggering condition is constructed by using the event-triggered observation to exponentially track the PDE state. By the estimated state, a feedback controller is proposed. It has been shown by the Lyapunov technique, and a variant of Poincaré–Wirtinger inequality that the resulting closed-loop coupled PDEs is exponentially stable if a sufficient condition presented in terms of standard linear matrix inequality (LMI) is satisfied. Moreover, a rigorous proof is provided for existence of a minimal dwell-time between two triggering times. Finally, numerical simulation results are given to show the effectiveness of the proposed design method.     

Dual ML-ADHDP method for heterogeneous discrete-time nonlinear multi-agent systems with unknown dynamics and time delay

This paper develops a new dual ML-ADHDP method to solve the optimal consensus problem (OCP) of a class of heterogeneous discrete-time nonlinear multi-agent systems (MASs) with unknown dynamics and time delay. A hierarchical and distributed control strategy is used to transform the original problem into nonlinear model reference adaptive control (MRAC) problems and an OCP of virtual linear MASs. For the nonlinear MRAC problems, a new multi-layer action-dependent heuristic dynamic programming (ML-ADHDP) method is developed to overcome the unknown dynamics and neural network estimation errors, which has higher control accuracy. In order to solve the OCP of virtual linear MASs and improve the convergence speed, a new multi-layer performance index is proposed. Then the ML-ADHDP method is used to solve the coupled Hamiltonian–Jacobi–Bellman equation and obtain the optimal virtual control. Theoretical analysis proves that the original MASs can achieve Nash equilibrium, and simulation results show that the developed dual ML-ADHDP method ensures better convergence speed and higher control accuracy of original MASs.     

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.