Cooperative Control Of Multi-agent Systems Research Articles

Optimal distributed cooperative control for multi-agent systems with constrains on convergence speed and control input

This paper focuses on the distributed optimal cooperative control for multi-agent systems (MASs) over fixed communication graphs. Firstly, it is proved that the optimal distributed control for the local quadratic performance indexes of all agents is equivalent to solve a globally optimal problem, the resulting optimal Laplacian matrix associates with a complete graph hence the optimal distributed protocols do not exist. Consequently, we turn to solve the globally optimal distributed control problem for the candidate protocols with specified distributed structure. Furthermore, suboptimal fully distributed protocols can be designed when the Laplacian matrix and the initial states of all agents are unavailable. As a simple application, the minimum energy distributed cooperative control problem is addressed. Then, from a practical viewpoint, we solve the distributed optimal control problem with constrains on specified convergence speed and control input. Sufficient conditions for existence of the optimal solutions are derived. Finally, simulation examples are given to verify the effectiveness of the proposed results.

Distributed Estimation of Algebraic Connectivity.

The measurement algebraic connectivity plays an important role in many graph theory-based investigations, such as cooperative control of multiagent systems. In general, the measurement is considered to be centralized. In this article, a distributed model is proposed to estimate the algebraic connectivity (i.e., the second smallest eigenvalue of the corresponding Laplacian matrix) by the approach of distributed estimation via high-pass consensus filters. The global asymptotic convergence of the proposed model is theoretically guaranteed. Numerical examples are shown to verify the theoretical results and the superiority of the proposed distributed model.

Semiglobal Tracking Cooperative Control for Multiagent Systems With Input Saturation: A Multiple Saturation Levels Framework

This article proposes a multiple saturation levels framework to investigate the semiglobal tracking cooperative control problem of multiagent systems with switching communication topologies. This problem is solving by proposing a switching parametric Lyapunov approach and constructing a three-layer nodes model with mirroring nodes to reduce the complexity of controller design in which control inputs for different layers of nodes are with different saturation levels. A metamorphic low-gain feedback consensus protocol is developed, based only on the interaction information of different nodes, to ensure that the states of the followers approach that of the leader, if the dwell time can be reasonably selected and the switching derived topologies have a directed spanning tree. Moreover, the protocol is extended to the derived topology that frequently contains a directed spanning tree. Simulations are presented to verify the effectiveness of the new design techniques.

Event-Triggered Consensus for Euler-Lagrange Systems with Communication Delay

Distributed cooperative control of multi-agent systems, typically requires some form of information exchange in order to achieve coordination between individual agents. Especially in wireless communication systems, communication delays can lead to instability and can not be neglected during the design of the control law. We propose a novel coordination scheme for Euler-Lagrange systems taking into account constant communication delays. Additionally, in order to save limited resources, we propose an event-triggered strategy for the communication between agents, as well as for the local actuator updates of the individual agents. We show that with the proposed algorithms a stable interaction in consensus tasks can be guaranteed. Simulations illustrate the theoretical results.

Interaction Matrix Based Analysis and Asymptotic Cooperative Control of Multi-agent Systems

In this paper, we investigate a decentralized asymptotic cooperative control problem of multi-agent systems with leader-follower configuration. We firstly develop a new method using a proposed “interaction matrix” for the analysis of cooperation convergence of multi-agent systems, i.e. both consensus of the agents states and trajectory tracking of the whole group can be instantaneously concluded only by observing the minimum eigenvalue of the interaction matrix. For a multi-agent system, the external given desired trajectory can be partially obtained (through sensing or detecting) by the leaders, but higher-order derivatives such as acceleration and jerk of the desired trajectory cannot be obtained. In this case, by using some conventional control methods, the trajectory tracking performance is always not satisfactory when a trajectory varies aggressively w.r.t. time. For the sake of asymptotic tracking of an arbitrary given external trajectory of a multi-agent system, we develop a nonlinear cooperative controller based on the robust integral of signum of cooperative error (RISCE) technique, where the interaction matrix is used. The simulation results show asymptotic convergence of cooperation by using the proposed control, and better performance compared to composited nonlinear feedback based PD (CNF-PD) control.

Fault-Tolerant Cooperative Control of Multiagent Systems: A Survey of Trends and Methodologies

Fault-tolerant cooperative control of multiagent systems has attracted ever-increasing attention in recent years due to the fact that multiple agents can provide much more redundancy than a single agent system, thereby making the fault tolerant cooperative control design more flexible. However, multiagent systems may bring severe challenges that do not exist in single-agent systems. This article aims at presenting a survey of trends and methodologies of fault tolerant cooperative control in multiagent systems. Depending on the countermeasure against the faults, the existing fault-tolerant cooperative control methodologies are first classified into four categories: Individual methodologies, cooperative methodologies, topology reconfiguration-based methodologies, and composition reconfiguration-based methodologies. Then the characteristics and implementation schemes of four categories of methodologies are discussed in detail. Furthermore, the applicability of fault tolerant cooperative control in smart grids is outlined. Finally, several challenging issues are envisioned for future research.

Fully Distributed Resilience for Adaptive Exponential Synchronization of Heterogeneous Multiagent Systems Against Actuator Faults

Cooperative control of multiagent systems (MAS) on communication networks has received a great deal of attention, mostly for the case of homogeneous agents, which all have the same dynamics. An advantage of cooperative synchronization mechanisms is their local distributed nature, which makes them scalable to large networks. However, most existing design mechanisms require some global information, such as the leader's dynamics or global graph information, so that the control protocols are technically not fully distributed. Moreover, the distributed nature of the control protocols makes them susceptible to faults or uncertainties. In this paper, we study heterogeneous MAS, where all agents may have different dynamics. We provide adaptive resilience mechanisms for rejecting actuator faults, and guarantee exponential convergence of synchronization errors, whereas most existing results on actuator faults guarantee only boundedness of errors. Finally, we provide algorithms that are fully distributed, requiring no knowledge of either the leader's dynamics or of graph properties.

Cooperative Control of Multiple Agents With Unknown High-Frequency Gain Signs Under Unbalanced and Switching Topologies

Existing results on cooperative control of multi-agent systems with unknown control directions require that the underlying topology is either fixed with a strongly connected graph or switching between different strongly connected graphs. Furthermore, in most cases the graph is assumed to be balanced. This paper proposes a new class of nonlinear PI based algorithms to relax these requirements and allow for unbalanced and switching topologies having a jointly strongly connected basis. This is made possible for single-integrator (SI) and double-integrator (DI) agents with non-identical unknown control directions by a suitable selection of the distributed nonlinear PI functions. Moreover, as a special case, the proposed algorithms are applied to strongly connected and fixed graphs. Finally, simulation examples are given to show the validity of our theoretical results.

Prescribed Performance Cooperative Control for Multiagent Systems With Input Quantization.

This paper studies the quantized cooperative control problem for multiagent systems with unknown gains in the prescribed performance. Different from the finite-time control, a speed function is designed to realize that the tracking errors converge to a prescribed compact set in a given finite time for multiagent systems. Meanwhile, we consider the problem of unknown gains and input quantization, which can be addressed by using a lemma and Nussbaum function in cooperative control. Moreover, the fuzzy logic systems are proposed to approximate the nonlinear function defined on a compact set. A distributed controller and adaptive laws are constructed based on the Lyapunov stability theory and backstepping method. Finally, the effectiveness of the proposed approach is illustrated by some numerical simulation results.

A differential game for cooperative target defense

Multi-player pursuit–evasion games are crucial for addressing the maneuver decision problem arising in the cooperative control of multi-agent systems. This work addresses a particular pursuit–evasion game with three players, Target, Attacker, and Defender. The Attacker aims to capture the Target, while avoiding being captured by the Defender and the Defender tries to defend the Target from being captured by the Attacker, while trying to capture the Attacker at an opportune moment. A two-pronged pursuit–evasion problem in this game is considered and we focus on two aspects: the cooperation between the Target and Defender and balancing the roles of the Attacker between pursuer and evader. A barrier based on the explicit policy method and geometric analysis method is constructed to separate the whole state space into two disjoint parts that correspond to two winning regions for the Attacker and Target–Defender team. The main contributions of this work are obtaining the players’ winning regions and providing a complete game solution by analyzing the optimal strategies and trajectories of the players based on the barrier.

Encrypted Cooperative Control Based on Structured Feedback

Cooperative control for multi-agent systems usually requires some communication between the various subsystems. In the resulting networked control system, sensitive data is transmitted and shared between the agents. We propose a novel encrypted control scheme that ensures privacy of the individual agents’ data not only during transmission but also during controller evaluations at neighboring agents. Our control scheme efficiently combines the design of structured feedback laws for multi-agent systems with encrypted controllers for conventional linear systems. The underlying key technology is partial homomorphic encryption, which allows simple computations to be carried out on encrypted data.

An Overview of Recent Advances in Fixed-Time Cooperative Control of Multiagent Systems

Fixed-time cooperative control is currently a hot research topic in multiagent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multiagent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multiagent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then, recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.

Model-Free Cooperative Control for Multi-Agent Systems Using the Approximate Dynamic Programming Approach

In this paper, the approximate dynamic programming (ADP) technique is used to resolve the cooperative control problem for the completely model-free linear multi-agent systems in both continuous-time and discrete-time cases. To ensure the consensus achieved at a specified consensus speed, the modified LQR design technique is used. The sufficient condition for the consensus is derived. However, in actual applications, the precise models of the multi-agent systems cannot be easily obtained, and the nominal mathematical models are even unavailable. To overcome this difficulty, ADP-based model-free algorithms are developed to obtain the distributed protocols based on the proposed consensus design method. Moreover, the specified consensus speed can be guaranteed. Compared with the existing work, the superiority of the developed methods ensures that all the following agents synchronize to the leader with the error converging to zero instead of a bounded residual error. Two numerical examples are provided to show the effectiveness of the developed approaches.

A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems

Abstract Distributed cooperative control of multi-agent systems has been one of the most active research topics in the fields of automatic control and robotics. This paper provides a survey on recent advances in distributed cooperative control under a sampled-data setting, with special emphasis on the published results since 2011. First, some typical sampling mechanisms related to this topic, such as uniform sampling, nonuniform sampling, random sampling, and event-triggered sampling, are summarized in both asynchronous and synchronous paradigms. Then, based on different coordinated tasks, recent results on distributed sampled-data cooperative control of multi-agent systems are categorized into four classes, i.e., sampled-data leaderless consensus, sampled-data leader-following consensus, sampled-data containment control, and sampled-data formation control. For each class, some explicit research lines are identified according to various sampling mechanisms. In particular, depending on definitions of event triggering conditions, some representative event-triggered sampling mechanisms are sorted out and discussed in detail. Finally, several challenging issues for future research are proposed.

Decentralized event-triggered cooperative control for multi-agent systems with uncertain dynamics using local estimators

This paper presents a decentralized event triggered cooperative control design for uncertain multi-agent systems under limited communication resources. A local estimator is employed by each agent to generate self-state estimates. The estimated states are directly used in the consensus control design, and the estimator parameters are used in the event condition design. Once an event is triggered, the local estimator is repeatedly reset to its corresponding real state values, such that it can stabilize the uncertain dynamical systems without knowing the exact system model parameters. A theorem for this triggering condition is developed to provide stable thresholds that are robust to model uncertainties and guarantee the asymptotical stability by exploiting the M-matrix, algebraic graph theory and the Lyapunov method. It is rigorously proved that the overall system will achieve the consensus and has no zeno behavior under the introduced triggering condition. Simulation results are provided to show the effectiveness of the proposed decentralized event-triggered cooperative control strategy.

Adaptive distributed observer and the cooperative control of multi-agent systems

The distributed observer approach has been an effective way to synthesise a distributed control law for a multi-agent system. However, this approach assumes that all the followers know the system matrix of the leader system, and this assumption may not be desirable in some applications. In this note, we will further introduce an adaptive distributed observer, which is able to estimate both the state and the system matrix of the leader and thus does not require that all the followers know the system matrix of the leader system. We will also point out some applications of the adaptive distributed observer to several cooperative control problems of multi-agent systems such as the leader-following consensus problem, the cooperative output regulation problem and rendezvous and/or flocking.

A Distributed Feedforward Approach to Cooperative Control of AC Microgrids

This paper addresses the cooperative control problem of AC microgrids consisting of both voltage-controlled voltage-source inverters and current-controlled voltage-source inverters. The voltage-controlled voltage-source inverters dictate the frequency and voltage of the microgrid and the current-controlled voltage-source inverters provide quick and decoupled active and reactive power support to the microgrid. To handle the nonlinear and heterogeneous dynamics of the inverters, we have developed a distributed feedforward approach based on the cooperative control of multi-agent systems. The proposed controller presents three advantages in comparison with the existing works. First, all the inverters share one communication network, and the locations of the inverters over the communication network can be arbitrarily sited as long as all the inverters are connected. Second, the selection of the control gains does not rely on either the whole microgrid dynamics or the topology of the communication network. Third, the inverters’ dynamics after input-output feedback linearization are allowed to be different. The effectiveness of the proposed controller is verified by the simulation study of a microgrid system for three cases, i.e., frequency and voltage restoration after islanding, active and reactive power adjustment after abrupt load changes and system performance subject to communication link failure and restoration.

Cooperative control of multi-agent systems with unknown control directions

This paper deals with the cooperative control problem of high-order multi-agent systems with unknown control directions. Adaptive backstepping technology is utilized to handle the difficulties caused by the unknown control direction in every order’s dynamics. By using a conditional inequality related to multiple terms of the Nussbaum-type function at each step, the consensus problem for systems with undirected and connected topology is solved. Then, it is shown that cooperative asymptotic regulation problem can be addressed by the same design procedure. The agents can achieve consensus and converge to the equilibrium asymptotically as well. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods.

Approximately adaptive neural cooperative control for nonlinear multiagent systems with performance guarantee

ABSTRACTThis paper studies the cooperative control problem for a class of multiagent dynamical systems with partially unknown nonlinear system dynamics. In particular, the control objective is to solve the state consensus problem for multiagent systems based on the minimisation of certain cost functions for individual agents. Under the assumption that there exist admissible cooperative controls for such class of multiagent systems, the formulated problem is solved through finding the optimal cooperative control using the approximate dynamic programming and reinforcement learning approach. With the aid of neural network parameterisation and online adaptive learning, our method renders a practically implementable approximately adaptive neural cooperative control for multiagent systems. Specifically, based on the Bellman's principle of optimality, the Hamilton–Jacobi–Bellman (HJB) equation for multiagent systems is first derived. We then propose an approximately adaptive policy iteration algorithm for multiagent cooperative control based on neural network approximation of the value functions. The convergence of the proposed algorithm is rigorously proved using the contraction mapping method. The simulation results are included to validate the effectiveness of the proposed algorithm.

带有领航者的非线性Markov切换多智能体系统的均方一致性

近年来，随着科学技术的迅速发展及应用的需要，多智能体系统的协调控制成为控制领域的一个研究热点。一致性问题作为多智能体系统协调控制的基础，受到了各个领域的研究学者越来越多的关注。本文针对非线性多智能体系统设计了相应的一致性控制算法，利用黎卡迪方程方法以及Markov的特性使非线性系统达到均方一致性，最后通过仿真验证了结果的正确性和有效性。 In recent years, with the rapid development of science and application, cooperative control of multi-agent systems has become a hot research in the field of control. As the basis of the coordina-tion problem for multi-agent systems, the consensus problem has attracted more and more atten-tions. Aimed at nonlinear multi-agent systems, control algorithm has been designed, using Riccati equation, and some criteria for achieving the mean square consensus via the properties of Markov theory. Finally, some simulation examples are provided to illustrate the effectiveness of the theo-retical results.