Closed-loop Multi-agent Systems Research Articles

A Novel Distributed Adaptive Controller for Multi-Agent Systems with Double-Integrator Dynamics: A Hedging-Based Approach

In this paper, we focus on designing a model reference adaptive control-based distributed control law to drive a set of agents with double-integrator dynamics in a leader–follower fashion in the presence of system anomalies such as agent-based uncertainties, unknown control effectiveness, and actuator dynamics. In particular, we introduce a novel hedging-based reference model with second-order dynamics to allow an adaptation in the presence of actuator dynamics. We show the stability of the overall closed-loop multi-agent system by utilizing the Lyapunov Stability Theory, where we analyze the stability condition by using the Linear Matrix Inequalities method to show the boundedness of the reference model and actuator states. Finally, we illustrate the efficacy of the proposed distributed adaptive controller on an undirected and connected line graph in five cases.

Output feedback containment fuzzy control for multi-agent systems with quantitative input and tunable reference signals

For multi-agent systems with quantitative input, we propose a novel containment control scheme to guarantee that the agents can enter a convex hull generated by the leader's signals after starting from any initial position. The problem with existing schemes is that the reference signals of the agents are affected by the communication topology such that the position of the reference signal cannot be changed when this communication topology is determined. To solve this problem, the proposed scheme can generate a flexible and adjustable reference signal for each agent. This has the advantage of reducing the probability of collisions among agents. Meanwhile, to address the situation where some agents cannot receive reference signals, we design an estimator to generate an adjustable estimation signal for each specific agent to ensure that all agents continue moving within the convex hull. In addition, by combining the fuzzy observer with the command filter design method, we devise a novel controller design scheme for quantitative input, which ensures that all signals in closed-loop multi-agent systems are uniformly and ultimately bounded. Finally, the simulation results demonstrate the feasibility and superiority of the proposed scheme for controlling multi-agent systems.

Optimal Output Consensus of Heterogeneous Linear Multiagent Systems Over Weight-Unbalanced Directed Networks.

This article investigates the distributed optimal output consensus problem of heterogeneous linear multiagent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to steer the outputs of all the agents to converge to the optimal solution of the global cost function. Under the standard condition that the unbalanced digraph is strongly connected and the local cost functions are strongly convex with global Lipschitz gradients, the exponential convergence of the closed-loop multiagent system is established. Then, the proposed state feedback control law is extended to an observer-based output feedback setting. Two examples are finally provided to illustrate the effectiveness of the proposed control schemes.

Opposition-based differential evolution for synchronized control of multi-agent systems with uncertain nonlinear dynamics

Multi-agent systems (MAS) have gained increasing research attention in recent years due to their wide applications in cooperative control of autonomous vehicles, sensor networks, robotics, etc. However, designing effective distributed control strategies for MAS with complex dynamics remains challenging. This paper proposes an improved differential evolution (DE) based cooperative control strategy to stabilize and synchronize MAS with uncertain nonlinear dynamics. Specifically, we develop a new mutation strategy inspired by opposition-based learning to enhance the exploration ability and adopt an adaptive parameter mechanism to balance exploration and exploitation. Moreover, a distributed sliding mode term is incorporated in the control input to counteract uncertainties and external disturbances. Rigorous stability analysis shows that the closed-loop MAS can achieve synchronization under the proposed control strategy. Extensive simulations demonstrate that compared to other state-of-the-art DE algorithms and cooperative control methods, the proposed strategy achieves lower synchronization error, control cost, higher convergence speed, and higher accuracy for MAS with different scales, dynamics, and uncertainties.

Quadratic Programming for Continuous Control of Safety-Critical Multiagent Systems Under Uncertainty

This paper studies the control problem for safety-critical multi-agent systems based on quadratic programming (QP). Each controlled agent is modeled as a cascade connection of an integrator and an uncertain nonlinear actuation system. In particular, the integrator represents the position-velocity relation, and the actuation system describes the dynamic response of the actual velocity to the velocity reference signal. The notion of input-to-output stability (IOS) is employed to characterize the essential velocity-tracking capability of the actuation system. The standard QP algorithms for collision avoidance may be infeasible due to uncertain actuator dynamics. Even if feasible, the solutions may be non-Lipschitz because of possible violation of the full rank condition of the active constraints. Also, the interaction between the controlled integrator and the uncertain actuator dynamics may lead to significant robustness issues. Based on the current development of nonlinear control theory and numerical optimization methods, this paper first contributes a new feasible-set reshaping technique and a refined QP algorithm for feasibility, robustness, and local Lipschitz continuity. Then, we present a nonlinear small-gain analysis to handle the inherent interaction for guaranteed safety of the closed-loop multi-agent system. The proposed method is illustrated by numerical simulation and a physical experiment.

Dynamic Event-Triggered Reinforcement Learning-Based Consensus Tracking of Nonlinear Multi-Agent Systems

In this paper, we present a novel approach to address the event-triggered optimized consensus tracking control problem in a class of uncertain nonlinear multi-agent systems (MASs). To optimize control performance, we employ an adaptive reinforcement learning (RL) algorithm based on the actor-critic architecture and utilize the backstepping method. The proposed RL-based optimized controller employs a novel event-triggered strategy, dynamically adjusting sampling errors online to reduce communication resource usage and computational complexity through the intermittent transmission of state signals. We establish the boundedness of all signals in the closed-loop MAS through stability analysis using the Lyapunov method, and demonstrate the prevention of Zeno behavior. Numerical simulations of a practical multi-electromechanical system are provided to validate the effectiveness of the proposed scheme.

Fully Distributed Adaptive Formation Tracking for Directed Heterogeneous Multi-Agent Systems With Unknown Input

In this brief, the time-varying output formation tracking (TVOFT) problem for directed multi-agent systems is studied, where the leader has unknown input and each follower has nonidentical dynamics. The main object of this brief is to construct fully distributed controller so that the outputs of followers track the leader’s output and realize the expected formation simultaneously. Firstly, by exploiting the neighboring information and local estimation, two kinds of adaptive observers are, respectively, constructed to estimate the states of the leader and followers, which do not require the bound of leader’s unknown input. Then, by using the distributed observers and the expected time-varying formation vector, a TVOFT control protocol is developed in a fully distributed form, and the parameters of the controller are designed by an algorithm including three steps. Furthermore, on the basis of the Lyapunov stability theory and output regulation method, the TVOFT criteria for the considered closed-loop multi-agent systems are obtained on the basis of the presented control protocol. At last, in order to illustrate the theoretical results, a simulation example is given.

Distributed adaptive formation control of multi-agent systems with measurement noises

In this paper, we investigate the distributed adaptive formation control problem of leader-following multi-agent systems where the measurements are subject to noises. A distributed LMS-like algorithm is proposed to estimate the relative position between the followers and the leader. By employing the “certainty equivalence” principle, an adaptive motion controller is designed to achieve the desired formation under dynamically changing interaction topologies. The incompatibility in simultaneously satisfying the persistent excitation condition required by localization estimators and accomplishing the control tasks makes the theoretical analysis challenging. In order to deal with this issue, an excited noise signal is embedded into the control law. We give the upper bounds of both the estimation errors and formation error of the closed-loop multi-agent system under the distributed adaptive control law. Finally, the numerical simulations are provided to demonstrate the effectiveness of our theoretical results.

Distributed Nonrecursive Averaging Filters for Quantized Consensus: An Edge Sensitivity Design Approach

This article studies the distributed nonrecursive averaging filter design for the quantized consensus of discrete-time first-order multiagent systems over undirected and connected networks. The quantized consensus problem is cast into the robust consensus problem with sector bound uncertainties associated with the edges of communication graphs, and then an edge sensitivity design approach is utilized for the filter parameter design. Necessary and sufficient conditions for the filter parameter for preserving robust consensus with sector bound uncertainties are provided, which are shown to be dependent on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> norm of the edge complementary sensitivity transfer matrix of the closed-loop multiagent system. Then, the optimal filter parameter design is provided by solving a constrained optimization problem, under which robust consensus with maximal allowable sector bound parameter is reached. The results show that the supremum of the sector bound parameter of the logarithmic quantizer for preserving robust consensus is independent of the communication network topologies and the sampling period.

Adaptive Multigradient Recursive Reinforcement Learning Event-Triggered Tracking Control for Multiagent Systems.

This article proposes a fault-tolerant adaptive multigradient recursive reinforcement learning (RL) event-triggered tracking control scheme for strict-feedback discrete-time multiagent systems. The multigradient recursive RL algorithm is used to avoid the local optimal problem that may exist in the gradient descent scheme. Different from the existing event-triggered control results, a new lemma about the relative threshold event-triggered control strategy is proposed to handle the compensation error, which can improve the utilization of communication resources and weaken the negative impact on tracking accuracy and closed-loop system stability. To overcome the difficulty caused by sensor fault, a distributed control method is introduced by adopting the adaptive compensation technique, which can effectively decrease the number of online estimation parameters. Furthermore, by using the multigradient recursive RL algorithm with less learning parameters, the online estimation time can be effectively reduced. The stability of closed-loop multiagent systems is proved by using the Lyapunov stability theorem, and it is verified that all signals are semiglobally uniformly ultimately bounded. Finally, two simulation examples are given to show the availability of the presented control scheme.

Leader-Following Consensus of Heterogeneous Linear Multiagent Systems With Communication Time-Delays via Adaptive Distributed Observers.

This article investigates the leader-following consensus problem of heterogeneous linear multiagent systems under switching and directed topologies. It is assumed that the communication between agents suffers from time-varying delays and only the neighboring agents of the leader are able to get access to the information of the leader agent, including its agent matrices. A key technical lemma on the input to state stability of time-delayed systems is first established with which the main results of this article can be obtained. An adaptive distributed observer, taking into consideration of communication time delays, is proposed for each follower to estimate the leader's system matrices and its state. Then, a distributed controller based on this adaptive observer is developed. We show that the resulting closed-loop multiagent system achieves the leader-following output consensus. Two examples are finally given to illustrate the effectiveness of the proposed controller.

Consensusability Margin Optimization for Second-Order Multiagent Systems With Communication Uncertainties

In this article, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> optimization approach is used to study the consensusability margin optimization problems for distributed second-order sampled-data multiagent systems with communication uncertainties. The considered uncertainties are frequency-dependent and bounded in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> norms. Specifically, for both the state-based protocols with relative damping and absolute damping, this article attempts to answer two questions: 1) how to characterize the control parameters for achieving robust consensus; and 2) what is the maximal consensusability margin and how to find, if one exists, the parameter to achieve this optimal performance. It is shown that the consensusability margin optimization problems are constraint optimization problems, which are to be specified by specific problem parameters and can be discussed by designing the network complementary sensitivity function matrices of the closed-loop multiagent systems. Moreover, it is shown that the infimums of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> norms of the network complementary sensitivity function matrices under both protocols are independent of network topologies.

Quantized Fuzzy Cooperative Output Regulation for Heterogeneous Nonlinear Multiagent Systems With Directed Fixed/Switching Topologies.

This article investigates the cooperative output regulation problem for heterogeneous nonlinear multiagent systems subject to disturbances and quantization. The agent dynamics are modeled by the well-known Takagi-Sugeno fuzzy systems. Distributed reference generators are first devised to estimate the state of the exosystem under directed fixed and switching communication graphs, respectively. Then, distributed fuzzy cooperative controllers are designed for individual agents. Via the Lyapunov technique, sufficient conditions are obtained to guarantee the output synchronization of the resulting closed-loop multiagent system. Finally, the viability of proposed design approaches is demonstrated by an example of multiple single-link robot arms.

An edge-based augmented system approach for second-order nodal consensus

Many works on multi-agent consensus protocol designs rely on the full states of nodes or the node- observer-based procedures, under both of which the nodal information plays a key role in the consensus design. In this paper, we propose an edge-based augmented system approach for second-order nodal consensus, based on the edge loop transfer matrix of the closed-loop multi-agent system, which is defined by cutting the loop at the inputs of the edges. Each agent is allowed to be of single-output and additional poles and zeros are introduced into edges to construct the channel filter with previous data stored in the memories. We firstly focus on the consensus design by reserving two terms of the non-recursive filter and then propose a simplified design approach exploiting a single parameter, which is of low complexity and can be readily implemented. We also discuss the consensus design by using the non-recursive channel filter with higher-order realizations. Finally, as an extension, we discuss the consensus design based on the first-order recursive channel filter. The effectiveness of the proposed method is verified by the illustrative simulations.

Distributed Optimal Tracking Control of Discrete-Time Multiagent Systems via Event-Triggered Reinforcement Learning

In this paper, an event-triggered optimal tracking control of discrete-time multi-agent systems is addressed by using reinforcement learning. In contrast to traditional reinforcement learning-based methods for optimal coordination and control of multi-agent systems with a time-triggered control mechanism, an event-triggered mechanism is proposed to update the controller only when the designed events are triggered, which reduces the computational burden and transmission load. The stability analysis of the closed-loop multi-agent systems with event-triggered controller is described. Further, to implement the proposed scheme, an actor-critic neural network learning structure is proposed to approximate performance indices and to on-line learn the event-triggered optimal control. During the training process, event-triggered weight tuning law has been designed, wherein the weight parameters of the actor neural networks are adjusted only during triggering instances compared with traditional methods with fixed updating periods. Further, a convergence analysis of the actor-critic neural network is provided via Lyapunov method. Finally, two simulation examples show the effectiveness and performance of the obtained event-triggered reinforcement learning controller.

Finite frequency domain H ∞ consensus control of neutral multi-agent systems with input delay

The finite frequency domain consensus control problem of neutral multi-agent systems with the input delay is investigated in this paper for the first time. According to the linear transformation, the problem of consensus is converted into a set of stability problems. Through the Lyapunov theory, combined with the time-delay interval decomposition method, a less conservative controller design method for the state feedback controller is presented. And the obtained controller can ensure closed-loop multi-agent systems to fulfil the consensus. Utilizing the generalised Kalman-Yakubovich-Popov (GKYP) lemma, the sufficient condition is derived for multi-agent systems achieving the performance in the finite frequency domain (FFD). Then, via the orthogonal spatial information of the input matrix, the conservativeness of obtained design approach is further declined. Moreover, the design method with less conservativeness is proposed for the dynamic output feedback controller. Finally, a numerical case and a multi-pendulum system controlled by the multi-motor system are presented in this paper to demonstrate the availability and applicability of the proposed methods.

Distributed output agreement of PWM‐controlled double‐integrator multi‐agent systems with switching topologies

This paper studies the distributed pulse-width-modulation (PWM) control problem for double-integrator multi-agent systems with switching topologies. Usually, a PWM control signal updates only on discrete-time sample instants and only takes three constant values. This means that the methods based on linear and continuous designs are not directly applicable. The major contribution of this paper is that a new class of distributed PWM controllers, which feature nested saturated loops, is proposed. With the new design, the outputs of the controlled agents asymptotically converge to each other, as long as a mild connectivity condition is satisfied. The validity of the proposed PWM controller is proved based on a new invariant-set-like method. This work first shows that the state of each PWM-controlled agent stays within an appropriately chosen closed set if the interactions are bounded. Then, under a mild connectivity condition, the state boundedness and convergence of the closed-loop multi-agent system by analyzing the boundedness of the interactions are proved. A numerical example is employed to verify the effectiveness of the proposed design.

Distributed Quantized Consensus With Recursive Channel Filters Over Directed Networks

This brief investigates the quantized consensus in discrete-time multi-agent systems over directed networks with limited bandwidths of communication channels and limited capacities of physical memories. A dynamic consensus protocol based on the first-order recursive channel filter is proposed. Several conditions for preserving the asymptotic consensus are obtained, which are dependent on the filter parameters, the sampling period and the topologies of the communication networks. Then, by describing the closed-loop multi-agent system via a higher-order state-space model, the effects of the probabilistic quantization are analyzed. We prove that the quantized consensus is reached under the proposed protocol with quantized communications. Moreover, the distributed PI based protocol is discussed as a special case of the proposed dynamic protocol.

Triggered finite‐time consensus of first‐order multi‐agent systems with input saturation

Input saturation, which brings input non-linearity to systems and limits the closed-loop systems' performances severely, is an ubiquitous problem in practice. Here, triggered finite-time consensus problem of disturbed leader-follower multi-agent systems is addressed under input saturation constraint. To overcome the coupling of the non-linearity and finite-time convergence together with input saturation, non-linear triggered control protocol has been proposed, which is confirmed through a two-step stabilization procedure. First, the saturated closed-loop system is designed to be asymptotically stable, under which the systems converge into a desaturated region in finite time. Then in the second step, with the proposed control protocol, the desaturated closed-loop multi-agent systems can achieve practical finite-time consensus. In addition, to get rid of continuous communication in the monitoring of event-triggered condition, a self-triggered approach is further proposed. With rigorous analyses, practical finite-time consensus can be achieved for the overall closed-loop systems and Zeno behavior is also excluded. Simulations are carried out in detail to illustrate the theoretical results in this study.

Event-based consensus control for multi-agent systems against joint sensor and actuator attacks

The paper focuses on the observer-based consensus control issue for a class of discrete-time multi-agent systems suffering from the joint actuator and sensor attacks. An event-triggered communication rule with the adaptive threshold update is introduced to reduce the communication burden. A PI-type controller with a finite-time window integral loop is constructed to achieve bounded consensus in the mean-square sense (BCMS). With the help of common properties of Laplace matrices, the closed-loop multi-agent system is converted into an easy-to-analyze pattern. In light of such a pattern, a sufficient condition is derived to realize the desired consensus by the stochastic analysis. Furthermore, the expected gains of the controller and the observer are determined by resorting to matrix inequalities in combination with the cone complementarity linearization algorithm. Finally, a numerical example and a simulation of the platooning vehicle are proposed to illustrate the effectiveness of the proposed control scheme.