Consensus of Hybrid Multi-Agent Systems

Finite-time hybrid impulsive formation tracking control of multi-agent systems via aperiodic intermittent communication

This article studies the problem of formation tracking control in multi-agent systems, achieved in finite time, under challenging conditions such as strong nonlinearity, aperiodic intermittent communication, and time-delay effects, all within a hybrid impulsive framework. The impulses are categorized as either stabilizing control impulses or disruptive impulses. Furthermore, by integrating Lyapunov-based stability theory, graph theory, and the linear matrix inequality (LMI) method, new stability criteria are established. These criteria ensure finite-time intermittent formation tracking while considering weak Lyapunov inequality conditions, intermittent communication rates, and time-varying gain strengths. Additionally, the approach manages an indefinite number of impulsive moments and adjusts the control domain's width based on the average impulsive interval and state-dependent control width. Numerical simulations are provided to validate the applicability and effectiveness of the proposed formation tracking control protocols.

Heterogeneous decision-making dynamics of threshold-switching agents on complex networks

In the classical two-player decision-making scenario, individuals may have different tendencies to take a certain action, given that there exists a sufficient number of neighbors adopting a particular option. This is ubiquitous in many real-life contexts including traffic congestion, crowd evacuation, and minimal vertex cover problem. Under best-response dynamics, we investigate the decision-making behaviors of heterogeneous agents on complex networks. Results of the networked games are twofold: for networks of uniform degree distribution (e.g., the lattice) and fraction of the strategy is of a linear function of the threshold setting. Moreover, the equilibrium analysis is provided and the relationship between the equilibrium dynamics and the change of the threshold value is given quantitatively. Next, if the games are played on networks with non-uniform degree distribution (e.g., random regular and scale-free networks), influence of the threshold-switching will be weakened. Robust experiments indicate that it is not the value of the average degree, but the degree distribution that influences how the strategy evolves affected by the threshold settings. Our result shows that the decision-making behaviors can be effectively manipulated by tuning the parameters in the utility function (i.e., thresholds) of some agents for more regular network structures.

Group consensus of multi-agent systems with hybrid characteristics and directed topological networks

In this paper, the group consensus problem is investigated for multi-agent systems (MASs) with hybrid characteristics and directed topological networks. Firstly, the dynamical model of hybrid multi-agent system (MAS) is constructed, which includes discrete time agents and continuous time agents. A class of distributed control protocols are put forward for hybrid MASs. Then, under fixed and directed topological networks, sufficient and necessary conditions for the realization of group consensus are provided on basis of matrix theory and graph theory. Finally, simulations examples are given to further verify the validity of our theoretical results.

Parametric Dynamic Distributed Containment Control of Continuous-Time Linear Multi-Agent Systems with Specified Convergence Speed

This paper focuses on the distributed containment control of continuous-time linear multi-agent systems (MASs) with multiple leaders over fixed topology. A parametric dynamic compensated distributed control protocol is proposed in which both the information from the observer in the virtual layer and actual adjacent agents are employed. The necessary and sufficient conditions of the distributed containment control are derived based on the standard linear quadratic regulator (LQR). On this basis, the dominant poles are configured by using the modified linear quadratic regulator (MLQR) optimal control and Geršgorin's circle criterion, hence the containment control with specified convergence speed of the MAS is achieved. Another main advantage of the proposed design is, in the case of virtual layer failure, by adjusting parameters the dynamic control protocol reduces to static, and the convergence speed can still be specified through the dominant pole assignment method combined with inverse optimal control. Finally, typical numerical examples are presented to demonstrate the effectiveness of theoretical results.

Consensus Tracking for High-Order Uncertain Nonlinear MASs via Adaptive Backstepping Approach

In this article, we focus on the problems of consensus control for nonlinear uncertain multiagent systems (MASs) with both unknown state delays and unknown external disturbances. First, a nonlinear function approximator is proposed for the system uncertainties deriving from unknown nonlinearity for each agent according to adaptive radial basis function neural networks (RBFNNs). By taking advantage of the Lyapunov-Krasovskii functionals (LKFs) approach, we develop a compensation control strategy to eliminate the effects of state delays. Considering the combination of adaptive RBFNNs, LKFs, and backstepping techniques, an adaptive output-feedback approach is raised to construct consensus tracking control protocols and adaptive laws. Then, the proposed consensus tracking scheme can steer the nonlinear MAS synchronizing to the predefined reference signal on account of the Lyapunov stability theory and inequality properties. Finally, simulation results are carried out to verify the validity of the presented theoretical approach.

SMIX(λ): Enhancing Centralized Value Functions for Cooperative Multiagent Reinforcement Learning

Learning a stable and generalizable centralized value function (CVF) is a crucial but challenging task in multiagent reinforcement learning (MARL), as it has to deal with the issue that the joint action space increases exponentially with the number of agents in such scenarios. This article proposes an approach, named SMIX( λ ), that uses an OFF-policy training to achieve this by avoiding the greedy assumption commonly made in CVF learning. As importance sampling for such OFF-policy training is both computationally costly and numerically unstable, we proposed to use the λ -return as a proxy to compute the temporal difference (TD) error. With this new loss function objective, we adopt a modified QMIX network structure as the base to train our model. By further connecting it with the Q(λ) approach from a unified expectation correction viewpoint, we show that the proposed SMIX( λ ) is equivalent to Q(λ) and hence shares its convergence properties, while without being suffered from the aforementioned curse of dimensionality problem inherent in MARL. Experiments on the StarCraft Multiagent Challenge (SMAC) benchmark demonstrate that our approach not only outperforms several state-of-the-art MARL methods by a large margin but also can be used as a general tool to improve the overall performance of other centralized training with decentralized execution (CTDE)-type algorithms by enhancing their CVFs.

Consensus of Matrix-Weighted Hybrid Multiagent Systems

As we all know, heterogeneity is a very important feature of multiagent systems (MASs). In this article, we examine the consensus control problems of matrix-weighted hybrid MASs, which contain discrete-time and continuous-time dynamic agents. Under fixed and switched undirected networks, three consensus algorithms are proposed for matrix-weighted hybrid MASs. In the three consensus algorithms, the sampled data control method is utilized in the continuous-time subsystem to analyze the convergence of different dynamic agents in the matrix-weighted interaction mode. For the symmetric matrix-weighted fixed and switched multiagent networks, when the sampling period meets certain conditions, the consensus criteria are established via the matrix theory, Lyapunov stability theory, and analysis theory. Moreover, asymmetric matrix-weighted fixed multiagent networks which can be applied to some scenarios with scaled and rotated updates constraints are considered, and consensus criteria are also obtained when the sampling period meets certain conditions. Finally, a few simulation examples are supplied to validate the correctness of the obtained theoretical results.

Synchronous and asynchronous resilient impulsive control for group consensus of second-order multi-agent systems with communication delays

This paper studies the resilient group consensus of continuous-time second-order multi-agent systems (MASs) with malicious agents. Adopting the idea that each normal agent ignores the most extreme values from neighbors, synchronous resilient impulsive algorithm based on sampled data is proposed for normal agents with bounded communication delays to achieve group consensus. Meanwhile, asynchronous resilient impulsive algorithm is also proposed for MASs where each agent has its own time clock. Sufficient topological conditions are obtained for solving resilient group consensus under synchronous and asynchronous settings, respectively. Numerical examples are provided to illustrate the effectiveness of the theoretical results.

Globally fuzzy consensus of hybrid-order stochastic nonlinear multi-agent systems

This paper studies the globally fuzzy consensus of stochastic nonlinear multi-agent systems (MAS) with hybrid-order dynamics. The followers are modeled as hybrid first- and second-order systems. The leader is presented as second-order system and can transmit his own states to the first- and second-order followers. In view of the local characteristics of communication among agents, the followers can be decomposed into two categories: one is the set of followers who can communicate with the leader, and the other is the set of followers who cannot communicate with the leader. Using the design method of fuzzy feed-forward compensator and Lyapunov stability theory, a new hybrid fuzzy consensus controller is designed for the two kinds of follower sets. Compared with most stochastic MAS, the proposed algorithm not only solves the consensus of hybrid-order stochastic MAS based on fuzzy approximator, but also obtains the results of globally uniform ultimate bounded (GUUD). In the end, the simulation results further verify the validity of the proposed algorithm.

Coordinated control of quasilinear multiagent systems via output feedback predictive control

This study considers the coordinated control for quasilinear multiagent systems (QMASs). An output feedback predictive control (OFPC) strategy is given to implement both coordination and simultaneous stability and output consensus (SSOC). In the OFPC strategy, a cost function aiming at coordination relationship is minimized by predictive control thus coordination among QMASs is implemented. Further discussion derives a criterion to maintain the closed-loop QMASs realize the SSOC. Finally, two examples are proposed to richly illustrate the availability of the OPFC strategy.

Consensusability and Global Optimality of Discrete-Time Linear Multiagent Systems

The consensusability and global optimality problems are solved for the discrete-time linear multiagent system (MAS) with marginally stable and strictly unstable dynamics. A unified framework is proposed by capturing the maximal disc-guaranteed gain margin (GGM) of the discrete-time linear quadratic regulator (LQR). Sufficient and necessary conditions on consensusability are established. Two bounds of the consensus region are derived only in terms of the unstable eigenvalues of the agent' dynamics. For the single-input MAS, by proving that the radius of the consensus region exactly equals the reciprocal of the Mahler measure of the agent' dynamics, we incidentally reveal the relation between the maximal GGM and the intrinsic entropy rate of the system dynamics for single-input discrete-time linear systems. By employing the inverse optimal control approach, it is proved that the globally optimal consensus is achieved, if and only if the associated Laplacian matrix is a simple matrix and all its nonzero eigenvalues can be radially projected into a specific subset of the consensus region. Moreover, the limitation on the eigenvalues vanishes for the marginally stable MAS. As an application of the global optimality, the minimum-energy-distributed consensus control problem is solved for the marginally stable MAS. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.

Quasi-Consensus of Disturbed Nonlinear Multiagent Systems with Event-Triggered Impulsive Control

Considering the external disturbances, in this paper, the quasi-consensus of multiagent systems is studied via event-triggered impulsive control. By designing a novel event-triggered mechanism (ETM), sufficient conditions to realize leader-following quasi-consensus are derived with event-triggered impulsive control. Additionally, Zeno behavior is also excluded. It is shown that the event-triggered frequency is closely related to the parameters selected in the designed ETM, and less conservative results can be obtained compared with the existing results. Finally, a simulation example is given to demonstrate the effectiveness of our proposed results.

Asynchronous Tracking Control of Leader-Follower Multiagent Systems With Input Uncertainties Over Switching Signed Digraphs

Signed digraphs with both positive and negative weighted edges are widely applied to explain cooperative and competitive interactions arising from various social, biological, and physical systems. This article formulates and solves the asynchronous tracking control problem of multiagent systems with input uncertainties on switching signed digraphs. In the interaction setting, we assume that the leader moves at a time-varying acceleration that cannot be measured by the followers accurately, and further suppose that each agent receives its neighbors' states information at certain instants determined by its own clock, which is not necessary to be synchronized with those of other agents. Using dynamically changing spanning subdigraphs of signed digraphs to describe graphically asynchronous interactions, the asynchronous tracking problem is equivalently transformed into a convergence problem of products of general substochastic matrices (PGSSM), in which the matrix elements are not necessarily non-negative and the row sums are less than or equal to 1. With the help of the matrix analysis technique and the composition of binary relations, we propose a new and original method to deal with the convergence problem of PGSSM, and further establish a spanning tree condition for asynchronous tracking control. Finally, the validity of the theoretical findings is verified through several numerical examples.

Nonsmooth Continuous-Time Distributed Algorithms for Seeking Generalized Nash Equilibria of Noncooperative Games via Digraphs

In this article, the problem of distributed generalized Nash equilibrium (GNE) seeking in noncooperative games is investigated via multiagent networks, where each player aims to minimize his or her own cost function with a nonsmooth term. Each player's cost function and feasible action set in the noncooperative game are both determined by actions of others who may not be neighbors, as well as his/her own action. Particularly, feasible action sets are constrained by private convex inequalities and shared linear equations. Each player can only have access to his or her own cost function, private constraint, and a local block of shared constraints, and can only communicate with his or her neighbours via a digraph. To address this problem, a novel continuous-time distributed primal-dual algorithm involving Clarke's generalized gradient is proposed based on consensus algorithms and the primal-dual algorithm. Under mild assumptions on cost functions and graph, we prove that players' actions asymptotically converge to a GNE. Finally, a simulation is presented to demonstrate the effectiveness of our theoretical results.

Consensus of second-order heterogeneous multi-agent systems with and without input saturation

This paper seeks to investigate the consensus issue of heterogeneous multi-agent system formed by second-order linear and nonlinear agents. An input saturated algorithm and an input unsaturated algorithm are proposed respectively for the heterogeneous system. Through applications of graph theory, Lyapunov technique, Lasalle's invariance principle as well as other mathematical methods, it turns out that every agent of the heterogeneous system will be guaranteed to achieve consensus if some conditions are satisfied. Finally, some detailed simulation examples are utilized to verify our conclusion.

Adaptive Neural Network Stochastic-Filter-Based Controller for Attitude Tracking With Disturbance Rejection

This article proposes a real-time neural network (NN) stochastic filter-based controller on the Lie group of the special orthogonal group [Formula: see text] as a novel approach to the attitude tracking problem. The introduced solution consists of two parts: a filter and a controller. First, an adaptive NN-based stochastic filter is proposed, which estimates attitude components and dynamics using measurements supplied by onboard sensors directly. The filter design accounts for measurement uncertainties inherent to the attitude dynamics, namely, unknown bias and noise corrupting angular velocity measurements. The closed-loop signals of the proposed NN-based stochastic filter have been shown to be semiglobally uniformly ultimately bounded (SGUUB). Second, a novel control law on [Formula: see text] coupled with the proposed estimator is presented. The control law addresses unknown disturbances. In addition, the closed-loop signals of the proposed filter-based controller have been shown to be SGUUB. The proposed approach offers robust tracking performance by supplying the required control signal given data extracted from low-cost inertial measurement units. While the filter-based controller is presented in continuous form, the discrete implementation is also presented. In addition, the unit-quaternion form of the proposed approach is given. The effectiveness and robustness of the proposed filter-based controller are demonstrated using its discrete form and considering low sampling rate, high initialization error, high level of measurement uncertainties, and unknown disturbances.

Robust Cooperative Optimal Sliding-Mode Control for High-Order Nonlinear Systems: Directed Topologies

This article is concerned with the robust cooperative optimal control of nonlinear multiagent systems (MASs) with external disturbances and modeling uncertainties. Using the super-twisting algorithm, a continuous sliding-mode control protocol is presented for high-order nonlinear MASs with multiple inputs. The sliding-mode dynamics is modeled by the Takagi-Sugeno fuzzy approach, and the nominal control protocol that guarantees the robust optimization of the cost function is designed. Directed topologies are allowed using the presented protocol, and many assumptions about topologies are removed. Finally, three numerical examples are reported to demonstrate the effectiveness and improved performance of the presented protocol.

Distributed Observer-Based Leader-Follower Consensus of Multiple Euler-Lagrange Systems

This article investigates the leader-follower consensus problem of multiple Euler-Lagrange (EL) systems, where each agent suffers uncertain external disturbances, and the communication links among agents experience faults. Besides, we consider a more general case that only a portion of followers can measure partial components of leader's output and access the dynamic information of leader. The main idea of solving the consensus problem in this article is proceeded in two steps. First, we design an adaptive distributed observer to estimate the full state information of leader in real time with resilience to communication link faults. Second, based on the proposed distributed observer, we propose a proportional-integral (PI) control protocol for each agent to track the trajectory of leader, which is model-independent and robust to uncertain external disturbances. Distinct from the existing leader-follower consensus protocols of multiple EL systems, the proposed distributed observer-based PI consensus protocol in this article is model-independent, which is irrelevant to the structures or features of EL system model. Finally, we present a simulation example to show the resilience of the above adaptive distributed observer and the robustness of the distributed observer-based consensus protocol.

Consensus of Continuous-Time Linear Multiagent Systems With Discrete Measurements

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results.

Resilient Consensus for Multi-Agent Systems in the Presence of Sybil Attacks

This paper investigates the problem of resilient consensus control for discrete-time linear multi-agent systems under Sybil attacks. We consider a node to be a Sybil node if it can generate a large number of false identities in the graph as a way of gaining disproportionate influence on the consensus performance of the network. Such attacks can easily invalidate existing resilient consensus algorithms that assume an upper bound on the number of malicious nodes in the network. To this end, we first built a new attack model based on the characteristics of the Sybil nodes. In addition, a quantized-data-based transmission scheme was developed for identifying and resisting Sybil nodes in the network. Then, an attack-resilient consensus algorithm was developed, where each normal node sends the quantitative data information with a specific label, which is generated by truncated normal distribution sampling to their neighbors. We give sufficient graphical conditions for attack models considering limited energy to ensure the consensus of linear multi-agent systems. Finally, numerical simulation examples are provided to validate the effectiveness of the proposed methods.

Iterative Learning Control for Discrete-Time Systems With Full Learnability

This article considers iterative learning control (ILC) for a class of discrete-time systems with full learnability and unknown system dynamics. First, we give a framework to analyze the learnability of the control system and build the relationship between the learnability of the control system and the input-output coupling matrix (IOCM). The control system has full learnability if and only if the IOCM is full-row rank and the control system has no learnability almost everywhere if and only if the rank of the IOCM is less than the dimension of system output. Second, by using the repetitiveness of the control system, some data-based learning schemes are developed. It is shown that we can obtain all the needed information on system dynamics through the developed learning schemes if the control system is controllable. Third, by the dynamic characteristics of system outputs of the ILC system along the iteration direction, we show how to use the available information of system dynamics to design the iterative learning gain matrix and the current state feedback gain matrix. And we strictly prove that the iterative learning scheme with the current state feedback mechanism can guarantee the monotone convergence of the ILC process if the IOCM is full-row rank. Finally, a numerical example is provided to validate the effectiveness of the proposed iterative learning scheme with the current state feedback mechanism.

H∞ Scaled Consensus for MASs With Mixed Time Delays and Disturbances via Observer-Based Output Feedback

In this article, the H_∞ scaled consensus control problem for multiagent systems in the presence of external disturbances and mixed time delays in both input and Lipschitz nonlinearity is investigated. First, a state observer is introduced for each agent based on the output information of the agent. Then, a scaled consensus protocol is proposed via a truncated predictor output-feedback method, which can deal with the input delay. The integral terms with the mixed time delays that are contained in the transformed systems are analyzed by using the Lyapunov-Krasovskii functionals method, and sufficient conditions are obtained to achieve scaled consensus with guaranteed H_∞ performance. An iterative procedure is utilized to calculate the linear matrix inequality. By this, the feedback gain and observer gain are then designed. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.

Fractional-Order Adaptive Fault-Tolerant Synchronization Tracking Control of Networked Fixed-Wing UAVs Against Actuator-Sensor Faults via Intelligent Learning Mechanism

This article presents an enhanced fault-tolerant synchronization tracking control scheme using fractional-order (FO) calculus and intelligent learning architecture for networked fixed-wing unmanned aerial vehicles (UAVs) against actuator and sensor faults. To increase the flight safety of networked UAVs, a recurrent wavelet fuzzy neural network (RWFNN) learning system with feedback loops is first designed to compensate for the unknown terms induced by the inherent nonlinearities, unexpected actuator, and sensor faults. Then, FO sliding-mode control (FOSMC), involving the adjustable FO operators and the robustness of SMC, are dexterously proposed to further enhance flight safety and reduce synchronization tracking errors. Moreover, the dynamic parameters of the RWFNN learning system embedded in the networked fixed-wing UAVs are updated based on adaptive laws. Furthermore, the Lyapunov analysis ensures that all fixed-wing UAVs can synchronously track their references with bounded tracking errors. Finally, comparative simulations and hardware-in-the-loop experiments are conducted to demonstrate the validity of the proposed control scheme.

Distributed Algorithms Involving Fixed Step Size for Mixed Equilibrium Problems With Multiple Set Constraints

In this brief, the problem of distributively solving a mixed equilibrium problem (EP) with multiple sets is investigated. A network of agents is employed to cooperatively find a point in the intersection of multiple convex sets ensuring that the sum of multiple bifunctions with a free variable is nonnegative. Each agent can only access information associated with its own bifunction and a local convex set. To solve this problem, a distributed algorithm involving a fixed step size is proposed by combining the mirror descent algorithm, the primal-dual algorithm, and the consensus algorithm. Under mild conditions on bifunctions and the graph, we prove that all agents' states asymptotically converge to a solution of the mixed EP. A numerical simulation example is provided for demonstrating the effectiveness of theoretical results.

On Distributed Nash Equilibrium Computation: Hybrid Games and a Novel Consensus-Tracking Perspective

With the incentive to solve Nash equilibrium computation problems for networked games, this article tries to find answers for the following two problems: 1) how to accommodate hybrid games, which contain both continuous-time players and discrete-time players? and 2) are there any other potential perspectives for solving continuous-time networked games except for the consensus-based gradient-like algorithm established in our previous works? With these two problems in mind, the study of this article leads to the following results: 1) a hybrid gradient search algorithm and a consensus-based hybrid gradient-like algorithm are proposed for hybrid games with their convergence results analytically investigated. In the proposed hybrid strategies, continuous-time players adopt continuous-time algorithms for action updating, while discrete-time players update their actions at each sampling time instant and 2) based on the idea of consensus tracking, the Nash equilibrium learning problem for continuous-time games is reformulated and two new computation strategies are subsequently established. Finally, the proposed strategies are numerically validated.

Consensus of Nonlinear Multiagent Systems With Grouping Via State-Constraint Impulsive Protocols

In this article, the consensus problem of nonlinear multiagent systems with grouping via state-constraint impulsive protocols is investigated. Two types of cases with and without leader agent are studied by using two kinds of protocols. A judgement strategy is designed to decide to group in the nonlinear multiagent systems, and two kinds of state-constraint impulsive control protocols, which include partial state constraint and full state constraint, are proposed to make this system cut down the cost of communication and reduce irreversible damage to equipment. Then, based on the algebraic graph theory, the Lyapunov stability theory, and the matrix theory, some sufficient conditions are established to deal with the consensus problem in the nonlinear multiagent systems. The presented results can be used to solve the consensus problem in the nonlinear multiagent systems with grouping. Finally, some important simulations are presented to illustrate the feasibility of the theoretical results.

Neural-Network-Based Fully Distributed Adaptive Consensus for a Class of Uncertain Multiagent Systems

In this article, we revisit the problem of distributed neuroadaptive consensus for uncertain multiagent systems (MASs) in the presence of unmodeled nonlinearities as well as unknown disturbances. Robust consensus controllers comprising a linear feedback term, a discontinuous feedback term, and a neural network approximation term are constructed, where in each term, the weight part is endowed with some dynamical changing law. The asymptotic convergence of the consensus errors is theoretically proved based on the graph theory, nonsmooth analysis, and Barbalat's lemma. Both leaderless consensus and leader-follower tracking problems are considered before the results are further extended to containment problem in the presence of multileaders. A dramatic feature of the proposed method, in comparison with related works, is the fully distributed fashion of the information, requiring neither the underlying Laplacian eigenvalues nor the input upper bounds of the leaders (if exist). Several numerical examples are presented to testify the theoretical results.

Adaptive NN Distributed Control for Time-Varying Networks of Nonlinear Agents With Antagonistic Interactions

This article proposes an adaptive neural network (NN) distributed control algorithm for a group of high-order nonlinear agents with nonidentical unknown control directions (UCDs) under signed time-varying topologies. An important lemma on the convergence property is first established for agents with antagonistic time-varying interactions, and then by using Nussbaum-type functions, a new class of NN distributed control algorithms is proposed. If the signed time-varying topologies are cut-balanced and uniformly in time structurally balanced, then convergence is achieved for a group of nonlinear agents. Moreover, the proposed algorithms are adopted to achieve the bipartite consensus of high-order nonlinear agents with nonidentical UCDs under signed graphs, which are uniformly quasi-strongly δ -connected. Finally, simulation examples are given to illustrate the effectiveness of the NN distributed control algorithms.

Distributed Optimization for Two Types of Heterogeneous Multiagent Systems

This article studies distributed optimization algorithms for heterogeneous multiagent systems under an undirected and connected communication graph. Two types of heterogeneities are discussed. First, we consider a class of multiagent systems composed of both continuous-time dynamic agents and discrete-time dynamic agents. The agents coordinate with each other to minimize a global objective function that is the sum of their local convex objective functions. A distributed subgradient method is proposed for each agent in the network. It is proved that driven by the proposed updating law, the agents' position states converge to an optimal solution of the optimization problem, provided that the subgradients of the objective functions are bounded, the step size is not summable but square summable, and the sampling period is bounded by some constant. Second, we consider a class of multiagent systems composed of both first-order dynamic agents and second-order dynamic agents. It is proved that the agents' position states converge to the unique optimal solution if the objective functions are strongly convex, continuously differentiable, and the gradients are globally Lipschitz. Numerical examples are given to verify the conclusions.

Adaptive Neural Control for a Class of Nonlinear Multiagent Systems

This article studies the adaptive neural controller design for a class of uncertain multiagent systems described by ordinary differential equations (ODEs) and beams. Three kinds of agent models are considered in this study, i.e., beams, nonlinear ODEs, and coupled ODE and beams. Both beams and ODEs contain completely unknown nonlinearities. Moreover, the control signals are assumed to suffer from a class of generalized backlash nonlinearities. First, neural networks (NNs) are adopted to approximate the completely unknown nonlinearities. New barrier Lyapunov functions are constructed to guarantee the compact set conditions of the NNs. Second, new adaptive neural proportional integral (PI)-type controllers are proposed for the networked ODEs and beams. The parameters of the PI controllers are adaptively tuned by NNs, which can make the system output remain in a prescribed time-varying constraint. Two illustrative examples are presented to demonstrate the advantages of the obtained results.

The Complexity in Complete Graphic Characterizations of Multiagent Controllability

Establishing the graph-based criterion for the selection of any location and any number of leaders is the main difficulty in the complete graphic characterization of multiagent controllability. This greatly increases the complexity of the study, compared with the results derived for only one or several classes of leaders. Through a detailed analysis of graphs of six nodes, this article presents a systematic design and identification process for the complete graphic characterization by taking advantage of controllability destructive nodes. The topologies obtained by the proposed method allow directly determining controllability at the network topology level. The results are not only applicable to any leader's selection but also reveal the difficulty and complexity in the study of complete controllability graphic characterizations. Moreover, by comparing graphs composed of five and six nodes, the results reveal the graph-theory-based controllability complexity caused by adding only one node. Finally, results are derived to show how to design topology structures to ensure the controllability under any selection of leaders.

Consensus of Second-Order Hybrid Multiagent Systems by Event-Triggered Strategy

In this article, an event-triggered method is proposed to solve the consensus of the second-order hybrid multiagent systems (MASs), which contain discrete-time and continuous-time individuals. First, we give a selection criteria of the coupling gains, the eigenvalues of communication topology, and the event-triggered sampling interval to guarantee the hybrid consensus, which have an impact on system stability, due to the interaction and co-existence of discrete-time and continuous-time individuals. Second, the hybrid second-order consensus under the event-triggered strategy is proven, where the agents communicate with their neighbors and update their controllers only at the triggered instants. Finally, we give some simulation examples to prove the validity of the main results.

Limited-Budget Output Consensus for Descriptor Multiagent Systems With Energy Constraints

This article deals with limited-budget output consensus for descriptor multiagent systems with two types of switching communication topologies, that is, switching connected ones and jointly connected ones. First, a singular dynamic output feedback control protocol with switching communication topologies is proposed on the basis of the observable decomposition, where an energy constraint is involved and protocol states of neighboring agents are utilized to derive a new two-step design approach of gain matrices. Then, limited-budget output consensus problems are transformed into asymptotic stability ones and a valid candidate of the output consensus function is determined. Furthermore, sufficient conditions for limited-budget output consensus design and analysis for two types of switching communication topologies are proposed, respectively, and an explicit expression of the output consensus function is given, which is identical for two types of switching communication topologies. Finally, two numerical simulations are shown to demonstrate theoretical conclusions.

Fixed-Time Leader-Follower Consensus of Networked Nonlinear Systems via Event/Self-Triggered Control

This brief addresses the fixed-time event/self-triggered leader-follower consensus problems for networked multi-agent systems subject to nonlinear dynamics. First, we present an event-triggered control strategy to achieve the fixed-time consensus, and a new measurement error is designed to avoid Zeno behavior. Then, two new self-triggered control strategies are presented to avoid continuous triggering condition monitoring. Moreover, under the proposed self-triggered control strategies, a strictly positive minimal triggering interval of each follower is given to exclude Zeno behavior. Compared with the existing fixed-time event-triggered results, we propose two new self-triggered control strategies, and the nonlinear term is more general. Finally, the performances of the consensus tracking algorithms are illustrated by a simulation example.

Edge-Event-Triggered Synchronization for Multi-Agent Systems with Nonlinear Controller Outputs

This paper addresses the synchronization problem of multi-agent systems with nonlinear controller outputs via event-triggered control, in which the combined edge state information is utilized, and all controller outputs are nonlinear to describe their inherent nonlinear characteristics and the effects of data transmission in digital communication networks. First, an edge-event-triggered policy is proposed to implement intermittent controller updates without Zeno behavior. Then, an edge-self-triggered solution is further investigated to achieve discontinuous monitoring of sensors. Compared with the previous event-triggered mechanisms, our policy design considers the controller output nonlinearities. Furthermore, the system’s inherent nonlinear characteristics and networked data transmission effects are combined in a unified framework. Numerical simulations demonstrate the effectiveness of our theoretical results.