Passivity‐based state synchronization of homogeneous multiagent systems via static protocol in the presence of input saturation

This paper studies semiglobal and global state synchronization of homogeneous multiagent systems with partial‐state coupling (ie, agents are coupled through part of their states) via a static protocol. We consider 2 classes of agents, ie, G‐passive and G‐passifiable via input feedforward, which are subjected to input saturation. The proposed static protocol is purely decentralized, ie, without an additional channel for the exchange of controller states. For semiglobal synchronization, a static protocol is designed for an a priori given set of network graphs with a directed spanning tree. In other words, the static protocol only needs rough information on the network graph, ie, a lower bound for the real part and an upper bound for the modulus, of the nonzero eigenvalues of the corresponding Laplacian matrix. Whereas for global synchronization, only strongly connected and detailed balanced network graphs are considered. In this case, for G‐passive agents, the static protocol does not need any network information, whereas for G‐passifiable agents via input feedforward, the static protocol only needs an upper bound for the modulus of the eigenvalues of the corresponding Laplacian matrix.     

Squared‐down passivity–based state synchronization of homogeneous continuous‐time multiagent systems via static protocol in the presence of time‐varying topology

This paper studies state synchronization of homogeneous multiagent systems (MAS) via a static protocol with partial‐state coupling in the presence of a time‐varying communication topology, which includes general time‐varying graphs as well as switching graphs. If the agents are squared‐down passive or squared‐down passifiable (via static output feedback or static input feedforward), then a static protocol can be designed for balanced, time‐varying graphs. Moreover, this static protocol works for arbitrary switching directed graphs if the agents are squared‐down minimum phase with relative degree one. The static protocol is designed for each agent such that state synchronization is achieved without requiring exact knowledge about the time‐varying network.     

H2 and H∞ almost output synchronization of heterogeneous continuous‐time multi‐agent systems with passive agents and partial‐state coupling via static protocol

This paper studies H₂ and H_∞ almost output synchronization problems for heterogeneous continuous‐time multiagent systems with passive agents and strongly connected communication graph. For non‐introspective passive agents, a linear static protocol can be designed to achieve almost output synchronization with arbitrarily small H₂ norm. Moreover, we show that the H_∞ almost output synchronization problem via static protocol is not solvable for this class of systems.     

Distributed integral‐type event‐triggered synchronization of multiagent systems

This paper investigates the synchronization problem of generic linear multiagent systems via integral‐type event‐triggered control. Each agent can only utilize the intermittent information of its neighboring agents in the control scheme. Based on the integral‐type event conditions, an event‐triggered control protocol is designed to guarantee the synchronization of multiagent systems, and Zeno behavior is excluded by showing the existence of a positive lower bound on the inter‐event intervals. Then, we propose the integral‐type event‐triggered control algorithms to study the leader‐following synchronization. It is shown that under the control algorithms all the followers track the leader and no Zeno behavior occurs. The effectiveness of the proposed control schemes is demonstrated by simulation examples.     

Bipartite output synchronization of heterogeneous multiagent systems on signed digraphs

This paper studies the bipartite output synchronization problem of general linear heterogeneous multiagent systems on signed digraphs. We first show that, for heterogeneous multiagent systems, the bipartite output synchronization over the structurally balanced signed digraphs and the conventional output synchronization over the associated nonnegative digraphs are equivalent. Then, 3 different control protocols, using full‐state feedback, static output feedback, and dynamic output feedback are designed at each agent to solve the bipartite output synchronization problem based on solutions to the corresponding output regulator equations. Explicit local design procedures are proposed for all 3 control protocols. The compensators employed in these protocols incorporate only one copy of the virtual exosystem's dynamics, regardless of the dimensions of the outputs. This results in lower‐dimensional compensators and controllers and, hence, is more computationally tractable compared to the popular internal model principle‐based control protocols. Numerical simulations over 3 different signed communication digraphs validate the proposed control protocols.     

Adaptive‐impulsive consensus of multiagent systems

This paper studies the leader‐following consensus problem of multiagent nonlinear systems with uncertain parameters and control gain error. On the basis of the theory of impulsive differential equations, the adaptive control technique, and the Lyapunov stability theory, some novel adaptive‐impulsive consensus conditions are given to realize the consensus of a class of multiagent nonlinear systems. Compared with the existing investigations on the impulsive consensus of multiagent systems, the proposed impulsive control protocol with uncertain parameters and control gain error is more rigorous and effective in practical systems. Four numerical simulations are verified to confirm the effectiveness of the proposed methods.     

Input-constrained optimal output synchronization of heterogeneous multiagent systems via observer-based model-free reinforcement learning

This paper presents a new formulation of input-constrained optimal output synchronization problem and proposes an observer-based distributed optimal control protocol for discrete-time heterogeneous multiagent systems with input constraints via model-free reinforcement learning. First, distributed adaptive observers are designed for all agents to estimate the leader's trajectory without requiring its dynamics knowledge. Subsequently, the optimal control input associated with the optimal value function is derived based on the solution to the tracking Hamilton-Jacobi-Bellman equation, which is always difficult to solve analytically. To this end, motivated by reinforcement learning technique, a model-free Q-learning policy iteration algorithm is proposed, and the actor-critic neural network structure is implemented to iteratively find the optimal tracking control input without knowing system dynamics. Moreover, inputs of all agents are constrained in the permitted bounds by inserting a nonquadratic function into the performance function, where input constraints are encoded into the optimization problem. Finally, a numerical simulation example is provided to illustrate the effectiveness of the proposed theoretical results.     

Adaptive neural control for multiagent systems with asymmetric time‐varying state constraints and input saturation

This article investigates the leader‐follower consensus problem of a class of non‐strict‐feedback nonlinear multiagent systems with asymmetric time‐varying state constraints (ATVSC) and input saturation, and an adaptive neural control scheme is developed. By introducing the distributed sliding‐mode estimator, each follower can obtain the estimation of leader's trajectory and track it directly. Then, with the help of time‐varying asymmetric barrier Lyapunov function and radial basis function neural networks, the controller is designed based on backstepping technique. Furthermore, the mean‐value theorem and Nussbaum function are utilized to address the problems of input saturation and unknown control direction. Moreover, the number of adaptive laws is equal to that of the followers, which reduces the computational complexity. It is proved that the leader‐follower consensus tracking control is achieved without violating the ATVSC, and all closed‐loop signals are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the control scheme.     

A resilient consensus strategy of near‐optimal control for state‐saturated multiagent systems with round‐robin protocol

In this paper, the resilient consensus strategy design problem is investigated for the time‐varying state‐saturated multiagent systems (MASs). A round‐robin protocol is adopted to schedule the communication network among the MASs for the purpose of preventing the data from collision. In presence of the state‐saturation and gain perturbation phenomena, it is literally impossible to obtain the accurate value of the associate cost function, which describes the consensus performance. As an alternative, an upper bound is derived for the cost function to quantify the consensus performance. Then, the resilient consensus strategy is designed such that this upper bound can be minimized in an iterative manner. The sufficient condition is also provided to guarantee that the upper bound of the cost function exists as time goes to infinity. Finally, a numerical example is provided to illustrate the validity of the proposed methodology.     

Directed spanning tree–based adaptive protocols for second‐order consensus of multiagent systems

This paper discusses the consensus problem of second‐order multiagent systems with nonlinear dynamics. A directed spanning tree–based adaptive control protocol is developed, which overcomes the drawback that the spectrum of the Laplacian matrix must be known a priori. A scheme for reordering the nodes is proposed. Applying the developed method and the Lyapunov stability theory, some distributed adaptive laws are designed in the directed network. It is found that the consensus can be achieved by randomly choosing a directed spanning tree and using the developed distributed adaptive law. Finally, an example is presented to illustrate the theoretical analysis.     

Model‐free adaptive formation control for unknown multiinput‐multioutput nonlinear heterogeneous discrete‐time multiagent systems with bounded disturbance

Based on the model‐free adaptive control, the distributed formation control problem is investigated for a class of unknown heterogeneous nonlinear discrete‐time multiagent systems with bounded disturbance. Two equivalent data models to the unknown multiagent systems are established through the dynamic linearization technique considering the circumstances with measurable and unmeasurable disturbances. Based on the obtained data models, two distributed controllers are designed with only using the input/output and disturbance data of the neighbor agents system. The tracking error of the closed‐loop system driven by the proposed controllers is shown to be bounded by the contraction mapping principle and inductive methods. An example illustrates the effectiveness of the proposed two distributed controllers.     

Observer‐predictor feedback for consensus of discrete‐time multiagent systems with both state and input delays

This article is concerned with the consensus problem for discrete‐time multiagent systems with both state and input delays. Single observer‐predictor‐based protocols and multiple observer‐predictors feedback protocols are simultaneously established to predict the future state such that the input delay that can be arbitrarily large yet bounded is completely compensated. It is shown that the consensus of the multiagent system can be achieved by the single/multiple observer‐predictors feedback protocol. Moreover, sufficient conditions guaranteeing the consensus of the multiagent system are provided in terms of the stability of some simple observer‐error systems, and the separation principle is discovered. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed approaches.     

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

In this paper, the problem of distributed containment control for pure‐feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high‐order nonaffine pure‐feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed‐loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.     

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

This paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.     

Continuous adaptive observer for state affine sampled‐data systems

In this paper, a hybrid adaptive observer is designed for a class of nonlinear sampled‐data systems with constant unknown parameters. The proposed observer uses a predictor of the output between the sampling times. This predictor is re‐initialized at each sampling time. This observer is very simple to implement and converges exponentially under some sufficient conditions. An explicit relation between the bound of the maximum allowable sampling time (τ_MASP) and the parameters of the observer is also given. Copyright © 2012 John Wiley & Sons, Ltd.     

Leaderless and leader‐following fixed‐time consensus for multiagent systems via impulsive control

This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Controllability of heterogeneous multiagent systems

The existing results on controllability of multiagent systems (MASs) are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous MASs, where the agents are modeled as two types. One type is that the agents have the same high‐order dynamics, and the interconnection topologies of the information flow in different orders are supposed to be different; the other type is that the agents have generic linear dynamics, and the dynamics are supposed to be heterogeneous. For the first type, the necessary and sufficient condition for controllability of heterogeneous‐topology system is derived via combination of Laplacian matrices. For the second type, the contribution also has two parts. The first part supposes that the agents have the same dimensional states and proves that controllability of this kind of MASs is equivalent to the controllability of each node and the whole interconnection topology, while the last parameter of the state feedback vector must not be 0. The second part supposes that the agents may have different dimensional states. For this kind of systems, the concept of β‐controllability is proposed. The necessary and sufficient condition for β‐controllability of heterogeneous‐dynamic systems is also derived and it is also proved that the feedback gain vectors have the effect to improve controllability. Different illustrative examples are provided to demonstrate the effectiveness of the theoretical results in this paper.     

Distributed adaptive integral‐type event‐triggered cooperative output regulation of switched multiagent systems by agent‐dependent switching with dwell time

This article presents a distributed adaptive integral‐type event‐triggered scheme (ETS) and an agent‐dependent switching strategy with dwell time to solve the cooperative output regulation problem for switched multiagent systems. First, by constructing an adaptive law to dynamically update the time‐varying coupling weights for all the communication links, a fully distributed ETS is designed, where only the local information of the topology is adopted. Based on the integral‐type triggering condition, the interevent interval is substantially enlarged and Zeno behavior is explicitly ruled out. Second, each agent permits all the subsystems to be unstabilizable. The switching signal for each agent is different, and any adjacent switches of each agent satisfy the preset dwell time. Under the designed switching strategy, the solvability of the regulation problem is guaranteed. Finally, the effectiveness of the designed ETS and switching strategy is substantiated by an example.     

Decentralized consensus protocol for a class of high‐order multiagent systems

This paper proposes a consensus protocol for a class of high‐order multiagent systems under directed networks. It is supposed that each agent is exposed to an external disturbance additive to its control input. Based on the optimization theory, the consensus protocol gains are designed in order to attenuate the effects of the external disturbances on the performance of the multiagent system. The main problem of existing high‐order consensus protocols in the literature is the dependency of the design on the information of coupling matrices associated with networks topologies. Despite existing high‐order consensus protocols in the literature, the proposed consensus protocol can be designed in a fully decentralized manner based on no global information. The main idea of the design is to propose an control formulation in which the coupling information of the agents is considered as exogenous signals, while the coupling effects of these signals lead to achieving consensus in the multiagent system. Numerical examples verify the effectiveness of the proposed consensus protocol. Copyright © 2016 John Wiley & Sons, Ltd.