Continuous-time double integrator consensus algorithms improved by an appropriate sampling

<abstract><p>This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.</p></abstract>

Estimates of agents in a distributed consensus control are aligned with a particular value through interacting on communication graphs, which are of particular interest for researchers in the field of multi-agent coordination. Following this pattern, a discrete-time constrained consensus issue with generalized time delays is first established in this article, which is manipulated into an optimization problem via a quadratic performance index introduced as a global objective function. Then, a novel consensus scheme is investigated and proposed for handling this problem, enabling the consensus to approach the desired state globally and rapidly with optimal system property ensured. Besides, to advance the convergence speed and stability in resisting constant bias or oscillation, an adjustment control method is explored to construct a modified consensus scheme; further, to enhance the scene adaptability, fix topologies are extended to switching ones, and the latter is involved to develop another scheme on this basis. Moreover, the convergence and robustness of these three proposed consensus schemes are substantiated by theoretical analysis and numerical simulations. To highlight the practical implementations, the proposed consensus schemes are incorporated with a winner-take-all operation to accomplish multi-agent competitive coordination in a distributed way, and the results embody their effectiveness and superior consensus control ability, along with strong plasticity. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is dedicated to investigating and optimizing distributed consensus schemes with time delays and output saturation with application to the competitive coordination of multi-agent systems. On the one hand, the consensus problem with output saturation receives limited attention, and few consensus algorithms consider both saturation limitation and channel gain. On the other hand, most existing studies on consensus with saturation consider simply the dynamic behaviour of agents without employing optimization, thus limiting further improvement of system performance. In this paper, a consensus algorithm is built from an optimization perspective that guarantees the state consensus of a multi-agent system with output constraints and generalized time delays. In addition, a consensus scheme is designed in a discrete-time framework and further modified and perfected along with the idea of considering time delays and expanding diverse topologies. Finally, experiments are conducted by applying the consensus scheme to a winner-take-all operation, with contributions of this paper verified.

In this paper, consensus algorithms are investigated for networks of continuous-time and discrete-time linear multi-agent systems under switching and directed topologies. These algorithms adopt internal model control technology to guarantee that the consensus for all states in each agent is achieved. And the “virtual state” is also employed to solve the consensus problem. Numerical simulation results are provided to demonstrate the effectiveness of the theoretical results for the consensus for multi-agent systems under switching and directed topologies.

We consider networks of dynamic agents that execute cooperative, distributed control algorithms in order to coordinate themselves and to collectively achieve goals. The agents rely on consensus algorithms that are based on local interactions with their nearest neighbors in the communication graph. However, such systems are not robust to one or more malicious agents and there are no performance guarantees when one or more agents do not cooperate. Recent results in network science deal with this problem by requiring specific graph topological properties. Nevertheless, the required network topologies imply high connectivity levels, which may be difficult to achieve in systems that exhibit time-varying communication graphs. In this paper, we propose an approach that provides resilience for networks of dynamic agents whose communication graphs are time-varying. We show that in the case where the required connectivity constraints cannot be satisfied at all times, we can resort to a consensus protocol that guarantees resilience when the union of communication graphs over a bounded period of time satisfies certain robustness properties. We propose a control policy to attain resilient behavior in the context of perimeter surveillance with a team of robots. We provide simulations that support our theoretical analyses.

In this dissertation, new algorithms for formation control of multi agent systems (MAS) based on continuum mechanics principles will be suggested. For this purpose, agents of the MAS are considered as particles in a continuum, evolving in R^n, whose desired configuration is required to satisfy an admissible deformation function. Considered is a specific class of mappings that are called homogenous where the Jacobian of the mapping is only a function of time and is not spatially varying. The primary objectives of this dissertation are to develop the necessary theory and its validation on a mobile-agent based swarm test bed that includes two primary tasks: 1) homogenous transformation of MAS and 2) deployment of a random distribution of agents on a desired configuration. Developed will be a framework based on homogenous transformations for the evolution of an MAS in an n-dimensional space (n=1,2, and 3), under1) no inter-agent communication (predefined motion plan), 2) local inter-agent communication, and 3) intelligent perception by agents. In this dissertation, different communication protocols for MAS evolution that are based on certain special features of a homogenous transformation will be developed. It is also aimed to deal with the robustness of tracking of a desired motion by an MAS evolving in R^n. Furthermore, the effect of communication delays in an MAS evolving under consensus algorithms or homogenous maps is investigated. In this regard, the maximum allowable communication delay for MAS evolution is formulated on the basis of eigen-analysis.

The study of multi-agent systems (MAS) focuses on systems in which many intelligent agents interact within an environment. The agents are considered to be autonomous entities. MAS can be used to solve problems that are difficult or impossible for an individual agent to solve. The main feature which is achieved when developing MAS, if they work, is flexibility, since MAS can be added to, modified and reconstructed, without the need for detailed rewriting of the application. MAS can manifest self-organization as well as self-steering related complex behaviors even when the individual strategies of all their agents are simple. The goal of MAS research is to find methods that allow us to build complex systems composed of autonomous agents who, while operating on local knowledge and possessing only limited abilities, are nonetheless capable of enacting the desired global behaviors. We want to know how to take a description of what a system of agents should do and break it down into individual agent behaviors. This thesis investigates the problem when discrete-time MAS are consensusable under undirected graph. A discussion is provided to show how the problem differs from continuous time system. Then a consensusability condition is derived in terms of the Mahler measure of the agent system for single input single out systems (SISO) and result shows that there is an improved consensusability by a power of two. An algorithm is proposed for distributed consensus feedback control law when the consensusability holds. Also the case of output feedback is considered in which the consensusability problem becomes more complicated. To solve this we decompose the problem into two parts i.e. state feedback and state estimation. Simulation results demonstrate the effectiveness of the established results.

This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this paper, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.

In this paper, we investigate the fault-tolerant consensus problems for multi-agent systems with actuator faults. Based on the relative state information, fully distributed adaptive protocols are designed for these agents described by Lipschitz nonlinear dynamics under leaderless and leader-follower communication structures. As the special case, for linear multi-agent systems, fault-tolerant consensus problems are also solved with the proposed protocols. First, for the leaderless multi-agent systems, all agents reach an agreement on a common value with undirected connected communication graphs. Second, for the leader-follower multi-agent systems, in which the state of the leader is only available to a subset of the followers, the state of each follower converges to the state of the leader, asymptotically. A distinctive feature of this paper is that the adaptive protocols here are independent of the eigenvalues of the Laplacian matrix associated with the whole communication graph, which means the protocols can be implemented by each agent in a fully distributed fashion. Simulation examples are provided to illustrate the theoretical results.

In this paper, we study the problem of privacy-preserving average consensus from a different perspective. Previous research has mainly focused on designing privacy augmentation mechanisms for classical average consensus algorithms, which can lead to overhead (in the form of parameters exchanged between agents or extra privacy operations). Motivated by the framework on expressed and private opinions within social networks, we propose an alternative iterative algorithm to simultaneously update two state variables. One of these variables is used to transmit and interact among the network, while the other variable represents the real state evolution of agents and is not directly visible to other agents. We demonstrate that the algorithm can achieve the same performance as the well-known Laplacian consensus algorithm, but without the added overhead of extra privacy protection operations. Furthermore, our algorithm is viable on general strongly connected digraphs, and does not require the topology to be undirected or balanced, nor does it require nodes to know their out-neighbors, thus greatly weakening the topological requirements. Finally, we validate the effectiveness of the proposed algorithm via numerical simulations.

Applying the consensus algorithm in Multi-Agent System, this paper proposes a fully distributed economic dispatch strategy for power systems considering flexible loads. Without dispatch center collecting the global information, through the using of information interaction among local buses, the distributed economic dispatch strategy involving flexible loads is achieved. The strategy involves two consensus algorithms running in parallel. The first algorithm is a consensus algorithm which has a power mismatch correction term, the correction term is the global power mismatch calculated by the power mismatch on local bus to ensure the generation-demand balance. The second algorithm uses another distributed consensus algorithm to calculate the global power mismatch on the buses which is used in the first algorithm. The simulation example demonstrates the effectiveness of the distributed economic dispatch strategy for power systems involving flexible loads.

For the multi-agent systems with agent's dynamics described by high-order integrator, and usual consensus algorithm composed of the states' coordination control parts is proposed. Under communication delay, consensus algorithm in asynchronously-coupled form just can make the agents achieve a stationary consensus, and sufficient consensus condition is obtained based on frequency-domain analysis. To regain the original consensus state of high-order multi-agent systems without communication delay, besides, a predictor-based consensus algorithm is constructed via multiplying the delayed neighboring agents' states by a delay-related compensation part, and sufficient consensus condition is also obtained. Simulation illustrates the correctness of the results.

In this paper, differential games with incomplete information, or Bayesian games, are formulated for multiagent continuous-time dynamical systems in a communication graph. These new Bayesian graphical games model the situation where the agents are uncertain about their actual payoff functions and must employ the evidence observed from the behavior of other agents to improve their estimation of the real setting of their environment. Two different solutions are proposed for the game. First, the agents play their best response strategies with respect to the policies of their neighbors; then, the agents prepare themselves for the worst-case neighbor policies. A tight relationship between the beliefs of an agent and its distributed control policy is established. Two belief update methodologies are proposed for the agents to review their strategies using information obtained from the graph topology.

Iterative learning control for continuous-time multi-agent differential inclusion systems with full learnability

Containment control of singular heterogeneous multi-agent systems

For multi-agent systems under Denial-of-Service (DoS) attacks, a relative threshold strategy for event triggering and a state-constrained control method with prescribed performance are proposed. Within the framework of combining graph theory with the leader–follower approach, coordinate transformation is utilized to decouple the multi-agent system. Inspired by the three-way handshake technology of TCP communication, a DoS detection system is designed based on event-triggering. This system is used to detect DoS attacks, prevent the impacts brought by DoS attacks, and reduce the update frequency of the controller. Fuzzy logic systems are employed to approximate the unknown nonlinear functions within the system. By using a first-order filter to approximate the derivative of the virtual controller, the computational complexity issue in the backstepping method is addressed. Furthermore, The Barrier Lyapunov Function (BLF) possesses unique mathematical properties. When the system state approaches the pre-set boundary, it can exhibit a special variation trend, thereby imposing a restrictive effect on the system state. The Prescribed Performance Function (PPF), on the other hand, defines the expected performance standards that the system aims to achieve in the tracking task, covering key indicators such as tracking accuracy and response speed. By organically integrating these two functions, the system can continuously monitor and adjust its own state during operation. When there is a tendency for the tracking error to deviate from the specified range, the combined function mechanism will promptly come into play. Through the reasonable adjustment of the system’s control input, it ensures that the tracking error always remains within the pre-specified range. Finally, through Lyapunov analysis, the proposed control protocol ensures that all closed-loop signals remain bounded under attacks, with the outputs of all followers synchronizing with the leader’s output in the communication graph.