Consensus Of Discrete-time Multi-agent Systems Research Articles

Min–max group consensus of discrete-time multi-agent systems under directed random networks

This paper studies the min–max group consensus of discrete-time multi-agent systems under a directed random graph, where the presence of each directed edge is randomly determined by a probability and independent of the presence of other edges. Firstly, we propose a min–max consensus protocol without memory, and give the necessary and sufficient conditions to ensure that the multi-agent system can achieve the min–max group consensus in the sense of almost sure and mean square, respectively. Secondly, we design a novel consensus protocol with memory and a behavior mechanism. Using the stochastic analysis theory and the extremal algebra, some necessary and sufficient conditions are obtained for achieving the min–max group consensus in the sense of almost sure and mean square, respectively. It is shown that the protocol with memory can solve the loss problem of the maximum and minimum initial states. Finally, the effectiveness of the two group consensus protocols and the behavior mechanism is verified by four numerical simulations.

Consensus of Discrete-Time Multiagent Systems With Transient Performance Constraints

Consensus of Discrete-Time Multiagent Systems With Transient Performance Constraints

Two-Layer Reinforcement Learning for Output Consensus of Multiagent Systems Under Switching Topology.

In this article, the data-based output consensus of discrete-time multiagent systems under switching topology (ST) is studied via reinforcement learning. Due to the existence of ST, the kernel matrix of value function is switching-varying, which cannot be applied to existing algorithms. To overcome the inapplicability of varying kernel matrix, a two-layer reinforcement learning algorithm is proposed in this article. To further implement the proposed algorithm, a data-based distributed control policy is presented, which is applicable to both fixed topology and ST. Besides, the proposed method does not need assumptions on the eigenvalues of leader's dynamic matrix, it avoids the assumptions in the previous method. Subsequently, the convergence of algorithm is analyzed. Finally, three simulation examples are provided to verify the proposed algorithm.

Leader-following Consensus for Discrete-time Multi-agent Systems With Nonidentical Channel Fading

Leader-following Consensus for Discrete-time Multi-agent Systems With Nonidentical Channel Fading

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.

Event-Triggered Semi-Global Output Consensus of Discrete-Time Multi-Agent Systems With Input Saturation and External Disturbances

In this brief, the event-triggered semi-global output consensus is investigated for discrete-time multi-agent systems subject to input saturation and external disturbances. Under the assumption that the dynamics of all nodes are identical, based on output regulation, a protocol view is proposed by using relative state information. On the basis of Lyapunov stability theory, sufficient conditions for output consensus are obtained. Finally, a simulation result is given to illustrate the theoretical findings.

Optimal bipartite consensus for discrete-time multi-agent systems with event-triggered mechanism based on adaptive dynamic programming

This paper proposes optimal bipartite consensus issue for discrete-time multi-agent system (DTMAS) using event-triggered control (ETC) and quantized event-triggered control (QETC). Firstly, a novel event-triggered control strategy is introduced along with specific conditions to ensure the stability for DTMAS. Due to the intractability of the Hamilton–Jacobi–Bellman (HJB) equation, through two neural networks (NNs), the value function and optimal control are approximated by the adaptive dynamic programming (ADP) method. The weight matrix of the action neural network is updated only when triggered, while also taking into account the quantization effect of the information. The stability of the weights errors and the convergence of the system dynamic are demonstrated using Lyapunov stability theory. Finally, the practicality of the improved method is confirmed a numerical example.

Attack-free protocols design for leader-following consensus of discrete-time multi-agent systems with multiple input delays

The consensus problem for leader-following multi-agent systems (MASs) characterised by discrete-time multiple input delays linear systems with directed communication topologies is investigated. Under reasonable assumptions, full-order observer-based output feedback protocols are first established by using the relative outputs and inputs of neighbouring agents. In order to overcome the impact of potential network attacks, we truncate the relative inputs of the proposed protocols, namely the exchange of communication information between neighbouring agents is forbidden, so that the closed-loop leader-following MAS is inherently immune to being attacked and achieves consensus. Additionally, the improved attack-free protocols not only allow arbitrarily large yet bounded delays, but also only relative output measurement can be available, which reduces the communication burden and thus are easy to implement in practice. A numerical example is worked out to illustrate the effectiveness of the proposed approach.

Differentially Private Consensus for Multi-Agent Systems Under Switching Topology

Existing results on differentially private consensus of multi-agent systems are limited to fixed interaction topology. This paper focuses on differentially private consensus of discrete-time multi-agent systems over switching networks for the first time. With the design of a distributed communication mechanism, in which the interactive information of each agent transmitted to its neighbors is obscured by uncorrelated random noise, the differential privacy of the agents’ initial states is preserved and the mean-square consensus of the multi-agent system is achieved. Moreover, a weaker noise constraint is given to broaden the existing range of noise selection. Finally, a numerical example verifies the effectiveness of the results.

Model-free algorithm for consensus of discrete-time multi-agent systems using reinforcement learning method

In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.

Observer-Based Dynamic Event-Triggered Bipartite Consensus of Discrete-Time Multi-Agent Systems

In this brief, the dynamic event-triggered bipartite consensus is explored for discrete-time multi-agent systems (MASs) under competitive network. Different from the existing works on dynamic event-triggered consensus of discrete-time MASs, observer based protocol is proposed by using the related output information. With the help of Lyapunov function method, some sufficient conditions are obtained and the control gains can be determined by solving discrete-time algebraic Riccati equations. Finally, a simulation example is presented to effectively verify the theoretical results.

Consensus of discrete-time multi-agent systems with consecutive packet losses in directed communication topology

In this paper, consensus analysis and design are investigated for discrete-time multi-agent systems (MASs) with consecutive packet losses in communication links of directed communication topology. It is assumed that at each transmitted instant, the packet loss is stochastic and described by Bernoulli distribution, but during a given time window, the data could be successfully transmitted to the agent from each of its neighbors. First, we utilize the incidence matrix of a directed spanning tree of the communication topology to construct a linear transformation matrix so that the consensus problem is equivalently transformed into a mean square asymptotic stability problem of a reduced-order system. Second, by using Lyapunov–Krasovskii functional approach, we derive some sufficient conditions of consensus criterion in terms of linear matrix inequalities (LMIs). These conditions express the relationship among the control gain matrix, packet loss rate, and the number of consecutive packet losses. Based on the conditions, gain matrix in the consensus protocol is designed to guarantee the MAS with stochastic packet losses to achieve mean square asymptotic consensus. Moreover, for the special case of undirected communication topology, by using the matrix decomposition method, the variables of LMIs are transformed into the low-order conditions independent of the network size. Finally, some numerical examples are given to show the effectiveness of the proposed method.

Leader-following almost output consensus for discrete-time heterogeneous multi-agent systems in the presence of external disturbances

In this paper, we consider the problem of leader-following almost output consensus for discrete-time multi-agent systems with heterogeneous follower agents. Conditions on agent dynamics, the communication topology and how the disturbance enters the agent dynamics are established under which leader-following almost output consensus can be achieved, that is, the leader-following output consensus can be reached with any pre-specified level of accuracy and the effect of the disturbance on the leader-following consensus can be attenuated to any pre-specified level. A family of state feedback consensus protocols are constructed by using the low gain feedback design technique and a modified discrete-time Riccati equation. These consensus protocols are shown to achieve leader-following almost output consensus. Additional conditions are identified under which output feedback results are established. Simulation results demonstrate the effectiveness of the proposed consensus protocols.

Necessary and Sufficient Conditions for Leader–Follower Consensus of Discrete-Time Multiagent Systems With Smart Leader

In this article, the leader-follower consensus is investigated for discrete-time second-order multiagent systems with smart leader, where the smart leader can obtain the feedback information from its neighbours. Different from the existing results, an objective function is provided to determine whether the leader utilizes the feedback information from its neighboring agents, with the purpose of making the system have better performance. Under the directed interconnected topology, a novel distributed consensus protocol is designed for second-order discrete-time multiagent systems. Some necessary and sufficient conditions are derived for the leader-follower consensus of discrete-time second-order multiagent systems with smart leader under fixed/switching topology. Finally, two simulation examples are presented to demonstrate the feasibility of the theoretical results.

Consensusability of discrete-time multi-agent systems under binary encoding with bit errors

This paper is concerned with the consensusability problem for a class of discrete-time multi-agent systems (DT-MASs). A binary encoding scheme (BES) is employed during the data transmission, and only a finite-length binary bit string is transmitted due primarily to the limited network bandwidth in practice. Meanwhile, the binary bit string, transmitted via memoryless binary symmetric channels, might suffer from random bit errors with a certain probability. The purpose of this paper is to derive some consensusability conditions, under which there must exist a distributed controller such that the mean-square bounded consensus is achieved by the considered DT-MASs with BESs subject to random bit errors. To this end, the statistical properties are first revealed for the BES-induced quantization errors and the random bit errors. Then, by resorting to the solvability analysis of a modified Riccati inequality, some sufficient conditions are, respectively, derived to ensure the mean-square bounded consensus under the undirected communication topology in two scenarios: (1) identical bit-error rates (BERs); and (2) non-identical BERs. In particular, a necessary and sufficient condition is established for a single input case with identical BERs. Furthermore, the ultimate upper bound of the consensus errors in the mean-square sense is established to examine the effects of the length of bit string and the BERs. Finally, an illustrative simulation example is provided to validate the effectiveness of the theoretical results.

Robust distributed model predictive consensus of discrete-time multi-agent systems: a self-triggered approach

Robust distributed model predictive consensus of discrete-time multi-agent systems: a self-triggered approach

Observer-based bipartite consensus for uncertain Markovian-jumping multi-agent systems with actuator saturation

This paper addresses the problem of bipartite consensus for discrete-time multi-agent systems with Markovian-jumping parameters under the influence of time-varying communication delay and actuator saturation. The main aim of this work is to propose an observer-based control protocol such that the bipartite consensus of the uncertain Markovian-jumping multi-agent system under consideration can be achieved. An undirected structurally balanced signed graph is utilized to describe the cooperative and antagonistic interaction among neighboring agents. Combining algebraic graph theory together with Lyapunov stability theory, a new set of sufficient conditions is derived by using Jensen’s inequality and Abel-lemma based finite sum inequality to achieve bipartite consensus. At last, a numerical example is provided with simulations to validate the effectiveness of the developed theoretical results.

Consensus of discrete-time multi-agent systems over packet dropouts channels

In this paper, we investigate the consensus problem for discrete linear multi-agent systems (MASs) with Markovian packet dropouts. Both identical and nonidentical packet dropouts are studied. For the discrete-time MASs under identical packet dropouts, we present the expectation of the total sojourn time of packet dropouts and successful message transmission, the switching number from packet dropouts to successful message transmission, and the awaken number of packet dropouts and successful message transmission. Based on these expectations, a linear consensus controller is designed through analyzing the transient properties of the Markov process such that the MASs can reach consensus almost surely for any initial distribution of packet dropouts. When it comes to the nonidentical packet dropouts where all the packets are independent and stochastic, a Markovian-lossy-channel based switching model (MLCBS model) is proposed. Based on the MLCBS model, we also propose an easy-to-implement linear consensus controller such that the MASs with nonidentical packet dropouts can achieve consensus almost surely. Finally, the theoretical results are illustrated by simulation examples.

Robust distributed adaptive consensus for discrete-time multiagent systems with uncertain topologies

This paper considers the stochastic consensus problem of high-order linear discrete-time multiagent systems (MASs) with uncertain topologies and external disturbances. The randomly switching interaction signed topologies are governed by a time-homogenous Markov chain with incomplete knowledge of the transition probabilities. Based on Lyapunov function theory and adaptive control strategies, we employ a homogeneous parameter-dependent Lyapunov function to propose sufficient conditions under a set of linear matrix inequality (LMI) constraints. A free-weighting matrix method is introduced to give the proposed LMIs extra freedom to search feasible solutions. Furthermore, the adaptive controllers applied in this paper are independent of topologies and fully distributed; i.e., the system achieves robust consensus without continuously updating the controller and dealing with global data. Additionally, we extend the theoretical framework to analyze the disturbance rejection performance of MASs under the stochastic process. Two numerical examples are provided to show the effectiveness of the algorithms.

Linear quadratic optimal consensus of discrete-time multi-agent systems with optimal steady state: A distributed model predictive control approach

This paper develops a distributed model predictive control algorithm for linear quadratic optimal consensus of discrete-time multi-agent systems. The consensus state and control sequence are both optimized at every predictive step on a finite horizon and then implemented in the real system. The stability of the closed-loop system is analyzed, establishing a distributed consensus condition depending only on individual agent’s local parameters. The consensus condition is then relaxed for controllable systems, making it easy to choose the weighted matrices and control period for each agent. The proposed algorithm is applied to the formation control of multi-vehicle systems verified by numerical simulations.