Multi-agent Dynamical Systems Research Articles

Resilient coordination of multi-agent systems in the presence of unknown heterogeneous actuation efficiency and coupled dynamics: distributed approaches

To guarantee the stability and performance of an overall heterogeneous multi-agent system, feedback control structures must be capable of addressing the presence of heterogeneous agent-based nonlinear uncertainties, unknown actuation performance, and coupling effects. Additionally, some tasks require agents to track the leader's state and reach different states in a distributed way. Therefore, this paper proposes a distributed adaptive controller that drives a set of agents to user-assigned positions in the presence of the mentioned heterogeneous system anomalies. To address actuator dynamics, a hedging-based reference model is used to decouple adaptive updating from the actuator dynamics. To deal with the coupled dynamics, an observer-based estimation algorithm is proposed. Finally, the low-frequency learning method is used to deal with the high-frequency control response and, therefore, to obtain a better transient performance. The overall closed-loop system's stability is investigated using the Lyapunov Stability Theory, and the Linear Matrix Inequalities (LMI) technique is employed to identify stability limits regarding the actuator bandwidths of each agent. Illustrative numerical examples are presented to demonstrate the designed controller's performance in a heterogeneous uncertain multi-agent system's dynamics with unknown actuation capabilities and coupled dynamics.

Optimized leader–follower consensus control for high-order nonlinear multi-agent system modeled in canonical dynamic form

This paper addresses the optimized leader–follower consensus control problem of nonlinear canonical dynamic multi-agent system (MAS). Since every agent is modeled in high-order dynamic, they contain the various state variables having derivative relations. Consequently, to attain the optimized consensus control, backstepping technique and reinforcement learning (RL) are combined together. In the first backstepping step, the virtual control is formulated to have the consensus error term consisting of neighbor agents’ output states. In the last backstepping step, since the nonlinearity dynamic is arisen, the optimized actual control is derived by performing the critic-actor RL. It is worth mentioning that, in the traditional RL optimal control, the critic and actor updating laws are obtained by performing the gradient descent algorithm to square of the approximated Hamilton–Jacobi-Bellman (HJB) equation, which includes multiple nonlinearity items, as a result, the algorithm is very intricate. However, in this optimized consensus control, since the RL training laws are yielded in the light of negative gradient of a simple positive function that is relevant to the HJB equation, its algorithm is very simple. At the same time, it can also avoid the persistence excitation conditions. Finally, theory and simulation confirm the validity of this optimized consensus method.

Time-Varying Optimal Formation Control for Second-Order Multiagent Systems Based on Neural Network Observer and Reinforcement Learning.

This article addresses a distributed time-varying optimal formation protocol for a class of second-order uncertain nonlinear dynamic multiagent systems (MASs) based on an adaptive neural network (NN) state observer through the backstepping method and simplified reinforcement learning (RL). Each follower agent is subjected to only local information and measurable partial states due to actual sensor limitations. In view of the distributed optimized formation strategic needs, the uncertain nonlinear dynamics and undetectable states may jointly affect the stability of the time-varying cooperative formation control. Furthermore, focusing on Hamilton-Jacobi-Bellman optimization, it is almost incapable of directly dealing with unknown equations. Above uncertainty and immeasurability processed by adaptive state observer and NN simplified RL are further designed to achieve desired second-order formation configuration at the least cost. The optimization protocol can not only solve the undetectable states and realize the prescribed time-varying formation performance on the premise that all the errors are SGUUB, but also prove the stability and update the critics and actors easily. Through the above-mentioned approaches offer an optimal control scheme to address time-varying formation control. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and digital simulation.

Prosocial dynamics in multiagent systems

AbstractMeeting today's major scientific and societal challenges requires understanding dynamics of prosociality in complex adaptive systems. Artificial intelligence (AI) is intimately connected with these challenges, both as an application domain and as a source of new computational techniques: On the one hand, AI suggests new algorithmic recommendations and interaction paradigms, offering novel possibilities to engineer cooperation and alleviate conflict in multiagent (hybrid) systems; on the other hand, new learning algorithms provide improved techniques to simulate sophisticated agents and increasingly realistic environments. In various settings, prosocial actions are socially desirable yet individually costly, thereby introducing a social dilemma of cooperation. How can AI enable cooperation in such domains? How to understand long‐term dynamics in adaptive populations subject to such cooperation dilemmas? How to design cooperation incentives in multiagent learning systems? These are questions that I have been exploring and that I discussed during the New Faculty Highlights program at AAAI 2023. This paper summarizes and extends that talk.

Distributed Localization for Multi-Agent Systems With Random Noise Based on Iterative Learning.

This article is concerned with the real-time localization problem for the dynamic multi-agent systems with measurement and communication noises under directed graphs. The barycentric coordinates are introduced to describe the relative position between agents. A novel robust distributed localization estimation algorithm based on iterative learning is proposed. The relative-distance unbiased estimator constructed from the historical iterative information is used to suppress the measurement noise. The designed stochastic approximation method with two iterative-varying gains is used to inhibit the communication noise. Under the zero-mean and independent distributed conditions on the measurement and communication noises, the asymptotic convergence of the proposed methods is derived. The numerical simulation and the QBot-2e robot experiment are conducted to test and verify the effectiveness and the practicability of the proposed methods.

Opinion Dynamics in Multiagent Systems with Optimal Choice of Opinion Verification Moments

Opinion Dynamics in Multiagent Systems with Optimal Choice of Opinion Verification Moments

Flocking and swarming in a multi-agent dynamical system.

Over the past few decades, the research community has been interested in the study of multi-agent systems and their emerging collective dynamics. These systems are all around us in nature, such as bacterial colonies, fish schools, and bird flocks, as well as in technology, such as microswimmers and robotics, to name a few. Flocking and swarming are two key components of the collective behaviors of multi-agent systems. In flocking, the agents coordinate their direction of motion, but in swarming, they congregate in space to organize their spatial position. We propose a minimal mathematical model of a locally interacting multi-agent system where the agents simultaneously swarm in space and exhibit flocking behavior. Various cluster structures are found depending on the interaction range. When the coupling strength value exceeds a crucial threshold, flocking behavior is observed. We do in-depth simulations and report the findings by changing the other parameters and with the incorporation of noise.

Submodularity-based false data injection attack scheme in multi-agent dynamical systems

Consensus in multi-agent dynamical systems is prone to be sabotaged by the adversary, which has attracted much attention due to its key role in broad applications. In this paper, we study a new false data injection (FDI) attack design problem, where the adversary with limited capability aims to select a subset of agents and manipulate their local multi-dimensional states to maximize the consensus convergence error. We first formulate the FDI attack design problem as a combinatorial optimization problem and prove it is NP-hard. Then, based on the submodularity optimization theory, we provide the necessary and sufficient conditions to guarantee that the convergence error is a submodular function of the set of compromised agents, satisfying the property of diminishing marginal returns. In other words, the benefit of adding an extra agent to the compromised set decreases as that set becomes larger. With this property, we exploit the greedy scheme to find the optimal compromised agent set that can produce the maximum convergence error when adding one extra agent to that set each time. Thus, the FDI attack set selection algorithms are developed to obtain the near-optimal subset of the compromised agents. Furthermore, we derive the analytical suboptimality bounds and the worst-case running time under the proposed algorithm. Extensive simulation results are conducted to show the effectiveness of the proposed algorithm.

A kinetic approach to investigate the collective dynamics of multi-agent systems

A kinetic approach to investigate the collective dynamics of multi-agent systems

Leader–follower consensus control for a class of nonlinear multi-agent systems using dynamical neural networks

This paper addresses the formation consensus tracking control problem of uncertain dynamical multi-agent system with nonlinear dynamics based on a leader–follower configuration based on a undirected communication topology. The control design is based on a novel combination of consensus protocols and dynamical neural networks, known as differential neural networks, to approximate the modeling uncertainties and external disturbances of the follower agents. The proposed controller-identifier structure forces the state of each agent to maintain a formation with respect to the leader ensuring limited residual errors. The stability proof supports the control design and guarantees the multi-agent system states to be ultimately bounded. In order to show the effectiveness of the proposed tracking controller and the superior performance against the static RBFNNs approach, some simulation results are presented considering a multi-robotic system with five agents following a helical three-dimensional reference signal of a virtual leader.

Towards privacy-preserving cooperative control via encrypted distributed optimization

Abstract Cooperative control is crucial for the effective operation of dynamical multi-agent systems. Especially for distributed control schemes, it is essential to exchange data between the agents. This becomes a privacy threat if the data are sensitive. Encrypted control has shown the potential to address this risk and ensure confidentiality. However, existing approaches mainly focus on cloud-based control and distributed schemes are restrictive. In this paper, we present a novel privacy-preserving cooperative control scheme based on encrypted distributed optimization. More precisely, we focus on a secure distributed solution of a general consensus problem, which has manifold applications in cooperative control, by means of the alternating direction method of multipliers (ADMM). As a unique feature of our approach, we explicitly take into account the common situation that local decision variables contain copies of quantities associated with neighboring agents and ensure the neighbor’s privacy. We show the effectiveness of our method based on a numerical case study dealing with the formation of mobile robots.

Power Degrees in Dynamic Multi-Agent Systems

Power Degrees in Dynamic Multi-Agent Systems

3-D Localization of Multiagent Systems Under Random Environments Based on Iterative Learning

This work addresses the localization of dynamic multi-agent systems (MASs) in three-dimensional (3-D) space under random environments (i.e., random packet loss, measurement noise and simultaneous communication noise). It is more practical yet challenging to deal with than static systems under ideal environments. Barycentric coordinates based on the relative-distance are used to characterize the positions between agents. The sign coefficients are introduced to guarantee that the sum of barycentric coordinates is equal to one, thus eliminating the constraint that the agent needs to be located in the convex hull. Using the newly designed iteration-varying gains, a robust distributed estimation method based on iterative learning is proposed. The key to accurate localization is to construct an appropriate approximator via introducing two iterative-varying gains into the localization scheme. The convergence in the sense of mathematical expectation is proved. The simulation examples and experimental results verify the effectiveness of the proposed approach.

Evolutionary game dynamics of multi-agent systems using local information considering hide right

Promoting cooperation in the network has always been a focus of evolutionary game dynamics research. In this paper, a three-strategy local decision model is designed to promote cooperative behavior between agents. The hide right is introduced to accurately describe the agents which tend to choose conservative strategy to achieve stable payoffs. Agents only consider their own and non-defective neighbors’ payoffs information to make their decisions for next move. According to the adaptive dynamics, the equilibrium states under different conditions have been studied. It is found that the introduction of hide strategy helps to reduce the occurrence of defection. The conclusion of this paper will provide a reference for the cooperation promotion mechanism of selfish agents that are closer to the actual situation.

Cooperative distributed extremum seeking control for coupled multiagent systems based on distributed identification‐gradient tracking

SummaryThis paper proposes a cooperative distributed extremum seeking control (ESC) approach for solving distributed optimization problems in static and dynamical multiagent systems, where the agents' coupled dynamics are unknown and only local cost values can be measured. The approach begins with each agent estimating the local gradient information of the unknown local cost function through recursive identification using measured local cost values. Subsequently, the distributed identification‐gradient tracking (DIGT) algorithm is employed to enable each agent to track the global gradient information of the global cost function, utilizing the estimated local gradient information from itself and its neighbors in the network. The proposed cooperative distributed ESC method enables the multiagent system to reach the extreme point of the global cost function under model‐free scenarios. Furthermore, the convergence properties of the approach are established for both static and dynamical multiagent systems. Finally, numerical examples are presented to demonstrate the effectiveness and stability of the proposed approach.

Controllability properties for multi-agent linear systems. A geometric approach

This work addresses the controlability of a class of multi-agent linear systems that they are interconnected via communication channels. Multiagent systems have attracted much attention because they have great applicability in multiple areas, such as power grids, bioinformatics, sensor networks, vehicles, robotics and neuroscience, for example. Consequently, they have been widely studied by scientists in different fields specially in the field of control theory. Recently has taken interest to analyze the control properties as consensus controllability of multi-agent dynamical systems motivated by the fact that the architecture of communication network in engineering multi-agent systems is usually adjustable. In this paper, the control condition is analyzed under geometrical point of view. in the case of multiagent linear systems that can be described by k agents with dynamics x''_i = A_i x_i + B_i u_i, i = 1, . . . , k.

Distributed Localization Estimation for Dynamic Multiagent Systems

This article investigates the real-time localization problem of dynamic multiagent systems with repetitive operation characteristics under directed graph. A distributed localization estimation algorithm based on iterative learning is proposed. The barycentric coordinates calculated based on the relative distance are used to estimate the real coordinates of the agent. Different from the traditional estimation methods along the time axis, the proposed method utilizes the information of iteration axis simultaneously. In this method, the current estimation coordinates are updated by using the estimation coordinates of the same sampling time in previous iteration, the estimation accuracy is improved, and the velocity constraint is removed. Additionally, the real-time localization problem of dynamic multiagent systems under arbitrary deployment is concerned. An improved distributed localization estimation algorithm with signed coefficients based on iterative learning is proposed. Meanwhile, the results are also extended to the localization estimation of multiagent systems with arbitrary deployment in 3-D space. By introducing Richardson iteration and infinite norm, the global asymptotic convergence of the proposed methods is guaranteed. Finally, numerical simulations and the Qbot-2e robot experiment are provided to show the effectiveness and validity of the obtained results.

AI’s 10 to Watch, 2022

AI’s 10 to Watch, 2022

Uncertain Multiagent Systems With Distributed Constrained Optimization Missions and Event-Triggered Communications: Application to Resource Allocation

This article deals with solving distributed optimization problems with equality constraints by a class of uncertain nonlinear heterogeneous dynamic multiagent systems. It is assumed that each agent with an uncertain dynamic model has limited information about the main problem and limited access to the information of the state variables of the other agents. A distributed algorithm that guarantees cooperatively solving of the constrained optimization problem by the agents is proposed. Via applying this algorithm, the agents do not need to continuously broadcast their data. It is shown that the proposed algorithm can be useful in solving resource allocation problems.

Opinion dynamics in multiagent systems with optimal choice of opinion verification moments

In this paper, we consider a model of opinion dynamics in the social network, that is a multiagent system with finite number of agents. There exists a center of influence on agent's opinion by choosing control, which is an influence level at every time period. In the model, center's costs are represented by a linear-quadratic function of a state variable and its controls. The center of influence aims to choose a finite number of opinion verification moments to compare agents' opinion with the target one. We provide a solution of this dynamic problem. In the numerical simulations, we show how to find optimal opinion verification moments, corresponding optimal state trajectories and controls.