Containment Control Problem Research Articles

Nonfragile containment control of nonlinear multi‐agent systems via a disturbance observer‐based approach

AbstractIn 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.

Formula omitted] containment control for multi-unmanned aerial vehicle systems: A self-triggered control scheme

This paper is concerned with the containment control problem for multi-unmanned aerial vehicle (multi-UAV) systems with data transmission among agents during a limited-bandwidth network. A good deal of data transmitted during a limited-bandwidth network may result in data collision, which brings negative effects on controller design and containment tracking implementation. To reduce the network load during data transmission, a consensus condition and a triggering subsidiary condition are first proposed to realize the containment tracking with H∞ performance by using the triggered states. Then a self-triggered scheme is established under a multi-agent framework, in which the next triggering instant is calculated beforehand by using the past states. Combined with the self-triggered scheme, a containment controller is obtained via solving the derived consensus condition, which ensures that follower UAVs are driven into a convex set surrounded by leader UAVs. Finally, the validity of the self-triggered containment control method is proved through a simulation experience.

Adaptive fixed-time containment control of uncertain underactuated underwater vehicles under dynamic event-driven mechanism

This paper presents a dynamic event-driven fixed-time design strategy for the three-dimensional containment control of underactuated underwater vehicles under a directed topology. Our main contribution is the development of a novel error transformation approach based on adaptive multi-leader estimation to address the fixed-time containment (FTC) control problem in the presence of underactuation input and unknown leaders’ velocity. An adaptive FTC control law using stabilizing auxiliary variables and nonlinear filters is constructed based on event-driven conditions. The dynamic thresholds, which depend on containment errors, are presented to efficiently reduce communication resources required for implementing the FTC controller. According to Lyapunov theory, it is shown that the trajectories of the followers converge to the convex hull spanned by multiple leader signals within a fixed time while ensuring the avoidance of the Zeno phenomenon. Finally, the effectiveness of the suggested control approach is verified through simulation results.

Distributed Fuzzy Containment Control for Stochastic Nonlinear Multiagent Systems Under Denial-of-Service Attacks

The paper investigates distributed fuzzy adaptive containment control problem of stochastic nonlinear multi-agent systems under an directed communication topology suffering Denial-of-Service (DoS) attacks. Firstly, considering unknown stochastic disturbance and nonlinear characteristics for the followers, the mathematical models are modeled as It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\hat{o}$</tex-math></inline-formula> stochastic nonlinearities terms approximated through fuzzy logic systems (FLS). Secondly, the proposed dynamically adjusted event-triggered condition can effectively avoid inefficient transmission behavior. Moreover, an adaptive compensation protocol for input saturation is constructed to eliminate the effects of nonlinearities caused by input saturation. Finally, instead of the previous uniformly ultimately bounded containment control results, stability and asymptotic performance are guaranteed through valid reasonable adaptive control laws acquired through backstepping control approach despite suffers DoS cyber attacks. Moreover, a simulation is given to verify the feasibility of the proposed method.

Observer-based distributed convex optimization of bipartite containment control for higher order nonlinear uncertain multi-agent systems

This paper studies the distributed convex optimization of bipartite containment control problem for a class of higher order nonlinear multi-agent systems with uncertain states. For the optimization problem, the penalty function is constructed by summing the local objective function of each agent and combining the penalty term formed by the adjacency matrix. For the unknown nonlinear function and unpredictable states in the system, this paper construct radial basis function Neural-networks and state observer for approaching, respectively. In order to avoid “explosion of complexity,” under the framework of Lyapunov function theory, we propose the dynamic surface control (DSC) technology and design the distributed adaptive backstepping neural network controller to ensure all the signals remain semi-global uniformly ultimately bounded in the closed-loop system and all agents can converge to the convex hull containing each boundary trajectory as well as its opposite trajectory different in sign. Simulation results confirm the feasibility of the proposed control method.

Fixed-time containment control for nonlinear multi-agent systems via dynamic event-triggered mechanism over directed graphs

This paper focus on a dynamic event-triggered mechanism to solve fixed-time containment control problems for nonlinear multi-agent systems (MASs) with uncertain disturbances over directed graphs. An event-triggered algorithm based on dynamic variables is proposed to achieve the fixed-time containment control of MASs, which can effectively reduce the number of event-triggered instants. By modifying the auxiliary variables and reconstructing the dynamic variables, the effect of input time-delays in MASs is successfully eliminated. It is noteworthy that only the auxiliary variables are modified while the structure of the dynamic variables is not changed, which further indicates that the designed dynamic event-triggered algorithm is also suitable for solving multi-agent systems with input time-delays. In addition, the setting time associated with the time-delays is also computed and the Zeno behavior is successfully avoided by computing the minimum time interval between event triggering as non-negative. Finally, simulation results are given to verify the effectiveness of proposed control protocol.

Adaptive prescribed-time containment control for multiple unmanned surface vehicles with uncertain dynamics and actuator dead-zones

This paper investigates the containment control problem of multiple unmanned surface vehicles (USVs) with directed communication topology. The unknown dynamics, external disturbances and actuator dead-zones of each USV are taken into account. Firstly, an event-triggered quantized (ETQ) control strategy and an improved prescribed-time control technique are combined, such that a balance is achieved between reducing the channel burden and ensuring control performance. Then, with the aid of backstepping method, finite-time differentiators, neural networks and parametric adaptive techniques, a fully-distributed adaptive containment controller is developed. The idea of single-parameter learning and estimating the upper bound of disturbances greatly reduce the calculation of the controller. Importantly, the degradation of the control performance caused by saving channel resources and reducing calculation is not worth worrying about, thanks to the performance prescribed control scheme. It is proved that all signals in the closed-loop system are bounded and the containment error of the multi-USV system is semi-globally practically finite-time stable. Finally, the effectiveness of the proposed controller was verified by simulations of 1:70 scale ship models.

Adaptive Neural Network Event-Triggered Output-Feedback Containment Control for Nonlinear MASs With Input Quantization.

This article investigates the adaptive neural network (NN) event-triggered containment control problem for a class of nonlinear multiagent systems (MASs). Since the considered nonlinear MASs contain unknown nonlinear dynamics, immeasurable states, and quantized input signals, the NNs are adopted to model unknown agents, and an NN state observer is established by using the intermittent output signal. Subsequently, a novel event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels are established. By decomposing quantized input signals into the sum of two bounded nonlinear functions and based on the adaptive backstepping control and first-order filter design theories, an adaptive NN event-triggered output-feedback containment control scheme is formulated. It is proved that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) and the followers are within a convex hull formed by the leaders. Finally, a simulation example is given to validate the effectiveness of the presented NN containment control scheme.

Fully Distributed, Event-Triggered Containment Control of Multi-Agent Systems Based on Wireless Sensor Networks and Time Base Generators

In this study, wireless sensor networks and time base generators are used to solve the fixed-time containment control problem in multi-agent systems with fixed topologies. A new event-triggered control protocol is proposed, which combines a fully distributed method and a time base generator (TBG). The goal is to converge the states of all followers to the convex hull formed by the leader. The controller reduces communication and improves control efficiency by integrating a fully distributed control mechanism using wireless sensor networks. In addition, a time base generator (TBG) is added to ensure that the dwell time continues to be pre-specified and independent of initial conditions. Using matrix theory, the original system is transformed into an error system, and its stability is analyzed by the Lyapunov method. The necessary and sufficient conditions for solving the time consensus containment control problem in multi-agent systems are determined and Zeno behavior is avoided. The effectiveness of the proposed control algorithm is illustrated by numerical examples.

Non-singular fixed-time robust containment control for autonomous surface vehicles

For the containment control problem of autonomous surface vehicles with external disturbances, a novel non-singular fixed-time control scheme is developed, where the multi-ship system consists of real leaders and followers. In contrast with traditional containment cases studied in most of the existing literature, real leaders are required to track the desired trajectories, and the followers need to get into the convex hull spanned by the real leaders in a fixed time. The method for solving the fixed-time containment control problem is divided into the following steps: Firstly, a fixed-time disturbance observer is designed to estimate the external disturbance for the leaders and the followers, and the estimation result is used to compensate for the input of the control system; Second, combined with fixed-time stability theory and a switch function, a non-singular fixed-time trajectory tracking controller for leaders is designed, such that the position tracking error could be bounded within a fixed time; Third, to achieve formation efficiently, a non-singular fixed-time containment controller strategy incorporating with graph theory is proposed for coordinating followers, such that the fixed-time stability can be ensured. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method.

Neural-Network-Based Finite-Time Bipartite Containment Control for Fractional-Order Multi-Agent Systems.

This article focuses on the adaptive bipartite containment control problem for the nonaffine fractional-order multi-agent systems (FOMASs) with disturbances and completely unknown high-order dynamics. Different from the existing finite-time theory of fractional-order system, a lemma is developed that can be applied to actualize the aim of finite-time bipartite containment for the considered FOMASs, in which the settling time and convergence accuracy can be estimated. Via applying the mean-value theorem, the difficulty of the controller design generated by the nonaffine nonlinear term is overcome. A neural network (NN) is employed to approximate the ideal input signal instead of the unknown nonaffine function, then a distributed adaptive NN bipartite containment control for the FOMASs is developed under the backstepping structure. It can be proved that the bipartite containment error under the proposed control scheme can achieve finite-time convergence even though the follower agents are subjected to completely unknown dynamic and disturbances. Finally, the feasibility and validity of the obtained results are exhibited by the simulation examples.

Optimal containment control for a class of heterogeneous multi‐agent systems with actuator faults

AbstractThis article investigates the optimal containment control problem for a class of heterogeneous multi‐agent systems with time‐varying actuator faults and unmatched disturbances based on adaptive dynamic programming. Since there exist unknown input signals in each leader, distributed observers are utilized to estimate trajectories in the convex hull spanned by leaders. The containment control problem is then transformed into an optimal tracking problem. To compensate for the actuator faults and unmatched disturbances, a novel performance index function is designed. We prove that the optimal control policy can ensure that the tracking error system of each follower is uniformly ultimately bounded. The online policy iteration algorithm is implemented using critic neural networks to obtain the optimal control policy. A numerical example is provided to demonstrate the effectiveness of the proposed control policy.

Second‐order extended state observers‐based adaptive event‐triggered containment control for nonlinear multiagent systems with mismatched stochastic disturbances

SummaryThis article investigates the event‐triggered containment control problem for nonlinear multiagent systems with mismatched stochastic disturbances. A set of second‐order extended state observers (ESOs) is constructed to solve the problem of bounded stochastic disturbances. The observers are able to estimate the disturbances in each control input channel in real‐time and solve the problem of stochastic disturbances path non‐differentiability. Based on backstepping technique, adaptive controllers are designed to ensure that the output of the followers converge to the convex hull formed by the leaders. Moreover, a simplified event‐triggered threshold condition is designed, which effectively reduces the update frequency of the controller and the complexity of threshold condition. Based on the Lyapunov stability theorem, it is proved that all signals in the closed‐loop systems are the practically bounded. Finally, the effectiveness of the proposed control scheme is verified by simulation results.

IT2 fuzzy adaptive containment control for fractional-order heterogeneous multi-agent systems with input saturation

In this paper, the containment control problem of second-order nonlinear heterogeneous multi-agent system is studied. In order to deal with complex uncertainties such as unknown parts, uncertainties, and input constraints in the system, we designed a distributed fuzzy adaptive controller. The interval type-II (IT2) fuzzy set is adopted to deal with the uncertainty of membership functions. We construct a matrix equality and a matrix inequality to deal with the asymmetric Laplace matrix. The controller designed is simple and the designed controller only uses the information of itself and its neighbors. Therefore, it is very easy to be compensated in practice. Finally, a simulation example is introduced to verify the effectiveness of the proposed methods.

Bearing‐only containment control of multi‐agent systems

AbstractBearing‐only containment control means to achieve containment using only the bearing information, rather than the complete relative position information including both the bearing and the distance. Compared with the most existing relative position based containment control algorithms, the bearing‐only containment control algorithm is nonlinear due to the nonlinearity of the bearing, which renders the stability analysis challenging. In this article, the bearing‐only containment control problem of multi‐agent systems with dynamically changing topologies is investigated for two cases, where the leaders are stationary or dynamic. First, when the leaders are stationary, it is shown that the nonlinearity of the bearing leads to the unknown nonlinear time‐varying parameters in the system. Based on the boundedness of the nonlinear parameters and the connectivity of the switching directed sensing graphs, it is proven that all the followers converge to the stationary convex hull formed by the leaders asymptotically. Second, when the leaders are dynamic, a distributed estimator is proposed for each follower to keep a local estimate of the velocity of the leaders. Based on the optimality of the projection and the shift invariance of the normal cone, it is proven that all the followers converge to the dynamic convex hull formed by the leaders asymptotically under the conditions on the switching directed sensing and communication graphs. It is shown from the two cases that the distance information is not necessary for containment control, and containment can be achieved as long as the bearing information is provided. Numerical examples are presented to illustrate the theoretical results.

Output containment control in heterogeneous multi-agent systems without exchange of controller states

In this paper, we propose an observer-based distributed protocol for solving the output containment problem in linear heterogeneous multi-agent systems under the external disturbances. The distinct feature of the proposed protocol is that it does not require exchange of the internal controller states, which significantly reduces or completely eliminates communication burden. A sufficient local stability condition is derived and a novel controller design procedure is proposed based on tools from H∞ theory and algebraic Riccati equations. An extensive solvability analysis of the output containment control problem under the proposed protocol is carried out and theoretical guarantees for the existence of a solution for a wide class of agents’ dynamics and graph topologies are established. Numerical simulations that demonstrate the effectiveness of the proposed protocol are performed.

Team-based fixed-time containment control for multi-agent systems with disturbances

We investigate the fixed-time containment control (FCC) problem of multi-agent systems (MASs) under discontinuous communication. A saturation function is used in the controller to achieve the containment control in MASs. One difference from using a symbolic function is that it avoids the differential calculation process for discontinuous functions, which further ensures the continuity of the control input. Considering the discontinuous communication, a dynamic variable is constructed, which is always non-negative between any two communications of the agent. Based on the designed variable, the dynamic event-triggered algorithm is proposed to achieve FCC, which can effectively reduce controller updating. In addition, we further design a new event-triggered algorithm to achieve FCC, called the team-trigger mechanism, which combines the self-triggering technique with the proposed dynamic event trigger mechanism. It has faster convergence than the proposed dynamic event triggering technique and achieves the tradeoff between communication cost, convergence time and number of triggers in MASs. Finally, Zeno behavior is excluded and the validity of the proposed theory is confirmed by simulation.

Learning‐based containment control in the absence of leaders' information

AbstractThis article considers the containment control problem of continuous‐time dynamic agents without leaders' state information. The leaders have first‐ and second‐order dynamics, respectively, while first‐order dynamics always govern the followers. Each agent has inherent nonlinear dynamics and can only measure the output information of its neighbors. The output of each leader is expressed as the product of an unknown coefficient and a position‐like state, while the output of each follower is equal to its position‐like state. To stabilize the position‐like states of the followers to the convex hull spanned by leaders, the unknown coefficients are asymptotically tracked by leveraging reinforcement learning based on the inherent dynamics and the output information. Two distributed learning‐based containment protocols are proposed, respectively. It is proved that if the directed communication topology has a spanning forest and certain conditions in terms of the inherent nonlinear dynamics are satisfied, then the proposed controllers with proper control gains solve the containment control problem asymptotically under arbitrary initial states. An exciting conclusion is that the learning algorithms' convergence rate plays an important role in achieving containment control. Numerical simulations are performed to validate the effectiveness of the obtained theoretical results.

Distributed Fault-Tolerant Containment Control Protocols for the Discrete-Time Multiagent Systems via Reinforcement Learning Method.

This article investigates the model-free fault-tolerant containment control problem for multiagent systems (MASs) with time-varying actuator faults. Depending on the relative state information of neighbors, a distributed containment control method based on reinforcement learning (RL) is adopted to achieve containment control objective without prior knowledge on the system dynamics. First, based on the information of agent itself and its neighbors, a containment error system is established. Then, the optimal containment control problem is transformed into an optimal regulation problem for the containment error system. Furthermore, the RL-based policy iteration method is employed to deal with the corresponding optimal regulation problem, and the nominal controller is proposed for the original fault-free system. Based on the nominal controller, a fault-tolerant controller is further developed to compensate for the influence of actuator faults on MAS. Meanwhile, the uniform boundedness of the containment errors can be guaranteed by using the presented control scheme. Finally, numerical simulations are given to show the effectiveness and advantages of the proposed method.

Event‐triggered containment control for multi‐agent systems under hybrid cyber attacks

AbstractThis paper studies event‐triggered containment control problem of multi‐agent systems (MASs) under deception attacks and denial‐of‐service (DoS) attacks. First, to save limited network resources, an event‐triggered mechanism is proposed for MASs under hybrid cyber attacks. Different from the existing event‐triggered mechanisms, the negative influences of deception attacks and DoS attacks are considered in the proposed triggering function. The communication frequencies between agents are reduced. Then, based on the proposed event‐triggered mechanism, a corresponding control protocol is proposed to ensure that the followers will converge to the convex hull formed by the leaders under deception attacks and DoS attacks. Compared with the previous researches about containment control, in addition to hybrid cyber attacks being considered, the nonlinear functions related to the states of the agents are applied to describe the deception attack signals in the MAS. By orthogonal transformation of deception attack signals, the containment control problem under deception attacks and DoS attacks is reformulated as a stability problem. Then, the sufficient conditions on containment control can be obtained. Finally, a set of simulation example is used to verify the effectiveness of the proposed method.