Class Of Second-order Multi-agent Systems Research Articles

Adaptive-Critic-Based Event-Triggered Intelligent Cooperative Control for a Class of Second-Order Constrained Multiagent Systems

An event-based intelligent cooperative control policy is developed in this paper for a class of second-order multiagent systems (MASs). The followers are subject to external disturbances and output constraints, in which the constraint ranges are asymmetric and time-varying. By using one-to-one nonlinear mapping technique to obtain equivalent unconstrained systems and designing a distributed observer to estimate the leader's states, a simplified unconstrained tracking control task is established for each follower. After that, event-driven distributed optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> controllers are designed to mitigate the effects of external disturbances, which are obtained from a set of decoupled Hamilton-Jacobi-Isaacs (HJI) equations, where the proposed event-triggered strategy is dynamic. Aiming at solving the HJI equations more efficiently, an event-based adaptive dynamic programming (ADP) learning algorithm applying only critic neural networks (NNs) is developed. And the critic NN weights are convergent by using stored data under finite excitation condition. Finally, the validity of the developed control scheme is demonstrated by multiple single-link robot arm systems.

Adaptive observer-based event-triggered finite time formation tracking for multi-agent systems with a non-cooperative leader

The event-triggered time-varying formation tracking for a class of second-order multi-agent systems (MASs) subject to a non-cooperative leader is investigated in this paper. First, in the presence of the unknown input of the leader and external disturbances, a distributed observer with adaptive parameters is put forward for followers to estimate the velocity tracking error. Then, based on the estimated tracking error and an auxiliary variable, a finite time formation controller is further constructed, which is updated depending on a pre-designed event-triggered mechanism. As a result, the desired time-varying formation configuration can be realized in finite time with less communication resource consumption. It’s noted that the constructed formation strategy doesn’t rely on any global information and thus is fully distributed. The stability of the controlled multi-agent system is proved rigorously and it’s verified that event-triggered intervals are with a positive lower bound. At last, simulations are carried out to illustrate the effectiveness of the presented algorithm.

Observer-based fixed-time consensus tracking for second-order multi-agent systems with disturbances

This paper researches into a fixed-time consensus tracking problem for a class of second-order multi-agent systems (MASs) subject to external disturbances based on a fixed-time observer. First, we adopt a state observer to change the states of each agent from unknown to known. The observer is designed so that observed states and the leader’s state reach consensus. Second, according to the designed controller, states of each agent and observed states achieve consensus, namely leader-following consensus is realized and the setting time of which is obtained without depending on initial states. By employing Lyapunov stability theory, some sufficient criteria are obtained to achieve fixed-time consensus tracking for second-order MASs with disturbances. Finally, the validity of the design is verified by numerical arithmetic examples.

Optimal Formation Control for Second-Order Multi-Agent Systems With Obstacle Avoidance

Dear Editor, The optimal formation control design problem is studied for a class of second-order multi-agent systems (MASs) with obstacle avoidance. Based on the actor-critic framework, an optimized formation controller is proposed by constructing a novel performance index function. Furthermore, the stability of MAS is proved by constructing the Lyapunov function. The simulation results are provided to depict the effectiveness of the proposed strategies.

Finite-Time Containment Control for Nonlinear Second-Order Multiagent System Under Directed Topology

This article investigates the finite-time containment control for a class of second-order multiagent systems with nonlinear dynamics and external disturbances under fixed directed interaction topology. Due to the existence of nonlinear dynamics and unknown but bounded external disturbances, there is an underlying technical difficulty for the design of containment controller. Furthermore, it is a challenge for the theoretical analysis of finite-time containment control problem due to the asymmetric Laplacian matrix arising from the constraint of one-way directed communication among the agents. In response to the above-mentioned challenges, a finite-time containment control algorithm is proposed. First, the multiagent system is considered with inherent nonlinear dynamics and unknown but bounded external disturbances. Second, the desired containment control protocol is presented under a directed interaction topology. Furthermore, by adding a power-integrator technique and Lyapunov function theory, the sufficient conditions are derived for the existence of the finite-time containment controller of a class of second-order multiagent systems. Finally, a numerical example is given to verify the usefulness of the proposed finite-time containment control protocol.

Sampled-Hold-Based Consensus Control for Second-Order Multiagent Systems Under Aperiodically Intermittent Communication

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

Prescribed finite-time consensus with severe unknown nonlinearities and mismatched disturbances

This paper considers the problem of prescribed finite-time leader-following consensus for a class of second-order multi-agent systems (MAS). Compared to the existing methods, the dynamics of the followers in the proposed method is rather general, containing some severe unknown nonlinearities and mismatched disturbances. First, a time-varying distributed observer is proposed to estimate the leader information in prescribed finite time. The leader is driven by a control input that is unknown to all the followers. Then, a new composite controller with a time-varying disturbance observer is presented. By gracefully combining the barrier Lyapunov functions and logic-based switching rules, we show that the unknown nonlinearities and mismatched disturbances can be well handled. Thus, the prescribed finite-time consensus problem can be solved. Finally, by the properties of Lyapunov functions and time-varying gains, we present a new method to show that the control signals are bounded. A simulation example is provided to verify the effectiveness of the proposed method.

Distributed Adaptive Finite-Time Consensus for Second-Order Multiagent Systems With Mismatched Disturbances Under Directed Networks.

In this paper, the finite-time output consensus problem is considered for a class of second-order multiagent systems (MASs), where the mismatched disturbance exists in the dynamics of each agent, and the communication topology is directed. First of all, a basic backstepping control protocol is proposed to solve the finite-time consensus problem without mismatched disturbance. Then, a finite-time disturbance observer is designed to estimate the mismatched disturbance, based on which, two adaptive finite-time consensus protocols are proposed to solve the finite-time output consensus and tracking consensus problems without using any global information with respect to the communication topology. Finally, two simulation examples are illustrated to verify the theoretical results.

Consensus Formation Control and Obstacle Avoidance of Multiagent Systems with Directed Topology

This study addresses the problems of formation control and obstacle avoidance for a class of second-order multiagent systems with directed topology. Formation and velocity control laws are designed to solve the formation tracking problem. A new obstacle avoidance control law is also proposed to avoid obstacles. Then, the consensus control protocol consists of the formation, velocity, and obstacle avoidance control laws. The convergence of the proposed control protocol is analyzed by a redesigned Lyapunov function. Finally, the effectiveness of theoretical results is illustrated by simulation examples. The simulation results show that the formation tracking problem of the given multiagent systems can be realized and obstacles can be avoided under the proposed control protocol.

Rotating Consensus of Second-Order Multi-Agent Systems with Signed Directed Graphs

This paper investigates the rotating motion control for a class of second-order multi-agent systems with both cooperative and antagonistic interactions. Compared with some existing results, the multi-agent systems are assumed to have a signed directed graph rather than an undirected graph. By using the local relative information, we design a control protocol and give a sufficient condition for rotating consensus problem with antagonistic networks. Furthermore, we derive the lower bound of parameters in the control protocol. Finally, the correctness of our results is confirmed by the simulation results.

Distributed Control for Leader-Following Consensus Problem of Second-Order Multi-Agent Systems and Its Application to Motion Synchronization

This paper solves the leader-following consensus problem for a class of second-order multi-agent systems with input quantized by a newly proposed adaptive dynamic quantizer. The novel dynamic quantizer is an adaptive quantizer that combines the logarithmic quantizer and the uniform quantizer by introducing dynamic gain parameters to achieve quantizer adaptive adjustment. It has advantages of logarithmic, uniform, and adaptive dynamic quantizers in ensuring reducible communication expenses and acceptable quantizer errors for better system performance. On this basis, we transform the guide way climbing frame (GWCF) under ideal conditions into a second-order multi-agent system and solve the motion synchronization problem of GWCF. Finally, we illustrate our approach by numerical examples.

Containment control for second-order nonlinear multi-agent systems with aperiodically intermittent position measurements

In some real systems, the intermittent communications and the inaccurate velocity measurements are usually inevitable. To overcome these two communication limitations, this article aims at investigating the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics and aperiodically intermittent position measurements. Under the case that the velocity information is unavailable, a distributed filter is introduced for each second-order follower. Based on the distributed filter, a novel intermittent containment control protocol without velocity measurements is designed. Some sufficient conditions are derived under the common assumption that only relative position measurements between the neighbouring agents are utilized intermittently, and these conditions ensure that the second-order nonlinear multi-agent systems can achieve containment control. Furthermore, some simpler containment conditions are obtained for multi-agent systems with double-integrator dynamics under aperiodically intermittent communications. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.

Delayed Impulsive Control for Consensus of Multiagent Systems With Switching Communication Graphs

Delayed impulsive controllers are proposed in this paper to enable the agents in a class of second-order multiagent systems (MASs) to achieve state consensus, based, respectively, on the relative full-state and partial-state sampled-data measurements among neighboring agents. It is a challenging task to analyze the consensus behaviors of the considered MASs as the dynamics of such MASs will be subjected to joint effects from delay-dependent impulses, aperiodic sampling, and switchings among different communication graphs. A novel analytical approach, based upon the discretization method, state augmentation, and linear state transformation, is developed to establish the sufficient consensus criteria on the range of the impulsive intervals and the control parameters. Remarkably, it is found that consensus in the closed-loop MASs can be always ensured by skillfully selecting the control parameters as long as the nonuniform delays and the impulsive intervals are bounded. A numerical example is finally performed to validate the effectiveness of the proposed delayed impulsive controllers.

Global finite-time event-triggered consensus for a class of second-order multi-agent systems with the power of positive odd rational number and quantized control inputs

In this paper, we mainly investigate the global finite-time event-triggered consensus problem for a class of second-order multi-agent systems with the power of positive odd rational number and quantized control inputs under directed network topology. Under an appropriate assumption, a novel finite-time event-triggered consensus protocol is proposed to reduce the communication burden from the controller to the actuator. Based on the backstepping method, a synthetic trigger function is derived, and it is proven theoretically that the Zeno behavior is avoided for each agent under this trigger condition. Moreover, to avoid the chattering phenomenon caused by unknown input disturbances, the hysteretic quantizers are incorporated to quantize the input signals. It is shown that the proposed finite-time event-triggered consensus protocol enables the local neighbor position error, and the velocity error between any two agents converges toward a small range of the origin in a finite time. Finally, the proposed method is validated through a numerical example.

Containment control for second-order nonlinear multi-agent systems with intermittent communications

ABSTRACTThis article investigates the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics, under the common assumption that each agent can only obtain the relative information of its neighbours intermittently. A kind of distributed protocol based only on the relative local intermittent measurements of neighbouring agents is designed for containment control under fixed directed topology. In the absence of delays, based on the Lyapunov function technology and the intermittent control method, some sufficient conditions are presented to guarantee the intermittent containment control of second-order nonlinear multi-agent systems. In the presence of delays, some containment conditions are also obtained for a second-order multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Moreover, the similar results are obtained for second-order nonlinear multi-agent systems under switching directed topology. Finally, simulation examples are given to illustrate the correctness and effectiveness of the theoretical analysis.

Adaptive finite-time practical consensus protocols for second-order multiagent systems with nonsymmetric input dead zone and uncertain dynamics

This paper investigates adaptive finite-time practical consensus protocols for a class of second-order multiagent systems with a positive odd power, nonsymmetric input dead zone and uncertain dynamics under a directed communication topology. In this study, three major steps are employed to address the existence of the positive odd power, nonsymmetric input dead zone and uncertain dynamics. Overall, based on the technique of adding one power integrator, useful preliminary results are obtained by configuring a suitable fraction power. Furthermore, to circumvent input dead-zone nonlinearity, an adaptive fuzzy logic (FL) method is used to estimate the width of the dead zone. Finally, the difficulty in designing finite-time practical consensus protocols for the multiagent systems with uncertain dynamics is handled by using radial basis function neural networks (RBFNNs) to approximate the related unknown nonlinear functions. Then, given some reasonable assumptions, it is shown that finite-time practical consensus of the second-order multiagent systems is obtained by using the proposed distributed control protocols and adaptive laws. In addition, the proper approach for selecting parameters is provided such that the neighborhood position error and parameter estimate errors for each agent converge to predesigned small regions of the origin in a finite time. The effectiveness of the developed algorithm is finally validated through a numerical simulation.

Distributed Fault Tolerant Control for Multi-agent Systems with Complex-weighted Directed Communication Topology subject to Actuator Faults

In this paper, under the complex-weighted directed communication topology, the problem of distributed fault tolerant control (FTC) for a class of second-order multi-agent systems (MAS) in the presence of actuator faults is studied. The faults can simultaneously occur in more than one agent. First, a real representation of the secondorder dynamic agent with the complex weighted graph is proposed. Second, based on the proposed representation, distributed finite-time convergent observer is proposed for each agent to estimate the state and fault in a finite time. Then, using the fault information obtained online, an adaptive FTC protocol is proposed to compensate for the failure effects and to enable all the agents to achieve the control goal. Also, we show that the closed-loop system can be guaranteed to be asymptotically stable in the presence of faults. Finally, an illustration example is given to demonstrate the effectiveness of the proposed scheme.

Extended adaptive event-triggered formation tracking control of a class of multi-agent systems with time-varying delay

Abstract This paper considers the adaptive event-triggered formation tracking control of a class of second-order multi-agent systems (MASs) with time-varying delay. Firstly, a distributed control protocol is constructed and some extended adaptive event-triggered schemes are presented, where the triggering thresholds rely on the real-time variation of the MASs but not not pre-selected constants. Then by choosing an augmented Lyapunov–Krasovskii functional (LKF), two delay-dependent criteria are formulated in terms of linear matrix inequalities (LMIs). Especially, during estimating the upper bound on LKF’s derivative, since some novel integral inequalities and a new convex technique are utilized, the conservatism can be greatly reduced. Finally, two numerical examples with some simulations are provided to illustrate our methods.

Robust consensus control for a class of second-order multi-agent systems with uncertain topology and disturbances

Abstract In the paper, the robust consensus control is investigated for a class of second-order multi-agent systems with time-varying interaction topology and disturbances. Firstly, due to the variation considered being bounded, the topology is modeled as time-varyingly uncertain topology with polytopic type. Then, regarding the uncertain parameters as independent variables and formulating the multi-agent system as a special polynomial system, the robust consensus problem is converted to the robust stability analysis of the error model via stability theory of control systems. Furthermore, the idea is generalized to study the disturbance attenuation problem. Sufficient conditions for the solutions to the robust consensus problems without and with disturbance attenuation are formulated in terms of homogeneous parameter-dependent linear matrix inequalities (HPD-LMIs) which can be solved via semidefinite programming relaxations based on the sum of squares technique. Finally, simulation results are provided to illustrate the effectiveness of the approach.

A further result on consensus problems of second-order multi-agent systems with directed graphs, a moving mode and multiple delays

This paper considers a consensus problem of a class of second-order multi-agent systems with a moving mode and multiple delays on directed graphs. Using local information, a distributed algorithm is adopted to make all agents reach a consensus while moving together with a constant velocity in the presence of delays. To study the effects of the coexistence of the moving mode and delays on the consensus convergence, a frequency domain approach is employed through analyzing the relationship between the components of the eigenvector associated with the eigenvalue on imaginary axis. Then based on the continuity of the system function, an upper bound for the delays is given to ensure the consensus convergence of the system. A numerical example is included to illustrate the obtained theoretical results.