Bipartite Formation Research Articles

Bipartite formation control of second-order multi-agent systems with antagonistic interactions under dynamic event-triggered adaptive schemes

This article examines the adaptive leader-following bipartite formation (LBF) of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions over a directed signed graph. To save the scarce communication resources efficiently, a novel distributed controller is designed for the LBF of the MASs, where a dynamic event-triggered (DET) control protocol with dynamic parameters is proposed. Meanwhile, the optimal control gains for realizing adaptive bipartite formation are obtained in accordance with the designed adaptive updating laws. By employing the DET mechanism and the Lyapunov functionals in conjunction, sufficient criteria for the adaptive LBF of the second-order MASs with antagonistic interactions and a directed signed graph are obtained. Furthermore, it has been demonstrated that Zeno phenomenon doesn't exist. Finally, the efficacy of the theoretical outcomes and the control protocol is validated through a numerical simulation.

Observer-based guaranteed-cost bipartite time-varying formation tracking control for multiagent systems subject to communication delays

The paper centers on the guaranteed-cost bipartite time-varying formation tracking control for multiagent systems with nonuniform time-varying communication delays under the framework of a distributed observer. An integral quadratic cost function is presented, founded on formation tracking and observation error. Firstly, distributed state observers, using the relative measurement output between neighbors, are established so that the leader and follower can accurately estimate each agent's unmeasurable state. Subsequently, a bipartite formation tracking protocol is proposed, incorporating estimation information and nonuniform time-varying communication delays. This protocol aims to achieve bipartite time-varying formation tracking for multiagent systems. Next, a new augmented Lyapunov-Krasovskii functional with delay-product and triple integral terms is constructed. By integrating the second-order Bessel-Legendre inequality technique, the delay-dependent reciprocally convex combination inequality method, and the free weight matrix technique, a new guaranteed-cost bipartite time-varying formation tracking criterion is developed, offering less conservatism. Compared to certain existing delay conditions, the stability conditions assure a greater allowable upper bound of delay. Finally, a numerical example is conducted to confirm the validity and superiority of the theoretical findings.

Observer‐based adaptive time‐varying bipartite formation tracking of multi‐agent systems with multiple nonautonomous leaders

AbstractIn this article, the problem of bipartite time‐varying formation (BTVF) tracking for multi‐agent systems (MASs) under signed digraphs is investigated, in which the inputs of leaders are unknown and bounded. A novel kind of adaptive nonsmooth BTVF tracking protocol for MASs is proposed that did not utilize eigenvalue of Laplacian matrix. Based on the state observer, the problem that the system states are not measurable is solved. In addition, in order to avoid undesirable chattering caused by leaders' nonzero inputs, continuous protocols are proposed. And in this case, the error is uniformly ultimately bounded. Lyapunov method reflects the convergence analysis of the submitted protocols. At last, the desired theoretical results are achieved on a multirobot system.

Multi-AUV heterogeneous bipartite consensus formation obstacle avoidance algorithm based on event triggering-RMPC under measurement-communication union framework

This paper investigates a robust model predictive control-based event triggering (ET-RMPC) for heterogeneous autonomous underwater vehicle (AUV) bipartite consensus formation in obstacle avoidance. Firstly, a scheme of heterogeneous AUV bipartite formation control base on signed graph theory and implicit interactive measure-communication union framework is proposed. Next, a RMPC based on the proposed framework for heterogeneous AUV bipartite consensus formation is designed. Additionally, to alleviate the computational burden, a novel event-triggering mechanism is devised based on the error between the estimated state and actual state of the AUV formation trajectory. Then, the stability of the system and the upper and lower bounds of the trigger interval are analyzed based on innovation and Lyapunov theory. Finally, the effectiveness of the proposed method is validated through bipartite consensus formation tracking and obstacle avoidance scenarios.

Parameter variational based adaptive bipartite formation control of second-order multi-agent systems with antagonistic interactions

This article mainly concentrates on researching the leader-following bipartite formation of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions and time-varying delay. A novel distributed feedback control and impulsive control strategy is proposed for realizing the bipartite formation. By establishing an error system, the bipartite formation issue of the MASs is transformed into the stability issue of the error systems. Sufficient conditions for achieving the bipartite formation of second-order nonlinear MASs are obtained by jointly employing the extended parameters variation formula, the comparison principle and the definition of average impulsive interval. In addition, in order to obtain the optimal control gains and control effects, an adaptive control strategy is taken into account by designing the adaptive updating laws. Ultimately, the effectiveness of the theoretical results is demonstrated by two numerical simulations.

Neural network-based predefined-time bipartite formation tracking control of uncertain heterogeneous Euler–Lagrange systems in task space

The main problem addressed in this paper is the task-space bipartite formation tracking problem of uncertain heterogeneous Euler–Lagrange systems in predefined time. To solve this problem, an effective hierarchical predefined-time control algorithm is designed. This algorithm utilizes a non-singular sliding surface, allowing for the adjustment of the upper bound of the settling time as a flexible parameter. Key components of the proposed approach include an estimator for the leader’s states and a controller tailored to the formation problem. To mitigate the effects of dynamic uncertainties in the system, the radial basis function neural network is integrated into the methodology. Finally, the effectiveness and validity of the proposed algorithm are demonstrated through numerical simulations, showcasing their practical applicability and efficacy.

Fault-Tolerant Cooperative Bipartite Formation Tracking of Multiagent Systems on Signed Directed Networks With Actuator Faults

Fault-Tolerant Cooperative Bipartite Formation Tracking of Multiagent Systems on Signed Directed Networks With Actuator Faults

Bipartite Formation Control of Nonlinear Multi-Agent Systems with Fixed and Switching Topologies under Aperiodic DoS Attacks

This paper concentrates on bipartite formation control for nonlinear leader-following multi-agent systems (MASs) with fixed and switching topologies under aperiodic Denial-of-Service (DoS) attacks. Firstly, distributed control protocols are proposed under the aperiodic DoS attacks based on fixed and switching topologies. Then, considering control gains, as well as attack frequency and attack length ratio of the aperiodic DoS attacks, using algebraic graph theory and the Lyapunov stability method, some criteria are acquired to ensure that the nonlinear leader-following MASs with either fixed or switching topologies can realize bipartite formation under aperiodic DoS attacks. Finally, numerical simulations are carried out to validate the correctness of the theoretical results.

Optimized bipartite formation control for multiagent systems with obstacle and collision avoidance

This paper considers an optimal bipartite formation control problem for high-order nonlinear multiagent systems (MASs) with the consideration of obstacle/collision avoidance. Contrary to existing literature, the control strategy designed in this paper can render the agents in a bipartite formation to complete the obstacle/collision avoidance tasks without requiring the obstacles to be located on the coordinate axis. To save resources, an identifier-critic-actor-based optimized formation control scheme is designed for MASs. An obstacle/collision avoidance approach based on dynamical systems (DS) is designed for high-order nonlinear MASs. Different from the existing related results, the proposed DS-based obstacle/collision avoidance approach can avoid the phenomenon that the control quantities approach infinity near obstacles or other agents, and eliminate the dependence on global information. Finally, a simulation example is given to validate the proposed control method.

Observers Efficiently Extract the Minimal and Maximal Element in Perceptual Magnitude Sets: Evidence for a Bipartite Format.

The mind represents abstract magnitude information, including time, space, and number, but in what format is this information stored? We show support for the bipartite format of perceptual magnitudes, in which the measured value on a dimension is scaled to the dynamic range of the input, leading to a privileged status for values at the lowest and highest end of the range. In six experiments with college undergraduates, we show that observers are faster and more accurate to find the endpoints (i.e., the minimum and maximum) than any of the inner values, even as the number of items increases beyond visual short-term memory limits. Our results show that length, size, and number are represented in a dynamic format that allows for comparison-free sorting, with endpoints represented with an immediately accessible status, consistent with the bipartite model of perceptual magnitudes. We discuss the implications for theories of visual search and ensemble perception.

Data-based bipartite formation control for multi-agent systems with communication constraints.

This article investigates data-driven distributed bipartite formation issues for discrete-time multi-agent systems with communication constraints. We propose a quantized data-driven distributed bipartite formation control approach based on the plant's quantized and saturated information. Moreover, compared with existing results, we consider both the fixed and switching topologies of multi-agent systems with the cooperative-competitive interactions. We establish a time-varying linear data model for each agent by utilizing the dynamic linearization method. Then, using the incomplete input and output data of each agent and its neighbors, we construct the proposed quantized data-driven distributed bipartite formation control scheme without employing any dynamics information of multi-agent systems. We strictly prove the convergence of the proposed algorithm, where the proposed approach can ensure that the bipartite formation tracking errors converge to the origin, even though the communication topology of multi-agent systems is time-varying switching. Finally, simulation and hardware tests demonstrate the effectiveness of the proposed scheme.

Event-Triggered Distributed Data-Driven Iterative Learning Bipartite Formation Control for Unknown Nonlinear Multiagent Systems.

In this study, we investigate the event-triggering time-varying trajectory bipartite formation tracking problem for a class of unknown nonaffine nonlinear discrete-time multiagent systems (MASs). We first obtain an equivalent linear data model with a dynamic parameter of each agent by employing the pseudo-partial-derivative technique. Then, we propose an event-triggered distributed model-free adaptive iterative learning bipartite formation control scheme by using the input/output data of MASs without employing either the plant structure or any knowledge of the dynamics. To improve the flexibility and network communication resource utilization, we construct an observer-based event-triggering mechanism with a dead-zone operator. Furthermore, we rigorously prove the convergence of the proposed algorithm, where each agent's time-varying trajectory bipartite formation tracking error is reduced to a small range around zero. Finally, four simulation studies further validate the designed control approach's effectiveness, demonstrating that the proposed scheme is also suitable for the homogeneous MASs to achieve time-varying trajectory bipartite formation tracking.

Formation Control of Cooperative-Competitive Robot Manipulators with Inter-agent Constraints

This paper addresses the distributed formation control problem of networked robot manipulators in end-effector coordinates. We propose a distributed bipartite formation controller that guarantees collision avoidance and maximum distance maintenance for cooperative and competitive manipulators’ end-effectors. In the considered setting, two groups of manipulators are formed and reach bipartite consensus. On the other hand, the end-effectors in the same group achieve formation. We design a gradient-based control law using barrier-Lyapunov functions to ensure that the constraints on the end-effectors are satisfied. Moreover, we establish asymptotic stability of the bipartite formation manifold. Finally, we illustrate our theoretical results via numerical simulations.

Fully Distributed Bipartite Formation Control for Stochastic Heterogeneous Multi-Agent Systems Under Signed Markovian Switching Topology

Fully Distributed Bipartite Formation Control for Stochastic Heterogeneous Multi-Agent Systems Under Signed Markovian Switching Topology

Adaptive Event-Triggered Time-Varying Output Bipartite Formation Containment of Multiagent Systems Under Directed Graphs.

The time-varying output bipartite formation containment (TVOBFC) problem for linear multiagent systems (MASs) under directed graphs is an important problem. However, the methods in existing works rely on the global information of the MASs or do not use event-triggered communication. This article investigates two kinds of TVOBFC problems for heterogeneous linear MASs under signed digraphs by event-triggered communication. For the first case where leaders have the same dynamics, the innovative fully distributed event-triggered protocol for the follower is proposed. In this case, the followers form the preset formation shape. For the second case where leaders have different dynamics, the leaders are divided into two groups. One group can directly obtain the output information of the virtual leader, while the other group cannot. In order to make leaders achieve the formation shape and track the virtual leader, two kinds of innovative observers are designed for two kinds of leaders to estimate the state of the virtual leader, and the control protocol is designed for each leader based on the designed observers. Then, the control law for each follower is designed to solve the formation containment problem. Finally, two examples are introduced to illustrate the main results.

Prescribed‐time adaptive bipartite time‐varying formation tracking for multiple Lagrangian systems with arbitrary disturbance

SummaryThis article focuses on the problem of bipartite time‐varying formation tracking for multiple Lagrangian systems with prescribed‐time adaptive sliding mode under the signed digraph. First, for each Lagrangian system, the local prescribed‐time disturbance estimator is proposed to estimate arbitrary disturbances in the prescribed time with the condition of bounded disturbances. Then the distributed prescribed‐time observers are designed to observe the position and velocity of the leader, and the consensus problem is transformed into bipartite formation tracking via introducing above observers. Based on designing two types of observers and disturbance estimators, a new prescribed‐time adaptive sliding mode controller is designed to ensure the tracking errors of the sliding mode surface converge to origin in a prescribed time. Ultimately, the feasibility of the provided results is further demonstrated through numerical simulation.

Fully Distributed Dynamic Event-Triggered Bipartite Formation Tracking for Multiagent Systems With Multiple Nonautonomous Leaders.

Considering that cooperative interactions and antagonistic interactions between neighboring agents may exist simultaneously in practice, this article studies the bipartite time-varying output formation tracking (BTVOFT) problems for homogeneous/heterogeneous multiagent systems with multiple nonautonomous leaders under switching communication networks. First, a full-dimensional observer-based nonsmooth distributed dynamic event-triggered (DDET) output feedback control scheme is proposed to ensure that BTVOFT is achieved, and the Zeno behavior is excluded. Note that the nonsmooth distributed control scheme requires global communication network information and may cause unexpected chattering effect, and the design cost of full-dimensional observer is relatively high. Thus, a reduced-dimensional observer-based continuous fully DDET scheme is proposed. Compared with the existing event-triggered schemes, the dynamic event-triggered scheme can ensure larger interevent times by introducing an additional internal dynamic variable. Finally, the effectiveness and performance of the theoretical results are validated by numerical simulations.

Distributed global adaptive bipartite consensus of multi-agent systems with signed communication topology structure

This paper focuses on designing a fully distributed adaptive fuzzy bipartite consensus control protocol for unknown nonlinear multi-agent systems with a class of undirected signed graph. Utilizing the fuzzy logical system universal approximator as a compensator to describe the uncertain nonlinear dynamics, a fully distributed adaptive fuzzy control protocol is proposed by means of re-parameterized approach and bounding technique, the global bipartite consensus of leader-following multi-agent systems without using any dynamics of the leader is proven via constructing a new Lyapunov function. The proposed protocol overcomes the drawback of the semi-global consensus in existing literature. Furthermore, as an extension of the former result, a bipartite formation control problem is also solved. Finally, the proposed methods are validated by simulation examples.

Data-Driven Bipartite Formation for a Class of Nonlinear MIMO Multiagent Systems.

The bipartite formation control for the nonlinear discrete-time multiagent systems with signed digraph is considered in this article, in which the dynamics of the agents are completely unknown and multi-input multi-output (MIMO). First, the unknown nonlinear dynamic is converted into the compact-form dynamic linearization (CFDL) data model with a pseudo-Jacobian matrix (PJM). Based on the structurally balanced signed graph, a distance-based formation term is constructed and a bipartite formation model-free adaptive control (MFAC) protocol is designed. By employing the measured input and output data of the agents, the theoretical analysis is developed to prove the bounded-input bounded-output stability and the asymptotic convergence of the formation tracking error. Finally, the effectiveness of the proposed protocol is verified by two numerical examples.

Self-triggered Bipartite Formation-Containment Control for Heterogeneous Multi-agent Systems with Disturbances

The design of the bipartite formation containment tracking for heterogeneous multi-agent systems is discussed in the present paper. The external disturbances are considered in the agent dynamic systems and the all state vectors are inaccessible. Therefore, unknown input observers are constructed for the followers to obtain the state and the disturbance estimates using an interval observer. Then to achieve the formation containment control, an event-triggered compensator state system is constructed for each follower using information from its neighbours to obtain the estimation of the convex hull formed by the output vectors of the leaders where Zeno behaviour is also excluded. Finally, a self-triggered protocol is proposed so that the triggering instants can be calculated locally to realize a fully distribute formation containment control. The performances of the presented method are demonstrated by the simulation of formation containment control for a heterogeneous MAS with a group of vehicles and unmanned aerial vehicles.