This paper introduces an online data-driven learning scheme designed to address a novel problem in propensity formation and containment control for fully heterogeneous multi-agent systems. Unlike traditional approaches that rely on the eigenvalues of the Laplacian matrix, this problem considers the determination of follower positions based on propensity factors released by leaders. To address the challenge of incomplete utilization of leader information in existing multi-leader control methods, the concept of an influential transit formation leader (ITFL) is introduced. An adaptive observer is developed for the agents, including the ITFL, to estimate the state of the tracking leader or the leader’s formation. Building on these observations, a model-based control protocol is proposed, elucidating the relationship between the regulation equations and control gains, ensuring the asymptotic convergence of the agent’s state. To eliminate the necessity for model information throughout the control process, a new online data-driven learning algorithm is devised for the control protocol. Finally, numerical simulation results are given to verify the effectiveness of the proposed method.

In this article, we reformulate the distributed optimal coordination problem for multi-agent systems to broaden its applicability across a wider range of coordination scenarios, thereby introducing a Generalized Distributed Optimal Coordination (GDOC) problem. In GDOC, the inter-agent relationships evolve from equality (consensus) to affinity (coordination), while local cost functions are unified as blends of parameters and shared basis functions, enabling cohesive network optimization. To address the GDOC problem, we propose a weak coupling hierarchical control framework for heterogeneous multi-agent systems. This framework consists of three layers: a signal generator, a tracking controller, and a speed regulator. For the generator, a transformed consensus protocol is designed for agents to estimate the global cost function and feasible set in a distributed manner, with the gradient projection method applied to minimize the objective function locally. For the controller, an observer-based output feedback control law is designed through system decomposition. For the regulator, a dynamic adaptive parameter is introduced to adjust the updating speed of the reference signal based on the agent’s relative tracking ability. The proposed framework not only preserves the universality of hierarchical control but also addresses the limitation of topdown structural open-loop control by introducing a regulator to form a bottom-up feedback loop. Finally, the effectiveness of the proposed framework is verified by Lyapunov stability theory analysis and simulation experiments. Note to Practitioners—In numerous task scenarios, the coordinated control of multi-agent systems involves solving optimization problems. This paper proposes GDOC to mathematically characterize these scenarios in a unified way, with the goal of controlling each agent’s output to converge towards the minimum point of the aggregate cost functions while maintaining preset inter-agent relationships. To achieve this, the affine transformation matrix is introduced to describe these inter-agent relationships under diverse coordination scenarios. Furthermore, the cost function adopts a form involving parameters and shared basis functions, facilitating interaction and iteration within the cost function. Correspondingly, an engineering-friendly control framework is proposed to address the GDOC problem. This framework consists of a reference signal generator, a tracking controller, and a speed regulator, each of which can be designed separately. The speed regulator is a new addition, aimed at adjusting the updating speed of signals according to the physical dynamic response capability of each agent, thereby establishing an indirect bottom-up feedback loop. This control framework can be applied to addressing GDOC problems in situations with switching cost functions and multiple solutions.

This paper proposes a distributed accelerated Nash equilibrium (NE) seeking algorithm for constrained multi-cluster games with time-varying communication, where agents in the same cluster are cooperative, while there is competition among different clusters. Constraint sets and time-varying interaction networks are considered simultaneously, which is motivated by their widespread presence in practical applications, thereby the designed algorithm can deal with more scenarios where cooperation and competition coexist. To attain higher flexibility and faster convergence, two acceleration techniques, named the heavy-ball method and Nesterov momentum, are introduced into the algorithm with distinct parameters, and an average parameter is employed to handle constraints. Furthermore, the linear convergence of the algorithm to NE is confirmed based on the optimality gap, the state difference, the consensus error and the gradient tracking error, and explicit bounds for the step size and parameters are derived by the associated properties of the time-varying networks and cost function. Finally, the acceleration effect of the algorithm is demonstrated in the energy management system, which validates the feasibility of the designed algorithm.

This article investigates the distributed tracking problem of networked cyber-physical systems (CPSs), considering system uncertainties, output constraints, and false data injection (FDI) attacks. Notably, the FDI attacks modeled here are explicitly malicious, meaning they are designed to cause the system to violate prescribed output constraints. Motivated by the lack of constrained-control studies addressing situations where the reference signal does not meet the constraint, we introduce a new form of tracking error, termed barrier tracking error (BTE). It is valuable that any conventional control scheme can be combined with the BTE idea to deal with output constraints. Subsequently, a nonsingular finite-time controller is developed using the backstepping method and neural networks. It is worth mentioning that the controller employs an event-triggered quantized control strategy, effectively reducing the burden on channels and actuators. Finally, comprehensive stability analysis and simulations are provided.

In this paper, a time-varying group formation-containment tracking problem for nonlinear multiagent systems (NMASs) with intermittent actuator faults is considered. The NMASs are composed of multiple subgroups responsible for different target tracking, and they are interconnected through a weighted digraph. The unknown nonlinear dynamics of nonstrict- feedback NMASs are approximated by fuzzy-logic systems, and the adaptive backstepping is employed to design the virtual controllers along with their adaptive parameters. Then, two novel fault-tolerant controllers are designed for the formation leaders and followers to achieve group formation tracking and containment control, even in the presence of intermittent actuator faults. Both controllers are fully distributed as only neighbor information is required instead of global information. Finally, simulation experiments for multiple unmanned surface vehicles are provided.

The State of Charge (SoC) is an important parameter of a battery energy storage system (BESS), and its balance problem is also an issue worth studying in a multi-BESS network. Recently, some researchers have proposed a power allocation method, claiming that as long as the power sharing state and SoC balance state can be obtained in real-time, it can not only maintain supply and demand balance, but also ensure that any BESS will not exit early due to insufficient energy storage. Considering this, we are attempting to design a distributed dynamic average tracking algorithm based on multiagent systems (MASs) with prescribed transient and steady state performance to estimate the power sharing and SoC balance states of a BESSs network with dynamic load in a distributed manner. Two versions of the solution are designed here, where one is event triggered and the other is self triggered. These two schemes ensure the performance of the estimators under intermittent communication to varying degrees, respectively. In each constructed estimation scheme, prescribed performance control (PPC) method is implemented to ensure the expected steady-state and dynamic performance, which is encapsulated in a performance function. Thus, it achieves almost zero error estimation of the fast time-varying power sharing and the SoC balance states. In addition, consensus and average tracking performance are decoupled, which provides convenience for parameters tuning. Finally, to verify the results of the theoretical analysis, some cases are studied and relevant simulations are performed on a 4 bus system.

The problem of noise-to-state practically finite-time output tracking control for random multi-agent systems (MASs) subjected to mismatched disturbances is considered in this paper. Firstly, the definition of noise-to-state practically finite-time stability (NSPFTS) and its criterion are proposed for a single system described by a random differential equation (RDE). Furthermore, the NSPFTS is extended to random MASs for the first time. By integrating dynamic surface control into the backstepping approach, a new control strategy based on the distributed finite-time observer is developed for random MASs with mismatched disturbances. The differential explosion problem typically encountered in the traditional backstepping method is overcome. By using the noise-to-state practically finite-time Lyapunov theorem proposed, tracking errors of followers can be adjusted arbitrarily small within a finite time. Additionally, the upper boundness of settling time is given explicitly in probability. Finally, two examples confirm the effectiveness of the proposed control approach.Note to Practitioners—Due to the fact that many mechanical systems work in stochastic environments, disturbances cannot be avoided. It is of practical significance to investigate random MASs with mismatched disturbances. In practical application, convergence rate is an essential indicator to gauge the performance of the system. Finite-time stability (FTS) is frequently mandated to be achieved for faster convergence, higher accuracy, and better anti-disturbance. Therefore, the definition and theorem of NSPFTS are given, which simplifies the process of controller design and stability analysis. Subsequently, a novel control strategy for random MASs with mismatched disturbances is put forth, drawing upon the proposed finite-time Lyapunov theorem. By integrating the state observer and the dynamic surface control method into the backstepping control design, the proposed controller avoids the differential explosion problem that often occurs in the backstepping method, which reduces the computational burden. All followers can track the leader within a finite time. The explicit establishment of the expectation of settling time allows for the estimation of an upper bound for convergence time in practical applications. This control strategy offers a practical and viable solution for implementation in various manufacturing environments.

This article addresses the containment control problem in multiagent systems with nonlinear heterogeneous followers and multiple unknown leaders whose dynamics are exclusively known to their neighbors. The primary goal is to ensure the convergence of each follower to the dynamic convex hull spanned by the leaders under the constraints of limited communication resources. To achieve this, this article introduces a modular event-triggered containment control scheme with three modules. The first module, Module I-signal generator, is designed for each follower to generate a reference signal asymptotically entering the dynamic convex hull without relying on follower dynamics. The second module, Module II-event-triggered mechanism, is tailored to save communication resources effectively by determining when to broadcast information based on perturbed system stability and input-to-state stability theories. The third module, Module III-tracking controller, treats each follower as an independent agent and is crafted to track the reference signal generated by Module I using an output regulation approach. It is established that the system achieves containment control without Zeno behavior under the influence of these modules, and the theoretical results are validated through simulation examples, demonstrating the practical validity of the proposed approach.

This article proposes a distributed consensus tracking controller for a class of nonlinear multiagent systems under a directed graph, in which all agents are subject to time-varying asymmetric full-state constraints, internal uncertainties, and external disturbances. The feasibility condition generally required in the existing constrained control is removed by using the proposed nonlinear mapping function (NMF)-based state reconstruction technology, and the Lipschitz condition usually needed in the consensus tracking is also canceled based on the adaptive command-filtered backstepping framework. The composite learning of the neural network-based function approximator (NN-FAP) and the finite-time smooth disturbance observer (DOB) provides a novel scheme for handling internal and external uncertainties simultaneously. One advantage of this scheme is that the use of online historical data of the closed-loop system strengthens the excitation of NN's learning. Another advantage is that the DOB with NN-FAP embedding realizes that the finite-time observation for external disturbance in the case of the system dynamics is unknown. A complete controller design, sufficient stability analysis, and numerical simulation are provided.

Semi-global bipartite fault-tolerant containment control framework on antagonistic communication networks is proposed in this article for heterogeneous multiagent systems (MASs) under the influence of input saturation and actuator faults. An observer is constructed to estimate the leaders' states on signed digraph, where the communication networks are antagonistic. A fully distributed virtual control approach is developed to acquire the containment trajectory. Based on the observer, a semi-global containment control method is developed to compensate for the detrimental impacts of both input saturation and actuator faults. Besides, the dynamics and state-space dimensions of the agents can be different. The proposed framework overcomes two drawbacks of the conventional containment control: 1) the containment trajectory is obtained under general antagonistic communication networks, which is more general in engineering applications and 2) both actuator faults and input saturation are solved for heterogeneous agents, which relaxes the limitation of homogeneous dynamics. Finally, a simulation example is conducted to test and verify the feasibility of the proposed method framework.

In this article, a model-free optimal solution is proposed for the containment control problem of fully heterogeneous discrete-time multiagent systems, in which both leaders and followers have heterogeneous dynamics. In order to make followers converge to the convex combination of leaders predefined by the users using only the collected data, a distributed control framework based on reinforcement learning (RL) for completely heterogeneous multiagent systems is developed. On the basis of the difference between follower states and target states, a local discounted performance function without considering the input index is designed for each agent to obtain the local optimal controller. The advantage of the designed performance function is that the relationship between the gain matrix of the local optimal controller and the solution of the regulation equation can be established, thus avoiding the need to solve the output regulation equation explicitly. A model-free distributed adaptive observer is designed for each follower to replace the leaders’ states in optimal controller without the need to know the dynamics of leaders. Combining the optimal controller, model-free adaptive observer, and RL, the data-based optimal containment control algorithm for fully heterogeneous multiagent systems is designed and employed. Finally, numerical simulation results are given to verify the effectiveness of the proposed method.

This article proposes a hierarchical control strategy, which consists of a task planning layer and a task execution layer, to solve the problem of tracking the trajectory of a noncooperative leader agent by heterogeneous follower agents under a directed communication topology. The noncooperative leader possesses escape capability due to its bounded input with an unknown bound: 1) the task planning layer is developed by building a distributed adaptive signal generator and a dynamic event-triggered communication mechanism and 2) the task execution layer is formulated by designing individual tracking controllers for each follower. This layered approach effectively handles challenges arising from heterogeneous dynamics. By introducing adaptive parameters, it eliminates reliance on the upper bound for the leader’s input while ensuring that the control strategy is fully distributed. The event-triggered mechanism saves communication resources effectively and does not require a large amount of additional computing resources to monitor the triggering condition. Furthermore, the results are extended to a more generalized nonlinear heterogeneous case in order to highlight the advantages offered by this hierarchical control strategy. Finally, the theoretical analysis and a simulation example, respectively, demonstrate and validate the correctness and validity of the theoretical results.

Privacy security research is one of the most important issues for the cyber-physical systems, and opacity as an information flow property, provides a new perspective for studying privacy security in complex information interaction scenarios. In the context of the discrete event systems, vital privacy can be modeled as secret states and based on the available observations (i.e., the sequence of observable events), intruders would analyse whether something secret has occurred. In this article, three kinds of strong W-limited opacity, named strong W,$(W,M)$, and$(W,\infty)$opacity for the partially observed discrete event system are investigated based on the security quantification consideration. It is assumed that the vicious eavesdropper has a complete knowledge of given systems’ structure and analyses something secret by limited observable information. Meanwhile, in addition to the current and delayed information analysis, predictive information analysis is first added to the strong opacity setting. W denotes the limited observable information and$M~(\infty)$represents the finite (infinite) predictability. Subsequently, a pivotal technique called labeled W-limited state estimator is constructed, based on which, verifications for the three kinds of strong W-limited opacity are accomplished with the help of secret-labeled states and secret-reaching states. The current work shows that the complexity is$O(2^{2|X|}(W+1)|\Sigma _{o}|)$. Finally, the upper bounds of W and M are also discussed, and it is proved to be$|X|(2^{|X|}-1)$and$2^{|X\backslash X_{S}|}-1$. (X is the state set,$X_{S}$is the secret state set, and$\Sigma _{o}$denotes the observable events set.)

Abstract The globally optimal generalised sequential fusion (GSF) algorithm in the sense of linear minimum variance for multi‐sensor stochastic uncertain systems is investigated by the authors. Specifically, in the GSF algorithm, the estimation of measurement noise is considered, and m a ( m a ≥ 1) sensors' measurement data are fused at the a th reception instant, which makes it very flexible and suitable for practical applications. The centralised and sequential fusion algorithms are special cases of the proposed GSF algorithm. Furthermore, for any m a , a = 1, 2, …, M , the estimated values of the GSF algorithm remain invariant and globally optimal. Moreover, the independence between the estimated values and fusion order is proved in the proposed GSF algorithm. Finally, simulation results are given to demonstrate the usefulness of the developed algorithm.

This article aims to develop a virtual-actuator-based control scheme for the consensus tracking problem of multiagent systems (MASs) against actuator faults and mismatched disturbances. The proposed scheme has a double-layer structure. In the cyber layer, the nominal controller is designed with neighboring information for the fault-free case. While in the physical layer, the fault compensator, working as the virtual actuator, is applied to reconfigure faulty plants adaptively. This design enjoys the advantages that the nominal controller needs no adjustment and all its properties can be preserved after failure. Moreover, the proposed control scheme is distinguished by the following features: 1) the commonly imposed rank condition on outage faults is removed; 2) the norm bound of the leader's input is allowed to be unknown even though the topologies are switching and directed; and 3) there is no need to use the estimates of faults in the virtual actuator design, which means the negative impacts caused by the inaccurate fault estimation can be avoided. Finally, a numerical example is given to validate the effectiveness of the theoretical results.

The problem of fault prognosis in the context of discrete event systems (DESs) is a crucial subject to study the security and maintenance of cyber-physical systems. In this article, the decentralized fault prognosis of partially observed DESs is analyzed with a universal state-estimate-based protocol. It follows (M,K) as the performance bound of any expected decentralized prognosers, where any fault can be predicted K steps before its occurrence and the fault is guaranteed to occur within M steps once a corresponding fault alarm is issued. To determine whether expected decentralized prognosers exist, the notion of state-estimate-coprognosability (SE-coprognosability) under the case of one fault type is proposed. Compared with existing other kinds of coprognosability, SE-coprognosability is a more generalized concept. Meanwhile, combining the formal method and algebraic state space approach, a novel state estimation algorithm is presented and based on which, the verification of SE-coprognosability is also solved.

This brief proposes a fuzzy adaptive event-triggered quantized finite-time control (FTC) (ETQFTC) scheme for uncertain strict-feedback nonlinear systems with full-state constraints. By means of state transformation, filtered backstepping technique and fuzzy adaptive control with the idea of minimum learning parameter, a$C^{1}$ETQFTC scheme with low differential calculation and few parameter updates is developed. In the proposed scheme, the feasibility condition generally required in the existing state-constrained control, and the control chattering and singularity problem, which are common in the existing FTC schemes are removed and avoided respectively. Finally, complete stability analysis and a set of comparative simulations are presented.

Facing different environments, i.e., states, there will be different game relationships among players, but there will also exist interactions among players to form a group. This article focuses on presenting the group-based state potential game (GSPG) and the strongly GSPG (SGSPG) to better describe such situations. Players who interact with each other can be regarded as a group and they will update strategies simultaneously. First, the concept of (strongly) GSPG is given and how to design two kinds of games is shown through the semi-tensor product (STP) of matrices. Subsequently, it is confirmed that their corresponding dynamics will converge almost surely to a strategy invariant set of (strongly) group-based recurrent state equilibriums and remain stable. Meanwhile, the equilibriums are acquired based on the algebraic forms of the games’ dynamics, and the algorithm of the (strongly) GSPG process is established. Finally, the results in this article are demonstrated effectively by a typical example.

In this paper, the consensus problem for a class of second-order multi-agent systems under aperiodically intermittent communication is investigated. First, a new sampled-hold-based intermittent control protocol is designed to achieve consensus and improve the consensus performance in the absence of continuous communication. Then, some necessary and sufficient conditions are obtained for second-order consensus based on the relationship of the control gains, the eigenvalues of the Laplacian matrix, and the intermittent communication architecture. Moreover, if the sampled-hold-based aperiodically intermittent control is degenerated into the aperiodically intermittent control or the sampled-hold-based periodically intermittent control, some simpler consensus conditions are also given. Finally, some experimental simulations are shown to verify the correctness of the theoretical analysis.

In this article, the leader–follower consensus is investigated for discrete-time second-order multiagent systems with smart leader, where the smart leader can obtain the feedback information from its neighbours. Different from the existing results, an objective function is provided to determine whether the leader utilizes the feedback information from its neighboring agents, with the purpose of making the system have better performance. Under the directed interconnected topology, a novel distributed consensus protocol is designed for second-order discrete-time multiagent systems. Some necessary and sufficient conditions are derived for the leader–follower consensus of discrete-time second-order multiagent systems with smart leader under fixed/switching topology. Finally, two simulation examples are presented to demonstrate the feasibility of the theoretical results.

This article studies the fault-tolerant leader-following consensus problem for multiagent systems with input saturation. The main contribution is to present a modified low-and-high gain feedback approach to deal with multiple actuator faults, including partial loss of effectiveness, outage, and stuck simultaneously. First, without consideration of saturation, a distributed fault-tolerant control scheme is put forward by the adaptive technique, and a practical finite-time stability result is established. Second, by employing the fault-tolerant theory and introducing a novel form of parametric algebraic Riccati equation, a modified low-and-high gain feedback approach is developed for the saturated control strategy. It is proven that the practical finite-time stability can be achieved, and both the steady-state consensus error and the settling time can be well estimated. Finally, numerical simulations are provided to validate the effectiveness of the theoretical results.

Krill herd algorithm (KHA) is an emerging nature-inspired approach that has been successfully applied to optimization. However, KHA may get stuck into local optima owing to its poor exploitation. In this paper, the orthogonal learning (OL) mechanism is incorporated to enhance the performance of KHA for the first time, then an improved method named orthogonal krill herd algorithm (OKHA) is obtained. Compared with the existing hybridizations of KHA, OKHA could discover more useful information from historical data and construct a more promising solution. The proposed algorithm is applied to solve CEC2017 numerical problems, and its robustness is verified based on the simulation results. Moreover, OKHA is applied to tackle data clustering problems selected from the UCI Machine Learning Repository. The experimental results illustrate that OKHA is superior to or at least competitive with other representative clustering techniques.

This paper studies the sampled data based containment control problem of second-order multi-agent systems with intermittent communications, where velocity measurements for each agent are unavailable. A novel controller for second-order containment is put forward via intermittent sampled position data measurement. Several necessary and sufficient conditions are derived to achieve intermittent sampled containment control by means of analyzing the relationship among control gains, eigenvalues of the Laplacian matrix, the sampling period, and the communication width. Finally, several simulation examples are used to testify the correctness and effectiveness of the theoretical results.

This paper investigates the distributed containment control problem for a class of general second-order multiagent systems with switched dynamics, which is composed of a continuous-time (CT) subsystem and a discrete-time (DT) subsystem. For this switched multiagent system under fixed directed topology, a distributed containment control protocol is proposed for each follower based on the relative local measurements of neighboring followers and leaders. Some necessary and sufficient conditions are derived under the condition that the network topology contains a directed spanning forest, and these conditions ensure that the general second-order containment control problem can be solved under arbitrary CT-DT switching. If the general second-order system is reduced to the double integrator system, some simpler containment conditions are presented. Furthermore, the similar results are also obtained under switching directed topology. Finally, some simulation examples are presented to show the efficiency of the theoretical results.

In this paper, we address the problems of enumerating siphons and minimal siphons in ordinary Petri nets (PNs) by resorting to the semi-tensor product (STP) of matrices. First, a matrix equation, called the siphon equation (SE), is established by using STP. Second, an algorithm is proposed to calculate all siphons in ordinary PNs. An example is presented to illustrate the theoretical results and show that the proposed method is more effective than other existing methods in calculating all siphons of PNs. Third, an efficient recursion algorithm is also proposed, which can be applied to computing all minimal siphons for any ordinary PNs. Last, some results on the computational complexity of the proposed algorithms, in this paper, are provided, as well as experimental results.