Initial States Of Agents Research Articles

Fixed-time scaled consensus of multi-agent systems with input delay

The design of fixed-time scaled consensus protocol for multi-agent systems with input delay is developed in this article. First, by virtue of Artstein model reduction method, the time-delay system is converted into a delay-free one. Then, two novel controllers are designed such that the fixed-time scaled consensus of multi-agent systems can be realized for the undirected and directed topology, respectively. Sufficient conditions are derived to guarantee that all agents converge to the assigned ratios instead of the same value under any bounded input delay. Besides, an explicit estimate can be given for the uniform convergence time independent of the initial conditions. Moreover, it is proved that the convergence value of the system is not affected by the initial states of agents any more, but only related to initial states of the virtual agents set in advance. Finally, numerical simulations are given to demonstrate the feasibility of the proposed algorithms.

Cucker-Smale flocking over cooperation-competition networks

This paper offers a novel distributed control scheme for the Cucker-Smale model to examine the leader-follower flocking behavior on networks with both cooperative and competitive interactions among agents. The core idea of the proposed scheme is to characterize the influence of cooperation and competition between agents through positive and negative weight functions with respect to the interaction distance, respectively. Based on the tool of infinite products of super-stochastic matrices, we establish mathematical inequalities about the intensities of cooperation and competition, and further obtain the algebraic conditions that depend on factors such as the initial states of agents, topological structure and weight functions. Moreover, we also discuss the influence of these factors on the least exponential convergence rate and the final position errors among agents. The obtained theoretical results are illustrated through simulation examples.

Autonomous Synchronization of Heterogeneous Multiagent Systems

This article formulates a new type of synchronization problem for heterogeneous multiagent systems (MASs), called autonomous synchronization. In this problem, neither the synchronized agent dynamics nor the synchronized states are specified a priori, instead, they are autonomously determined by the inherent properties and the initial states of agents, thus providing an MAS with more degrees of adaptability and higher synchronization efficiency. To achieve autonomous synchronization, a novel dynamics update law and a synchronizing control law are proposed and the sufficient solvability conditions are explicitly revealed. The results are supported by rigorous theoretical analysis and numerical simulation, in both continuous-time and discrete-time settings.

Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model

Multiagent systems are used in artificial intelligence, control theory, and social sciences. In this article, we studied a Cucker–Smale model with a continuous non-Lipschitz protocol. The methodology presented in the current paper is based on the explicit construction of a Lyapunov functional. By using the fixed-time control technology, we show that the flocking can occur in fixed-time and collision avoiding when a singular communication function with a weighted sum of sign functions of the relative velocities among agents, and we can obtain the estimation of the converging time which is independent of the initial states of agents. Theoretical results are supported by numerical simulations.

Fixed-Time Flocking Problem of a Cucker–Smale Model

In this paper, we studied a Cucker–Smale model with continuous non-Lipschitz protocol. The methodology presented in the current work is based on the explicit construction of a Lyapunov functional. By using the fixed-time control technology, we show that the flocking can occur in fixed time if the communication rate function is locally Lipschitz continuous and has a lower bound, and we can obtain the estimation of the converging time which is independent of the initial states of agents. Theoretical results are supported by numerical simulations.

Guaranteed-performance consensus for descriptor nonlinear multi-agent systems based on distributed nonlinear consensus protocol

In this paper, guaranteed-performance consensus (GPC) for descriptor nonlinear multi-agent systems (DNMASs) with a leader is studied. The interactions among followers are bidirectional for leader-following DNMASs. Firstly, one designs a novel distributed nonlinear consensus protocol based on state feedback to reach consensus for DNMASs. The performance function is constructed by state errors among agents, which is time integration of quadratic function. Secondly, not only are sufficient conditions presented for guaranteed-performance consensus to ensure the scalability of DNMASs based on the Riccati inequality, but also an upper bound of the cost function is derived. It is shown that the guaranteed-performance costs are dependent on initial states of agents. Moreover, the conclusions are extended to achieve the leaderless GPC. Finally, simulation examples are presented to demonstrate the effectiveness of theoretical results.

An iterative Q-learning based global consensus of discrete-time saturated multi-agent systems.

This paper addresses the consensus problem of discrete-time multiagent systems (DTMASs), which are subject to input saturation and lack of the information of agent dynamics. In the previous works, the DTMASs with input saturation can achieve semiglobal consensus by utilizing the low gain feedback (LGF) method, but computing the LGF matrices by solving the modified algebraic Riccati equation requires the knowledge of agent dynamics. In this paper, motivated by the reinforcement learning method, we propose a model-free Q-learning algorithm to obtain the LGF matrices for the DTMASs achieving global consensus. Firstly, we define a Q-learning function and deduce a Q-learning Bellman equation, whose solution can work out the LGF matrix. Then, we develop an iterative Q-learning algorithm to obtain the LGF matrix without the requirement of the knowledge about agent dynamics. Moreover, the DTMASs can achieve global consensus. Lastly, some simulation results are proposed to validate the effectiveness of the Q-learning algorithm and show the effect on the rate of convergence from the initial states of agents and the input saturation limit.

Robust Quantized Consensus of Discrete Multi-Agent Systems in the Input-to-State Sense

In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from additive noise. Due to the limited communication resources, each agent can only exchange quantized information of finite length with its neighbors through unreliable channels, where the transmitted signals may be delayed or even lost. Quantization errors, network delay, and packet loss result in quantization mismatch. To handle the additive noise and quantization mismatch, a quantized consensus protocol is proposed by implementing dynamic encoding and decoding policies at a finite bit rate. Particularly, the proposed consensus protocol introduces an internal saturation function into all the controllers of agents so that the control inputs of neighbor agents can be predicted locally by each agent even under distributed control law and quantization mismatch. Based on such shared control input information, the proposed consensus protocol can guarantee the achievement of the approximate consensus of all agents in the input-to-state sense, i.e., the consensus errors of agents are bounded from above by the sum of a class $\mathcal {K}_\infty $ function of the upper bound of the additive noise and a class $\mathcal {KL}$ function of the upper bound on the initial states of agents. It is shown that such approximate consensus in the input-to-state sense can be guaranteed at an as low bit rate as 1 bit per time step for each agent without requiring any global information, except an upper bound of the number of agents. Two specific situations, namely packet loss, and network delay, are further analyzed with the explicit expressions of quantization mismatch. The simulations are done to confirm the effectiveness of the proposed quantized consensus protocol.

Distributed Optimization for Multiagent Systems: An Edge-Based Fixed-Time Consensus Approach

This paper deals with the problem of distributed optimization for multiagent systems by using an edge-based fixed-time consensus approach. In the case of time-invariant cost functions, a new distributed protocol is proposed to achieve the state agreement in a fixed time while the sum of local convex functions known to individual agents is minimized. In the case of time-varying cost functions, based on the new distributed protocol in the case of time-invariant cost functions, a distributed protocol is provided by taking the Hessian matrix into account. In both cases, stability conditions are derived to ensure that the distributed optimization problem is solved under both fixed and switching communication topologies. A distinctive feature of the results in this paper is that an upper bound of settling time for consensus can be estimated without dependence on initial states of agents, and thus can be made arbitrarily small through adjusting system parameters. Therefore, the results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives. Case studies of a power output agreement for battery packages are provided to demonstrate the effectiveness of the theoretical results.

A nonlinear merging protocol for consensus in multi-agent systems on signed and weighted graphs

In this paper, we investigate the multi-agent consensus for networks with undirected graphs which are not connected, especially for the signed graph in which some edge weights are positive and some edges have negative weights, and the negative-weight graph whose edge weights are negative. We propose a novel nonlinear merging consensus protocol to drive the states of all agents to converge to the same state zero which is not dependent upon the initial states of agents. If the undirected graph whose edge weights are positive is connected, then the states of all agents converge to the same state more quickly when compared to most other protocols. While the undirected graph whose edge weights might be positive or negative is unconnected, the states of all agents can still converge to the same state zero under the premise that the undirected graph can be divided into several connected subgraphs with more than one node. Furthermore, we also discuss the impact of parameter r presented in our protocol. Current results can further deepen the understanding of consensus processes for multi-agent systems.

Distributed Fixed‐Time Coordinated Tracking for Nonlinear Multi‐Agent Systems Under Directed Graphs

AbstractThis paper is concerned with the fixed‐time coordinated tracking problem for a class of nonlinear multi‐agent systems under detail‐balanced directed communication graphs. Different from conventional finite‐time coordinated tracking strategies, the fixed‐time approach developed in this paper guarantees that a settling time bound is prescribed without dependence on initial states of agents. First, for the case of a single leader, a distributed protocol based on fixed‐time stability techniques is proposed for each follower to accomplish the consensus tracking in a fixed time. Second, in the presence of multiple leaders, a new distributed protocol is proposed such that states of followers converge to the dynamic convex hull spanned by those of leaders in a fixed time. In addition, for a class of linear multi‐agent systems, sufficient conditions that guarantee the fixed‐time coordinated tracking are provided. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Finite-Time Consensus of Switched Multiagent Systems

This paper focuses on the finite-time consensus (FTC) problem of switched multiagent system (MAS) which is composed of continuous-time and discrete-time subsystems. Different from the existing results, each agent of this system is controlled by switching control method. To achieve consensus in finite time for the switched MAS, two types of consensus protocols (the FTC protocol and the fixed-time consensus (F d TC) protocol) are proposed. By using algebraic graph theory, Lyapunov theory and matrix theory, it is proved that the FTC problem in strongly connected network and leader-following network can be solved, respectively. When the initial states of agents are not available, the F d TC protocol is applied to solve the FTC problem. Simulations are provided to illustrate the effectiveness of our theoretical results.

Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology

ABSTRACTThis paper is concerned with the fixed-time consensus problem of multi-agent systems. Unlike conventional consensus-based investigations, where nonlinear inherent dynamics satisfying the Lipschitz continuous condition is assumed or simply no inherent dynamics is involved for each agent, we are dealing with a more general case: agents with discontinuous nonlinear inherent dynamics. By using non-smooth analysis and fixed-time stability techniques, distributed protocols are proposed to achieve the fixed-time consensus over fixed and switching topology. Then, for a class of linear multi-agent systems, a new distributed controller is proposed to further reduce the calculation cost while achieving the agreement. A distinctive feature of the work is that the estimation of settling time for consensus is independent of initial states of agents, which provides flexibility for applications implemented in unknown environment. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Privacy Preserving Average Consensus

Average consensus is a widely used algorithm for distributed computing and control, where all the agents in the network constantly communicate and update their states in order to achieve an agreement. This approach could result in an undesirable disclosure of information on the initial state of agent i to the other agents. In this paper, we propose a privacy preserving average consensus algorithm to guarantee the privacy of the initial state and the convergence of the algorithm to the exact average of the initial values, by adding and subtracting random noises to the consensus process. We characterize the mean square convergence rate of our consensus algorithm and derive upper and lower bounds for the covariance matrix of the maximum likelihood estimate on the initial state. A numerical example is provided to illustrate the effectiveness of the proposed design.

Signed-average consensus for networks of agents: a nonlinear fixed-time convergence protocol

This paper addresses the consensus problem of multi-agent systems where the interactions between agents are not only cooperative but also antagonistic. A distributed nonlinear protocol is proposed to guarantee the agents to reach agreement bipartitely regarding a signed-average quantity that depends on both the initial states of agents and the topology structures of multi-agent systems. Moreover, this signed-average consensus can be achieved within a fixed settling time which is not dependent upon the initial states of agents but can be estimated by the design parameters of the presented protocol. Numerical simulations are performed to illustrate the fixed-time convergence performance of the established signed-average consensus results.

Event-Triggered Distributed Average Consensus Over Directed Digital Networks With Limited Communication Bandwidth.

In this paper, we consider the event-triggered distributed average-consensus of discrete-time first-order multiagent systems with limited communication data rate and general directed network topology. In the framework of digital communication network, each agent has a real-valued state but can only exchange finite-bit binary symbolic data sequence with its neighborhood agents at each time step due to the digital communication channels with energy constraints. Novel event-triggered dynamic encoder and decoder for each agent are designed, based on which a distributed control algorithm is proposed. A scheme that selects the number of channel quantization level (number of bits) at each time step is developed, under which all the quantizers in the network are never saturated. The convergence rate of consensus is explicitly characterized, which is related to the scale of network, the maximum degree of nodes, the network structure, the scaling function, the quantization interval, the initial states of agents, the control gain and the event gain. It is also found that under the designed event-triggered protocol, by selecting suitable parameters, for any directed digital network containing a spanning tree, the distributed average consensus can be always achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. Two simulation examples are provided to illustrate the feasibility of presented protocol and the correctness of the theoretical results.

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.

Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions.

This paper deals with finite-time consensus problems for multiagent systems that are subject to hybrid cooperative and antagonistic interactions. Two consensus protocols are constructed by employing the nearest neighbor rule. It is shown that under the presented protocols, the states of all agents can be guaranteed to reach an agreement in a finite time regarding consensus values that are the same in modulus but may not be the same in sign. In particular, the second protocol can enable all agents to reach a finite-time consensus with a settling time that is not dependent upon the initial states of agents. Simulation results are given to demonstrate the effectiveness and finite-time convergence of the proposed consensus protocols.

Multi-agent consensus with time-varying delays and switching topologies

The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and processes its own state information with time-varying self-delay respectively. The state time-delay feedback is introduced into the existing consensus protocol to begenerate an improved protocol. Then a sufficient condition is derived which can make the system with time-varying self-delays achieve the consensus. On this basis, a specific form of consensus equilibrium influenced by the initial states of agents, time-delays and state feedback intensity is figured out. In addition, the multi-agent consensus is considered with time-varying topologies. Finally, simulations are presented to illustrate the validity of theoretical results.

State Feedback Consensus for Multi-Agent System with Multiple Time-Delays

In this paper, we study the multi-agent system to achieve a faster consensus with multiple time-delays under a directed asymmetric information exchange topology. We first assume that an agent processes its own state information with self-delay and receives state information from its neighbors with communication delays. Based on state proportion derivative feedback, the improved consensus protocol can accelerate the system to achieve a consensus. A sufficient condition for reaching consensus is then derived based on the Nyquist stability criterion and frequency domain analysis. In addition, a specific form of consensus equilibrium is obtained which is influenced by the initial states of agents, time-delays and state feedback intensity. Finally, simulations are presented to verify the validity of the theoretical results.