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This paper presents a secure containment control problem of nonlinear Multi-Agent Systems (MASs) under aperiodic Denial of Service (DoS) attacks and external disturbances simultaneously. A novel adaptive neural network (NN)-based event-triggered control is considered that uses the nonlinear estimator to predict the state of other agents. Since data access is denied during DoS attacks, the overall system switches between two modes of stable and unstable containment behaviours. Therefore, the maximum of attack duration and frequency is determined such that the overall system evolution leads to containment convergence in the presence of DoS attacks. We proposed an adaptive NN-based distributed disturbance observer to estimate external disturbances in a nonlinear system's dynamics. The state estimator predicts neighbouring agents' states, and each agent's input and event times are determined without monitoring other agents. The directed graph topology is used to determine data exchange among agents instead of an undirected graph that reduces implementation conditions. Zeno-free behaviour is also proved by analysis of the system. Eventually, the numerical simulation of the proposed approach is shown. Abbreviations: DoS attacks, Containment control of multi-agent system [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of bipartite secure containment control for a specific class of discrete-time multi-agent systems with multiple dynamic leaders. The followers are divided into two subgroups that cooperate within each subgroup and compete with the other subgroup. Similarly, the leaders exhibit cooperative-competitive behavior towards these subgroups. The main objective is to ensure that cooperating followers gradually enter the dynamic convex hull formed by leaders while competing followers enter the opposite convex hull. To protect sensitive information, only the difference between the real state and the encrypted state of the position and velocity is quantized and transmitted, rather than the actual state itself. As a result, the permissible range of the gain parameters and other relevant parameters is determined. Furthermore, a precise definition of the minimum channel capacity is provided to understand the factors that influence the requirement for minimum channel capacity. Finally, an illustrative example is presented to demonstrate the effectiveness of the developed secure control method. [ABSTRACT FROM AUTHOR]

In this work, the containment control problem for a quadrotor team is addressed in the presence of multiple dynamic leaders with unknown bounded time-varying inputs. Both safety-critical constraints and input constraints are considered. Specifically, a linear extended state observer (ESO) is employed to handle the uncertainty and disturbance. A distributed fixed-time observer is designed to estimate the reference signal requiring no global information. The proposed nominal controller can guarantee the formation geometric constraint in steady states. Moreover, safety certificates for collision-free in transient states is enforced by using exponential control barrier functions (ECBFs). A real-time quadratic programming (QP) problem is constructed to modify the nominal controller such that both safety constraint and input constraint can be satisfied. Finally, simulations and experiments illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the containment control for fractional complex networks (FCNs) with double-integrator fractional-order dynamics under stochastic communication noises. It is assumed that the agents' communication channels are affected by stochastic noises, which depend on their relative positions. Then, a distributed containment protocol is designed for each follower to counteract the impact of stochastic communication noises. Next, by directly utilizing the properties of the integral mild solution, sufficient conditions are deduced for achieving containment control of the FCNs. The theoretical analysis shows that under the proposed protocol and given sufficient conditions, all followers converge towards into the convex hull spanned by the leaders in the mean square sense. Finally, several numerical examples are provided to validate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

This work addresses the discrete-time containment control problem for first-order and second-order systems, incorporating position constraints, nonuniform time delays, and switching topologies. Projection operators are introduced to maintain agent states within the position constraints. Then, model transformation methods, along with stochastic properties of matrices, are employed to handle coupled nonlinearities stemming from position constraints and time delays. By using local information, distributed projection-based control schemes are proposed for multi-agent systems. Theoretical analysis shows that all followers ultimately converge into the convex hull spanned by leaders if the union of the communication topologies contains a directed spanning tree within each specified time interval. Finally, the theoretical results are verified by numerical simulations. • Containment control is studied for systems with constraints, delays, and switching. • A projection-based algorithm improves convergence to the leader-forming convex hull. • Model transformation is used to eliminate effects of non-uniform communication delays. • Numerical simulations validate the theoretical results. [ABSTRACT FROM AUTHOR]

A practical fixed-time robust containment control method for multiple autonomous surface vehicles (multi-ASVs) is proposed in this study. This method addresses the containment control problem of multi-ASVs, considering both collision risks and external disturbances. This control scheme improves the cooperative performance of the formation and guarantees safe collision avoidance behavior. First, to enable the online estimation of unknown time-varying disturbances from the external environment, a fixed-time disturbance observer (FNDO) is designed based on fixed-time control theory. Second, the distributed kinematic controller is modified to include the partial derivatives of the artificial potential energy function (APEF), thereby preventing collisions among multi-ASVs. Third, by applying fixed-time theory, graph theory, and fixed-time dynamic surface control techniques, a practical fixed-time robust containment controller for multi-ASVs is proposed. Additionally, the entire closed-loop control system is guaranteed to be practical and fixed-time stable through stability analysis. Finally, the proposed control strategy has been validated by simulation results. [ABSTRACT FROM AUTHOR]

This paper presents a novel containment control scheme for multi-agent systems against denial of service attacks. The control goal is to ensure that the follower moves into the convex hull formed by dynamic leaders at any initial position. Different from existing results, the proposed scheme generates a position-adjustable reference signal for each follower. Simultaneously, if the convex hull information is not available, the follower will follow an estimated reference signal to reduce the probability of collision. Additionally, we also implemented adaptive fuzzy control and combined with the command filtered technique to optimize the control scheme. By utilizing Lyapunov theory, the stability analysis is carried out for closed-loop multi-agent systems. Finally, extensive simulations validate the superiority and feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the containment control problem for heterogeneous multi-agent systems with unknown leaders and actuator failures. The dynamics of the leaders are unavailable to all followers and the measurable information of leaders is available to some followers. A model-free adaptive observer for each follower is proposed to estimate the convex hull of the leaders states and the dynamic knowledge of the unknown leaders. The followers may be affected by the actuator failures. Based on the adaptive observer and the adaptive solution of the output regulation equation, an adaptive fault-tolerant control protocol is designed to mitigate the impact of actuator failure on containment performance such that the output containment errors are ultimately uniformly bounded. Two simulation examples are provided to demonstrate the feasibility of the presented control scheme. [ABSTRACT FROM AUTHOR]

Global Nash equilibrium is an optimal solution for each player in a graphical game. This paper proposes an iterative adaptive dynamic programming-based algorithm to solve the global Nash equilibrium solution for optimal containment control problem with robustness analysis to the iterative error. The containment control problem is transferred into the graphical game formulation. Sufficient conditions are given to decouple the Hamilton–Jacobi equations, which guarantee the solvability of the global Nash equilibrium solution. The iterative algorithm is designed to obtain the solution without any knowledge of system dynamics. Conditions of iterative error for global stability are given with rigorous proof. Compared with existing works, the design procedures of control gain and coupling strength are separated, which avoids trivial cases in the design procedure. The robustness analysis exactly quantifies the effect of the iterative error caused by various sources in engineering practice. The theoretical results are validated by two numerical examples with marginally stable and unstable dynamics of the leader. [ABSTRACT FROM AUTHOR]

A formation and containment control problem is discussed for the Nonlinear Multi-Autonomous Ship Systems (NM-ASSs) with uncertainties and disturbances based on the Interval Type-2 (IT-2) Takagi-Sugeno Fuzzy Model (T-SFM) in this paper. A different formation control scheme is provided by using the state feedback controller of leader ships. Because of this feature, information communication between leader ships, which are farthest from each other in formation and containment problems, isn't required. However, the analysis problem in the IT-2 fuzzy containment controller design method is caused by the leader's formation controller. A design concept for the unknown leader's input of linear multi-agent systems is successfully extended to solve the problem by the expression of IT-2 T-SFM. Nevertheless, the analysis process will become conservative while the agent number or fuzzy rule number is increased. Thus, a relaxed analysis method is also considered for the containment controller design. Additionally, the passive performance constraint is combined into the IT-2 fuzzy formation controller design method to dissipate the disturbance effect and improve the control performance. Finally, two examples are provided to illustrate the advantage of the proposed IT-2 fuzzy controller design method in the formation and containment control problem of NM-ASSs. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of adaptive containment fault‐tolerant control for nonlinear multiagent systems with periodic disturbances. Different from most existing fault‐tolerant control schemes, the form of multiple faults is explicitly considered in this paper, including actuator faults and sensor faults. By combining the Fourier series expansion with neural networks, the unknown nonlinear dynamics subject to time‐dependent periodic disturbances are approximated. Then, the "complexity of explosion" issue that exists in traditional backstepping‐based results is avoided by introducing a first‐order sliding‐mode differentiator. It is proved that the developed containment control policies can ensure that all signals of the close‐loop systems are uniformly ultimately bounded, and all followers can converge to a convex area formed by multiple leaders. Simulation results verify the validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

This contribution considers the containment control problem for linear multi‐agent systems (MAS) using continuum models in form of linear parabolic PDEs. For this, a networked controller is designed, that ensures the asymptotic convergence of finite‐dimensional agents into a containment area specified by dynamic leaders. This problem is traced back to an output regulation problem for a continuum model independent of the number of agents, which also takes disturbances into account. A prescribed formation is assigned for the MAS in the containment area by using Bézier curves. Using bilateral backstepping a tracking controller is designed, which allows to distribute the control effort between the two boundary agents. The states are estimated by an infinite‐dimensional disturbance observer. For this, both a folding observer with network communication and two boundary observers without network communication are introduced. A fully distributed solution of the containment control problem is obtained by employing a continuum signal model observer, which communicates the states of the leader and disturbance model to all agents. The desired communication topology is imposed after the design by a spatial discretization. A simulation example illustrates the effectiveness of the new method for the networked controller design. [ABSTRACT FROM AUTHOR]

In this paper, we propose the containment control problem for multi-agent systems with Markovian switching dynamics by proposing a novel adaptive dynamic event-triggered sliding mode control scheme based on radial basis function neural networks. First, the unknown nonlinear dynamics of the system were approximated by using radial basis function neural networks. The dynamic event-triggered control scheme designed in the framework of sliding mode control operated at specific event sampling moments, thereby reducing computational and communication burdens. The containment control was achieved through a synergistic approach integrating dynamic event-triggered control with neural network-based adaptive control in a stochastic switching system. Moreover, we proved that Zeno behavior was effectively avoided. The proposed distributed containment control technique was validated through simulations, demonstrating its effectiveness and superiority. [ABSTRACT FROM AUTHOR]

This article investigates a class of multi-agent systems (MASs) with known dynamics external disturbances, where the communication graph is directed, and the followers have undirected connections. To eliminate the impacts of external disturbance, the technologies of disturbance observer-based control are introduced into the containment control problems. Additionally, to save communication costs and energy consumption, a distributed disturbance observer-based event-triggered controller is employed to achieve containment control and reject disturbance. Furthermore, designing the event-triggered function using an exponential function is beneficial for a time-dependent term while ensuring the exclusion of Zeno behavior. Finally, a numerical simulation is provided to validate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper focuses on the containment control problem for a class of nonlinear multi-agent systems (MASs) with sampled-data. To enhance the efficiency of utilizing communication resources, a new distributed sampled-data-based event-triggered transmission strategy is proposed. This event-driven strategy requires that event detector works only at periodic sampling instants. By employing the techniques such as input delay method, inequality technique and the Lyapunov stability theory, sufficient criteria are derived to ensure that each follower converges to the convex hull spanned by the leaders. A convex optimization method is employed to search for the desired controller gain by maximizing the maximum-allowable bound of sampling intervals. Additionally, for some special scenarios, to reduce computational complexity, the matrix decoupling technique is utilized to reduce the dimension of matrix inequalities, thereby facilitating application to large-scale MASs. Finally, the effectiveness of the proposed theory is verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this article, a finite‐time optimal containment control method is proposed for nonlinear multi‐agent systems with prescribed performance. First, a neural network‐based reinforcement learning algorithm is developed under the optimized backstepping framework. The algorithm employs an identifier‐critic‐actor architecture, where the identifiers, critics and actors are used to estimate the unknown dynamics, evaluate the system performance, and optimize the system, respectively. Subsequently, in order to guarantee the transient performance of the tracking error, the original system is converted into an equivalent unconstrained system. Then, the tracking errors are allowed to converge to a prescribed set of residuals in finite time by combining prescribed performance control and finite‐time optimal control techniques. Furthermore, by using the Lyapunov stability theorem, it is verified that all signals are semi‐globally practical finite‐time stable, and all followers can converge to a convex region formed by multiple leaders. Finally, the effectiveness of the proposed scheme is demonstrated by a practical example. [ABSTRACT FROM AUTHOR]

This paper investigates the containment control problem of linear multiagent systems (MASs) with multiple non‐autonomous leaders on a directed graph. First, an event‐triggered compensator is designed for each follower to estimate the convex combination of non‐autonomous leaders' states. The compensator is designed with the following three features: (1) It can estimate the convex combination of non‐autonomous leaders' states over directed graphs; (2) it is fully distributed; and (3) the designed event‐triggered mechanisms (ETMs) are composite dynamic ETMs, and each follower does not have to monitor the sampling errors continuously. Then, a state observer is developed for each follower based on the output feedback. Based on the designed compensator and state observer, an event‐triggered controller is developed, ensuring that each follower's state converges exponentially to an arbitrarily small neighborhood centered on the convex combination of leaders' states. Additionally, the proposed DETMs are free of Zeno behavior. Finally, the effectiveness of the developed control protocol is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

Real-time semantic segmentation is a challenging task in computer vision, especially in complex scenes. In this study, a novel three-branch semantic segmentation model is designed, aiming to effectively use boundary information to improve the accuracy of semantic segmentation. The proposed model introduces the concept of containment control in a pioneering way, which treats image interior elements as well as image boundary elements as followers and leaders in containment control, respectively. Based on this, we utilize two learnable feature fusion matrices in the high-level semantic information stage of the model to quantify the fusion process of internal and boundary features. Further, we design a dedicated loss function to update the parameters of the feature fusion matrices based on the criterion of containment control, which enables fine-grained communication between target features. In addition, our model incorporates a Feature Enhancement Unit (FEU) to tackle the challenge of maximizing the utility of multi-scale features essential for semantic segmentation tasks through the meticulous reconstruction of these features. The proposed model proves effective on the publicly available Cityscapes and CamVid datasets, achieving a trade-off between effectiveness and speed. [ABSTRACT FROM AUTHOR]

This paper investigates a distributed adaptive finite‐time containment control scheme for multiple unmanned aerial vehicles subject to external disturbances and input saturation. Combined with a novel indicator of the saturation degree designed by the hyperbolic tangent function, an adaptive method is proposed to deal with the input saturation issue, which considers both symmetry and asymmetry saturation. Moreover, to address the problem of the "explosion of terms" inherent in the traditional backstepping controller design, a fixed‐time sliding mode differentiator is utilized to approximate the derivative of the virtual signal in the command‐filtered backstepping method. Finally, the convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

Copyright of Automatisierungstechnik is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the secondary control problem of shipboard microgrids (SMGs) with a high percentage of new energy sources under general noise. Firstly, a polymorphic SMG model is constructed, which enables the software-defined functionality of the control strategy and allows heterogeneous distributed generators (DGs) in AC SMGs to exchange packets of different types. Secondly, due to the presence of highly dynamic and high-power loads in the SMGs, a containment-based distributed secondary control strategy is proposed to improve the flexibility of the DG voltage regulation. Then, considering the complexity and diversity of disturbances during ship navigation, general noise is introduced instead of white noise to describe various disturbances. Furthermore, based on the random differential equations (RDEs), the NOS stability of the proposed strategy is proved using Lyapunov theory, which proves the effectiveness of the containment-based distributed secondary control strategy under general noise. And, the containment error is obtained to prove that the voltage and frequency of the system converge to the convex hull spanned by the virtual leaders, ensuring the high quality of the power supply. Finally, the validity of the proposed containment-based strategy is verified by an AC SMG model with four DGs in three cases. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the adaptive fixed-time fuzzy containment control for uncertain nonlinear multiagent systems, where the states and nonlinear functions are not feasible for the controller design. To address the issue of unmeasurable states, a state observer is developed, and fuzzy logic systems are utilized to approximate unknown nonlinear functions. Under the framework of fixed-time Lyapunov function theory and cooperative control, an adaptive fixed-time fuzzy containment control protocol is derived via the adaptive backstepping and adding one power integrator method. The derived fixed-time containment controller can confirm that the closed-loop systems are practical fixed-time stable, which implies that all signals in the systems are bounded and all follower agents can converge to the convex hull formed by the leader agents within fixed-time in the presence of unmeasurable states and unknown nonlinear functions . Simulation examples are conducted to test the validity of the present control algorithm.

This paper considers containment control (CC) of delayed nonlinear fractional‐order multi‐agent systems (FMASs). A reliable and effective method is proposed to deal with the difficulties brought from fractional calculus and delays. Utilizing improved Razumikhin method, algebraic graph theory, and matrix analysis technique, several simple algebraic conditions are provided to solve CC by choosing nondelayed or delayed communication protocols, respectively. Numerical results are also offered to clarify the efficiency of our theoretical method. [ABSTRACT FROM AUTHOR]

This work investigates the containment control for unknown time‐varying p‐normal (TVP) nonlinear multiagent systems (MASs) under directed topology. First, by innovatively constructing the dynamic update law in the distributed observer design process, the corresponding virtual leader trajectory can be accurately estimated at an exponential rate. Subsequently, the containment problem of MASs is transformed into a tracking problem through appropriate state transformation. Then, based on backstepping and power integrator techniques, a recursive algorithm is proposed to construct the adaptive controller to guarantee that the followers are driven into the convex hull consisting of dynamic leaders and the closed‐loop system is stable. Finally, the effectiveness of the containment control scheme is verified through a numerical simulation and a practical example of single‐link manipulators. [ABSTRACT FROM AUTHOR]

This article addresses the containment control issue for multi-AUV systems with the intervention of both external disturbance and input saturation. Firstly, a distributed estimator is established for the sake of acquiring precise estimation information of the desired position and its derivative for each follower AUV in the system. Next, on the basis of the proposed distributed estimator, a virtual control law is designed for each follower AUV. Then, due to the difficulty in obtaining accurate information about the derivative of the virtual control law, a linear tracking differentiator is introduced. Additionally, a disturbance observer is employed to tackle the composite disturbance, which mainly contains the internal model uncertainties and external bounded disturbances. Meanwhile, the issue of input saturation is handled by constructing the auxiliary system. Furthermore, a containment control law is designed with the assistance of the introduced linear tracking differentiator, the established disturbance observer, and the constructed auxiliary system. Additionally, the Lyapunov stability theory is applied to analyze the stability of the multi-AUV system. Finally, simulation results are given to confirm the feasibility of the proposed containment control scheme. [ABSTRACT FROM AUTHOR]

Aiming at the cooperative control problem of multi-agent system, the fixed-time containment control of general second-order multi-agent system under mismatched disturbances is studied. Firstly, the problem of multi-agent system fixed-time containment control in ideal state is analyzed, and a distributed control protocol based on variable structure control is proposed. Then, a nonlinear fixed-time disturbance observer is designed, aiming at the mismatched disturbance, and a fixed-time control protocol based on the nonlinear disturbance observer is proposed. Finally, the effectiveness of the proposed control protocol under switching topology and multi-source disturbance is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Due to the flexibility issue in existing containment control schemes for second-order multi-agent systems, we design an innovative control scheme. The proposed scheme involves the generation of a set of adjustable reference signals, and arbitrary adjustments of the reference signals are allowed. The innovative scheme not only enhances the flexibility of multi-agent systems, but also significantly decreases the likelihood of collision among multiple agents during their movements. Furthermore, the effectiveness of the proposed scheme is confirmed through simulation results. The proposed scheme addresses a critical issue in existing containment control schemes and presents a promising solution for improving the overall performance and safety of multi-agent systems. [ABSTRACT FROM AUTHOR]

The problems of prescribed-time leader-following consensus and prescribed-time containment control for double-integrator multiagent systems (MASs) with only position measurements are investigated in this paper. An observer-based prescribed-time control protocol is proposed, in which the two groups of observers for estimating the consensus errors of each follower both converge to zero within a specified time. Furthermore, the proposed controller only relies on its own observers and does not need to obtain the data from observers embedded in its neighbor nodes. The sufficient conditions for the MASs to achieve the defined prescribed-time consensus and to fulfill the goal of prescribed-time containment control are, respectively, given. The effectiveness of the proposed control protocol is further verified by computer simulations. [ABSTRACT FROM AUTHOR]

This article studies the distributed containment control of a second‐order discrete‐time multi‐agent system with convex constraints on positions, nonconvex constraints on velocities, bounded disturbances on static points and switching topologies. A distributed control algorithm with disturbance information and local information is proposed. It is proved that when the static points with disturbances and the joint graph have a directed spanning forest among each time interval, all agents are gradually driven to the neighborhood of a convex hull spanned by the static points, and an upper bound of the neighborhood is obtained. The most innovative point is to utilize a rigorous mathematical theory to deal with convex constraint error rather than a geometric explanation. Meanwhile, another control algorithm with static point information and local information is proposed to converge all agents to the convex hull in the absence of external disturbances. Additionally, a numerical example is conducted to illustrate this theory. [ABSTRACT FROM AUTHOR]

In this article, by creating a novel distributed full‐form dynamic linearization based model‐free adaptive containment control (FFDL‐MFACC) approach, the containment control problem of networked heterogeneous autonomous surface vehicles (ASVs), suffering from complex external disturbances and unavailable kinetic model‐information, is resolved. In light of the data‐driven strategy, a full‐form dynamic linearization‐based data model is efficiently established. Then, by further deploying the commonly used rotation matrix, a distributed FFDL‐MFACC scheme is thereafter developed such that accurate tracking of a predefined convex hull spanned for all follower vehicles can be achieved. Afterwards, a disturbance observer is further designed to accurately estimate the lumped disturbances and the estimation is served as a compensation within the distributed full‐form dynamic linearization. Rigorously theoretical analysis indicates the devised distributed FFDL‐MFACC method can ensure the asymptotic containment tracking of networked heterogeneous ASVs. Finally, simulation results are illustrated to verify the advantages of the devised approach. [ABSTRACT FROM AUTHOR]

Summary: This article addresses the issue of bipartite containment tracking for nonlinear strict feedback multi‐agent systems (MASs) with disturbances and measurement uncertainties. To provides a better performance against strong disturbance, a coordination transformation is applied such that all the nonlinear functions, controller disturbances and measurement uncertainties are lumped into a single disturbance signal in the last state equation. Then, the lumped disturbance is compensated through a novel disturbance rebuilding method. Moreover, in order to get better control performance, state constraints are also considered through a nonlinear transformation function (NTF). Different from traditional methods dealing with the state constraint problems, the NTF method can avoid using any discontinuous Lyapunov function. Finally, an adaptive finite‐time distributed controller is established via the disturbance estimates, backstepping technique and fuzzy logic system (FLS). The performance of the controller is illustrated by a simulation example in which the bipartite containment formation of followers is realized in a practical finite time. [ABSTRACT FROM AUTHOR]

Summary: This study investigates the issue of containment control (CC) of multi‐agent systems (MASs) that are heterogeneous, nonlinear, and fractional‐order while taking practical scenarios into account, such as uncertainties, unknown nonlinearities, time‐varying state delays, and distributed time‐varying delays. A fully distributed adaptive observer is created for each follower in accordance with the communication topology information among agents. This observer is designed to estimate the convex combination information of the leaders. The approach utilizes interval type‐2 fuzzy set theory and adaptive methods to design a distributed containment control strategy that only uses the self‐information of the followers and neighbor nodes' information. Sufficient conditions for implementing containment control are given. A new Lyapunov‐Krasovskii functional (LKF) is constructed, and the stability of the system with feedback loop is proven using fractional‐order theory and inequality methods. Lastly, a simulation example is presented to illustrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the secure containment control issue for heterogeneous multi-agent systems subject to hybrid attacks is studied. In the network channels among agents, adversaries launch replay attacks such that the followers can only retrieve the previous information of their neighbors. To characterize the effects of replay attacks, a distributed auxiliary system with heterogeneous time-varying delay is constructed to estimate the convex hull of the leaders' state. The control input of each follower may be contaminated by the malicious false data injection (FDI) attacks with unknown bounded time-varying signals, which are intended to compromise the containment performance of the whole system. A local adaptive compensator is designed for each follower to eliminate the adverse effects of the FDI attacks. Based on the distributed auxiliary system and the local adaptive compensator, a secure distributed control protocol is proposed to ensure that the output trajectories of each follower can converge to the dynamic convex hull spanned by the leader outputs. Finally, two illustrative examples are provided to show the feasibility of the proposed secure control scheme. • This paper introduces a secure control protocol to dispose a more complicated attack situation. • The original Laplacian matrix is divided into several sub-Laplacian matrices associated with the heterogeneous time-varying delays. • The designed adaptive compensator can fully eliminate the adverse effects of the FDI attacks without using any information of the FDI attacks. [ABSTRACT FROM AUTHOR]

A practical fixed-time robust containment control method for multiple autonomous surface vehicles (multi-ASVs) is proposed in this study. This method addresses the containment control problem of multi-ASVs, considering both collision risks and external disturbances. This control scheme improves the cooperative performance of the formation and guarantees safe collision avoidance behavior. First, to enable the online estimation of unknown time-varying disturbances from the external environment, a fixed-time disturbance observer (FNDO) is designed based on fixed-time control theory. Second, the distributed kinematic controller is modified to include the partial derivatives of the artificial potential energy function (APEF), thereby preventing collisions among multi-ASVs. Third, by applying fixed-time theory, graph theory, and fixed-time dynamic surface control techniques, a practical fixed-time robust containment controller for multi-ASVs is proposed. Additionally, the entire closed-loop control system is guaranteed to be practical and fixed-time stable through stability analysis. Finally, the proposed control strategy has been validated by simulation results.

In this article, we consider the nonfragile containment control problem of nonlinear multi‐agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer‐based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with nonfragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper deals with the containment control problem for multi-agent systems. The objective is to develop a distributed control scheme that leads a sub-group of the agents, called followers, within the convex hull that is formed by the leaders, which operate autonomously. Towards this direction, we propose a twofold approach comprising the following: (i) a cyber layer, where the agents establish, through the communication network, a consensus on a reference trajectory that converges exponentially fast within the convex hull of the leaders and (ii) a physical layer, where each agent tracks the aforementioned trajectory while avoiding collisions with other members of the multi-agent team. The main contributions of this work lie in the robustness of the proposed framework in both the trajectory estimation and the tracking control tasks, as well as the guaranteed collision avoidance, despite the presence of dynamic leaders and bounded but unstructured disturbances. A simulation study of a multi-agent system composed of five followers and four leaders demonstrates the applicability of the proposed scheme and verifies its robustness against both external disturbances that act on the follower model and the dynamic motion of the leaders. A comparison with a related work is also included to outline the strong properties of the proposed approach. [ABSTRACT FROM AUTHOR]

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Summary: In this paper, the fast finite‐time backstepping containment control strategy is considered for high‐order stochastic multi‐agent systems. The addition of the finite‐time command filter avoids calculating explosion which occurs in the differential process of virtual control signals for the high‐order system on the traditional backstepping and makes convergence speed of control system faster. The influence of filtering errors generated by filter for control systems is eliminated by establishing error compensation systems. The fuzzy logic systems approximate unknown dynamics of systems. It proves the closed‐loop systems are practically fast finite‐time stable in mean square. The given simulation results show the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Finite‐time containment control of second‐order nonlinear multi‐agent systems with disturbances is investigated. The network topology among agents is assumed to be directed. An event‐triggered terminal sliding mode controller is designed, which is robust with respect to disturbances. Based on the control strategy, the accessibility of sliding manifold and the consensus tracking of the obtained sliding‐mode dynamics are achieved in finite‐time. Continuous update of controller is avoided and the settling time of the system convergence is evaluated. Moreover, the Zeno‐behavior of the triggering time sequence for each agent is excluded. Finally, the feasibility of the developed scheme is evaluated in numerical simulations. [ABSTRACT FROM AUTHOR]

The goal of this paper is to mitigate disturbances and input delays while optimizing controller actuation updates for discrete-time multi-agent systems through the use of an event-triggered confinement control system, especially in resource-constrained scenarios. This approach when combined with event-triggered control techniques, then every follower in the system adjusts its condition at specified times based on an event-triggered condition that is suggested. The containment control system issue in the presence of disturbances and input delays was tackled by using both decentralized and centralized event-triggered control systems. Using matrix theory and the Lyapunov technique, convergence analysis is conducted to show that the proposed strategy stays free of zeno phenomena. Numerical boosts are used to further illustrate the impact of theoretical results.

This paper addresses the problem of containment control for second-order multi-agent systems with position constraints, time delays, and switching graphs. The approach involves treating position constraints with a scaling factor and transforming the system into a new one through model transformations. Based on the analysis of Lyapunov function, it is demonstrated that all followers will eventually enter the convex hull formed by the leaders, as long as there exists at least a directed path to one of the leaders for all followers in the union of the communication graphs. Finally, numerical results are presented to validate the effectiveness of the algorithm.

Real-time semantic segmentation is a challenging task in computer vision, especially in complex scenes. In this study, a novel three-branch semantic segmentation model is designed, aiming to effectively use boundary information to improve the accuracy of semantic segmentation. The proposed model introduces the concept of containment control in a pioneering way, which treats image interior elements as well as image boundary elements as followers and leaders in containment control, respectively. Based on this, we utilize two learnable feature fusion matrices in the high-level semantic information stage of the model to quantify the fusion process of internal and boundary features. Further, we design a dedicated loss function to update the parameters of the feature fusion matrices based on the criterion of containment control, which enables fine-grained communication between target features. In addition, our model incorporates a Feature Enhancement Unit (FEU) to tackle the challenge of maximizing the utility of multi-scale features essential for semantic segmentation tasks through the meticulous reconstruction of these features. The proposed model proves effective on the publicly available Cityscapes and CamVid datasets, achieving a trade-off between effectiveness and speed.

This paper investigates the secondary control problem of shipboard microgrids (SMGs) with a high percentage of new energy sources under general noise. Firstly, a polymorphic SMG model is constructed, which enables the software-defined functionality of the control strategy and allows heterogeneous distributed generators (DGs) in AC SMGs to exchange packets of different types. Secondly, due to the presence of highly dynamic and high-power loads in the SMGs, a containment-based distributed secondary control strategy is proposed to improve the flexibility of the DG voltage regulation. Then, considering the complexity and diversity of disturbances during ship navigation, general noise is introduced instead of white noise to describe various disturbances. Furthermore, based on the random differential equations (RDEs), the NOS stability of the proposed strategy is proved using Lyapunov theory, which proves the effectiveness of the containment-based distributed secondary control strategy under general noise. And, the containment error is obtained to prove that the voltage and frequency of the system converge to the convex hull spanned by the virtual leaders, ensuring the high quality of the power supply. Finally, the validity of the proposed containment-based strategy is verified by an AC SMG model with four DGs in three cases.

For the containment control problem of unmanned surface ship systems (USSs) with time delay and limited communication bandwidth, this paper proposes a distributed event-triggered control strategy using a joint connection switching topology. The communication of unmanned surface ship systems inevitably has delay and the topology is time-varying. Firstly, a joint connectivity switching topology model and the state control method of USSs with delay are designed. Secondly, an event-triggered control mechanism is established, and a new trigger condition of USSs communication is designed. In case of time delay, the USS updates its information and sends it to its neighboring USSs under time delay, minimizes communication consumption and saves energy, and rapidly converges to the steady state. Based on the Lyapunov method, the stability of the system is analyzed, and the Zeno behavior when event-triggered is excluded. It is proved that under the designed control strategy, if the communication topology is jointly connected in a certain time, the follower USS can converge to the convex hull formed by multiple leader USS within a certain delay range. Finally, the correctness and validity of the conclusions are verified by simulation.