First-order Multi-agent Systems Research Articles

Fixed-time cluster optimization of multi-agent systems on directed detail-balanced networks

This paper investigates the fixed-time cluster optimization problem of first-order multi-agent systems (MASs) under directed detail-balanced networks, in which the optimization objective is a linear combination of local objective functions. Two piecewise distributed control protocols are proposed to solve the optimization problem with time-invariant and time-varying objective functions, respectively. Under the two proposed piecewise control protocols, the fixed-time cluster optimization problem can be solved on the basis of maintaining the cluster consensus unchanged. Furthermore, the initial states of all the agents need not be restricted to the minimum of their local cost functions. Finally, we provide two examples to illustrate the effectiveness of the proposed control protocols.

Finite-time bearing-only formation of first-order multi-agent systems under pinning control

Finite-time bearing-only formation of first-order multi-agent systems under pinning control

Average-rendezvous with connectivity preservation for first-order multiagent systems with constant reference signals

Average-rendezvous problem with connectivity preservation of constant reference signals is investigated for first-order multiagent systems. According to a constructive potential function, a proportional–integral average-rendezvous algorithm is proposed to make agents converge to the average value of constant reference signals as well as the network connectivity is preserved all the time. Sufficient convergence conditions are obtained for the algorithm by designing the proper Lyapunov functions. Numerical examples illustrate the correctness of theoretical results.

Average Consensus Tracking of Weight-Balanced Multi-Agent Systems via Sampled Data

This paper studies the average consensus tracking problem of first-order multi-agent systems under directed topologies. A control protocol is constructed based on the neighbors’ agent sampled information. With the help of the matrix theory and frequency domain analysis, the necessary and sufficient condition can be induced for the average consensus tracking of multi-agent systems, although the weight-balanced condition is not satisfied. In addition, a numerical simulation example is given to illustrate the effectiveness of the proposed results.

$ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control

<abstract><p>The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.</p></abstract>

Resilient Consensus for Discrete-Time Multiagent Systems With a Dynamic Leader and Time Delay: Theory and Experiment.

The ever-present cyber-attacks have posed a significant challenge to consensus of multiagent systems (MASs), due to their capability of compromising agents. These threats underscore the critical need to design control strategies that can endow MASs with resilience. In this article, we address resilient consensus problems for first-and second-order discrete-time MASs, considering the presence of malicious agents, a dynamic leader, and communication delay. First, a resilient controller is designed for first-order MASs, and sufficient conditions are derived based on existing robust graph concepts to achieve consensus with ultimately bounded error. Next, since the derived error bound grows factorially with the system scale, a novel graph structure and a modified controller are proposed to limit the growth to a linear rate. Building upon the obtained results, an estimator-based control framework is introduced to solve resilient consensus problems for second-order MASs. Finally, comparative simulations and practical experiments based on unmanned ground vehicles and unmanned-aerial-vehicles are conducted to validate the effectiveness and practicability of the proposed control methods.

Predefined-Time Formation Control for Multiagent Systems-Based on Distributed Optimization.

This article presents a solution to the leaderless formation control problem for first-order multiagent systems, which minimizes a global function composed of a sum of local strongly convex functions for each agent under weighted undirected graphs within a predefined time. The proposed distributed optimization process consists of two steps: 1) the controller initially leads each agent to the minimizer of its local function and 2) then guides all agents toward achieving leaderless formation and reaching the global function's minimizer. The proposed scheme requires fewer adjustable parameters than most existing methods in the literature without the need for auxiliary variables or time-variable gains. Additionally, one can consider highly nonlinear multivalued strongly convex cost functions, while the agents do not share the gradients and Hessians. Extensive simulations and comparisons with state-of-the-art algorithms demonstrate the effectiveness of our approach.

Free-will arbitrary time consensus of heterogeneous nonlinear multi-agent systems

This paper addresses several kinds of free-will arbitrary time (FWAT) consensus problems for heterogeneous nonlinear multi-agent systems (MASs). For first-order MASs, both leaderless and leader-following FWAT consensus are studied. Based on the FWAT control technology, some novel distributed control protocols are proposed, under which FWAT consensus of first-order MASs is achieved within the arbitrary pre-specified time and maintained after then. Then, the backstepping method is employed to design the controller for second-order heterogeneous nonlinear MASs. FWAT consensus of second-order MASs can also be guaranteed by using the proposed controller. Finally, simulation examples are presented to illustrate the effectiveness of theoretical analysis.

Group consensus for competitive multiagent systems with input saturation and intermittent communication using current and outdated states

This paper investigates group consensus control for first-order multi-agent systems (MASs) with input saturation and intermittent communication. A novel class of distributed group consensus protocols is designed by combining current and outdated states of agents, which differs from the standard one using only current states. Sufficient conditions for group consensus are derived for MASs without two conservative assumptions required by previous literature. The proposed protocol can accelerate the convergence speed of MASs by choosing appropriate outdated states. Several examples are provided to illustrate the effectiveness of our results.

Fault-Tolerant Consensus Control for Discrete-Time Multi-Agent Systems: A Distributed Adaptive Sliding-Mode Scheme

In this brief paper, a fully distributed sliding mode controller with fault compensation is designed to deal with the consensus problem of discrete-time first-order multi-agent systems with actuator faults. A novel fully distributed integral sliding surface (ISS) without global information is proposed to guarantee consensus when agents move on the sliding surface. Based on such a sliding manifold combined with identified faults, a fully distributed sliding mode fault-tolerant controller is constructed, while a sufficient condition is derived to guarantee the finite-time reachability of the distributed ISS. Finally, simulation results verify the effectiveness of the proposed control algorithm.

The cooperatability of the first-order multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies

We investigate the cooperatability of the first-order leader-following multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies. Each agent exhibits first-order linear dynamics, and there are multiplicative noises along with information exchange among the agents. What is more, the communication topologies are Markov switching topologies. By utilizing the stability theory of the stochastic differential equations with Markovian switching and the Markov chain theory, we establish the necessary and sufficient conditions for the cooperatability of the leader-following multi-agent systems. The conditions are outlined below: (ⅰ) The product of the system parameter and the square of multiplicative noise intensities should be less than 1/2; (ⅱ) The transition rate from the unconnected graph to the connected graph should be twice the system parameter; (ⅲ) The transition rate from the connected graph to the unconnected graph should be less than a constant that is related to the system parameter, the intensities of multiplicative noises, and the transition rate from the unconnected graph to the connected graph. Finally, the effectiveness of our control strategy is demonstrated by the population growth systems.

Event-Based Distributed Secondary Control for AC Islanded Microgrid With Semi-Markov Switched Topology Under Cyber-Attacks

The operation of a microgrid (MG) is easily affected by the environment, which leads to the change of communication topology among distributed generations (DGs). Most of the existing results on secondary control of MG consider that the topology connection is fixed, or just simply switched by arbitrary form. In this article, a more general semi-Markov process is introduced to describe such switching, i.e., the switching of communication topology is regarded as a random change process of system mode under general probability distribution. Then, out of the comprehensive consideration of inevitable network constraints, this article proposes distributed resilient secondary control method for AC islanded MG. In our control strategy, the network security, communication burden, and transmission delay are all considered in the controller design. An event detection mechanism is used as the transmission protocol for information interaction among DGs, reducing the communication burden effectively. And a cyber-attack model is introduced to follow the Bernoulli distribution, and the neighbors' information of each DG may be attacked with possible probability. Based on feedback linearization, the studied secondary control problem is cast into distributed tracking synchronization of first-order multiagent systems. The Lyapunov functional method is used to prove the proposed strategy theoretically, and its effectiveness is verified by a modified IEEE 34 bus test system. The result shows that the proposed method can reduce the communication numbers by over 80% under the premise of realizing frequency restoration and accurate real power sharing of AC islanded MG, and the transmission rate is also reduced by about 40% compared with the existing general method.

Predefined-Time Bounded Consensus of Multiagent Systems With Unknown Nonlinearity via Distributed Adaptive Fuzzy Control.

This article investigates uniformly predefined-time bounded consensus of leader-following multiagent systems (MASs) with unknown system nonlinearity and external disturbance via distributed adaptive fuzzy control. First, uniformly predefined-time-bounded stability is analyzed and a sufficient condition is derived for the system to achieve semiglobally (globally) uniformly predefined-time-bounded consensus. Therein, the settling time is independent of initial conditions and can be defined in advance. Then, for first-order MASs, distributed adaptive fuzzy controllers are designed by combining neighboring consensus errors to drive all following agents to globally track the leader's state within predefined time. For second-order MASs, by formulating filtered errors, the consensus errors between following agents and the leader are shown to be bounded if the filtered errors are bounded. Furthermore, with the distributed controllers designed based on filtered errors, second-order MASs achieve semiglobally uniformly predefined-time-bounded leader-following consensus. Finally, two numerical examples are simulated, including: 1) a first-order leader-following MAS and 2) a second-order Lagrangian system consisting of single-link manipulators, to demonstrate the performance of the proposed controllers.

Consensus of Multi-Agent Systems With Asymmetric Input Saturation Over Directed Graph

In this brief, the consensus issue of continuous-time first-order multi-agent systems (MASs) subject to asymmetric input saturation under the directed graph containing a directed spanning tree is investigated. First, a fully distributed consensus protocol is proposed. We discuss the scenario where there are zeros in the partial saturation bounds. Based on the contradiction method and the graph theory, a necessary and sufficient criterion for guaranteeing the global consensus is given. After that, we extend the above findings to the discrete-time case, where an upper bound of the sample time is explicitly formulated. Finally, simulation examples verify the effectiveness of our proposed strategy.

Distributed $${H_\infty }$$ Consensus Problem for First-Order Multi-Agent Systems with Antagonistic Interactions and Nonconvex Constraints

Distributed $${H_\infty }$$ Consensus Problem for First-Order Multi-Agent Systems with Antagonistic Interactions and Nonconvex Constraints

Optimal Active Power Generation in Electrical Networks Using Distributed Fixed-Time Control of Multi-Agent Systems

This paper tackles the Economic Dispatch Problem (EDP) in power systems, with the objective of generating optimal active power at each source to minimize overall generation costs, while maintaining the power generation-demand equality and staying within the source generation limits. The main motivation behind this work is to create a power optimization strategy that accomplishes these goals while providing superior performance in terms of convergence speed and accuracy of the optimal solution. To this end, a fixed-time active power optimization protocol is proposed for power sources in electrical networks. Distributed and local fixed-time control laws of first-order multi-agent systems are developed for this purpose. This paper presents four technical contributions: i) minimizing active power generation costs in electrical network sources within a predetermined maximum settling time without violating their generation limits while ensuring generation-demand equality, ii) a distributed overall control system connected through a sparse communication network modeled as an undirected graph that avoids the pitfalls of centralized solutions, iii) a model-free optimization method that does not require previous knowledge of power system parameters, and iv) a continuous optimization law that provides smooth power variations. Simulations are conducted to demonstrate the effectiveness of the proposed approach.

Accelerating Distributed Optimization via Fixed-Time Convergent Flows

Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization algorithm for solving a potentially non-convex optimization problem using a first-order multi-agent system. Each agent in the network can access only its private objective function, while local information exchange is permitted between the neighbors. The proposed optimization algorithm combines a fixed-time convergent distributed parameter estimation scheme with a fixed-time distributed consensus scheme as its solution methodology. The results are presented under the assumption that the team objective function is strongly convex, as opposed to the common assumptions in the literature requiring each of the local objective functions to be strongly convex. The results extend to the class of possibly non-convex team objective functions satisfying only the Polyak-Lojasiewicz (PL) inequality. It is also shown that the proposed continuous-time scheme, when discretized using Euler's method, leads to consistent discretization.

Distributed predefined-time optimization in formation control under switching topologies

This paper presents a novel distributed zero-gradient-sum algorithm for addressing the formation control problem by minimizing the sum of strongly convex functions under switching topologies in first-order multi-agent systems. The main contribution of this work is the development of a two-step controller that allows agents to achieve leaderless formation and reach the global function's minimizer within a predefined time while maintaining the privacy of local objective functions, gradients and Hessians. The proposed algorithm exhibits a unique combination of features, including predefined-time stability, applicability to multi-valued strongly-convex functions, independence from initial conditions and adaptability to switching topologies without the need to know the number of agents. Furthermore, the algorithm avoids the use of auxiliary variables and time-variable gains. This work also provides numerical simulations to demonstrate the effectiveness and validity of the proposed algorithm.

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.

Finite-/fixed-time bipartite consensus for first-order multi-agent systems via impulsive control

This paper studies the finite-/fixed-time bipartite consensus (FNTBC and FXTBC) of multi-agent systems (MASs) over signed graph via discontinuous impulsive control while considering both leaderless and leader-following MASs. In contrast to the existing methods of FNTBC and FXTBC, the impulsive control has a better performance in convergence speed and less state information transmission, which is more practical and flexible in real applications. To realize FNTBC and FXTBC for leaderless and leader-following MASs, a class of distributed impulsive control protocols is proposed. Then by utilizing impulsive control theory and finite-/fixed-time stability theory, some sufficient criteria and the settling time which are based on the proposed impulsive control protocols for FNTBC and FXTBC for leaderless and leader-following MASs are derived. It has been shown that the settling time for FNTBC depends on initial conditions of systems, while this limitation is removed for FXTBC. Finally, the proposed impulsive protocols are validated by some simulations, separately.