Consensus Protocol Design Research Articles

Distribution of Roots of Quasi-Polynomials of Neutral Type and Its Application—Part II: Consensus Protocol Design of Multi-Agent Systems Using Delayed State Information

Distribution of Roots of Quasi-Polynomials of Neutral Type and Its Application—Part II: Consensus Protocol Design of Multi-Agent Systems Using Delayed State Information

Observer-Based Adaptive Consensus Protocol Design for Multi-Agent Systems with One-Sided Lipschitz Nonlinearity

This paper considers the observer-based leader–follower consensus problem of multi-agent systems with one-sided Lipschitz conditions and quadratic inner-boundedness nonlinearity. Based on the relative outputs of neighboring agents, an adaptive protocol over a directed graph is designed via assigning a time-varying coupling weight to each node. Compared with the existing protocols, the proposed protocol can not only be utilized in the unidirectional flow of information, but it does not require any global graph information for its design. It has been shown that the established criteria can not only make the observer error tendency zero, but one can also achieve the leader–follower consensus of such nonlinear multi-agent systems. Furthermore, the gains of observer and protocol parameters can be constructed by solving the linear matrix inequalities (LMIs), which are conveniently checked. The results are illustrated by numerical simulations.

Consensus Control of Multiagent Systems Under Switching Topology and Denial-of-Service Attacks

This article studies the consensus problem of multiagent systems (MASs) under denial-of-service (DoS) attacks and switching topology. Compared with the previous papers, under the switching topology, the impact of DoS attacks on the MAS is considered, and thus, the difficulty of consensus protocol design is further increased. First, a piecewise resilient consensus protocol is proposed to ensure that the MAS can achieve consensus under switching topology and DoS attacks. Then, by considering the different convergence rates caused by the switching topology in each sleep period of DoS attacks, a piecewise Lyapunov–Krasovskii function is established. The sufficient conditions on the global convergence of the system are obtained under switching topology and DoS attacks. In the meantime, the lower bound of average dwell time of the switching topology is determined under DoS attacks. The relationship between average dwell time and the parameters of DoS attacks is discussed. Finally, the simulation example is conducted to verify the effectiveness of the proposed method.

Fully distributed secure observation and consensus for multi-agent systems with uncertain communication topology

This article investigates the fully distributed secure observation and consensus problem for networked multi-agent systems (MASs) with uncertain communication topology. The complexities of dual-channel false data injection (FDI) attacks and fuzzy communication among agents are considered, bringing direct challenges to the acquisition of system states and the design of consensus protocols. To address these difficulties, on the one hand, adaptive coupling weights that vary with observation and consensus errors are neatly designed to avoid the use of global topology information in the whole mechanism. On the other hand, an auxiliary observation system is constructed based on intermediate variables to realize the simultaneous estimation of system states and dual-channel FDI attacks. After that, a distributed attack compensation controller that can guarantee secure consensus among agents is proposed. Finally, a simulation example and an experiment compared with existing results are given to examine the feasibility and advantages of the developed strategy.

Suboptimal consensus protocol design for a class of multiagent systems

This article presents a new technique for suboptimal consensus protocol design for a class of multiagent systems. The proposed technique is based upon the extension of newly developed sufficient conditions for suboptimal linear–quadratic optimal control design, which are derived in this paper by an explication of a noniterative solution technique of the infinite-horizon linear quadratic regulation problem in Krotov framework. For suboptimal consensus protocol design, the structural requirements on the overall feedback gain matrix, which are inherently imposed by agents dynamics and their interaction topology, are recast on a specific matrix introduced in a suitably formulated convex optimization problem. As a result, preassigning the identical feedback gain matrices to a network of homogeneous agents, which act on the relative state variables with respect to their neighbors is not required. The suboptimality of the computed control laws is quantified by implicitly deriving an upper bound on the cost in terms of the solution of a convex optimization problem and initial conditions of the agents instead of specifying it a priori. Numerical examples are provided to demonstrate the implementation of proposed approaches and their comparison with existing methods in the literature.

Design of non-smooth consensus protocol for multi-agent systems under DoS attacks

In this paper, we focus on the consensus problem of leaderless multi-agent systems with external disturbance under denial-of-service (DoS) attacks. First, the state predictor is constructed to reproduce the state information blocked during the active periods of DoS attacks. Then, a robust non-smooth consensus protocol is designed using the predictor states, which mitigates the open-loop phenomenon caused by the DoS attacks. Besides, we obtain the sufficient condition for agents to achieve consensus within a region, and demonstrate that the protocol can enhance the anti-disturbance and anti-attack capabilities of the systems. Finally, the theoretical results are verified through numerical simulations.

Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach With Linear Convergence

Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly desirable to design decentralized algorithms that can handle stochastic communication networks. However, most existing algorithms for DCCO only work in networks that are deterministically connected during bounded communication rounds, and therefore cannot be extended to stochastic networks. In this paper, we propose a new decentralized dual averaging (DDA) algorithm that can solve DCCO in stochastic networks. Under a rather mild condition on stochastic networks, we show that the proposed algorithm attains <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">global linear convergence</i> if each local objective function is strongly convex. Our algorithm substantially improves the existing DDA-type algorithms as the latter were only known to converge <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sublinearly</i> prior to our work. The key to achieving the improved rate is the design of a novel dynamic averaging consensus protocol for DDA, which intuitively leads to more accurate local estimates of the global dual variable. To the best of our knowledge, this is the first linearly convergent DDA-type decentralized algorithm and also the first algorithm that attains global linear convergence for solving DCCO in stochastic networks. Numerical results are also presented to support our design and analysis.

Sampled-Data Consensus Protocols for a Class of Second-Order Switched Nonlinear Multiagent Systems.

In this study, the sampled-data consensus problem is investigated for a class of heterogeneous multiagent systems (MASs) in which each agent is described by a second-order switched nonlinear system. Owing to the heterogeneity and the occurrence of dynamic switching in the MASs, the sampled-data consensus protocol design problem is challenging. In this study, two periodic sampled-data consensus protocols and an event-triggered consensus protocol are developed. Here, we first propose a new periodic sampled-data consensus protocol that involves the local objective trajectory interaction among agents. The protocol is then improved by applying the finite-time control and sliding-mode control techniques. Notably, the improved protocol can be implemented without the transmission of constructed auxiliary dynamical variables, which is a major feature of the present study. It is shown that complete consensus of the underlying MASs can be achieved by the two proposed protocols with only sampled-data measurements. To further reduce the communication load, we introduce an event-triggered mechanism to obtain a new protocol. Finally, the effectiveness of the given schemes is demonstrated by considering a numerical example.

SIM-P—A Simplified Consensus Protocol Simulator: Applications to Proof of Reputation-X and Proof of Contribution

Blockchain is a distributed ledger in which participating users with varying levels of trust agree on the ledger’s content using a consensus mechanism called consensus protocols. There has been a rising interest in the design of consensus protocols since they play a central role in blockchain architecture. However, many recently proposed consensus protocols lack experimental verification which hampers the possible deployment of these protocols in real-world blockchain networks. In this article, we propose a simple tool called simplified consensus protocol simulator (SIM-P) that can accurately simulate the behavior of these consensus protocols with ease. It is an agent-based stochastic simulator that relies on the sequential Monte Carlo method to model how block publishers are selected. The likelihood of each node (represented as agents) being selected as a block publisher is represented by independent trials in a binomial experiment. We provide a base SIM-P model that simulates Proof of Work (PoW) for benchmarking purposes. The PoW model also serves as the basic structure of the simulator that can be adapted to other protocols. We showcase the flexibility of SIM-P by proposing two additional simulation models for Proof of Reputation-X and Proof of Contribution, both of which lack experimental verification in their original design specifications. We show how the simulator can be used to produce vital metrics, such as throughput, resistance against the 51% attack, and energy consumption. We verify the accuracy of SIM-P by comparing PoW’s simulated results with theoretical estimates and historical Bitcoin data.

Leader-Following Almost Output Consensus for Linear Heterogeneous Multiagent Systems With Disturbance-Affected Unstable Zero Dynamics by Output Feedback

A novel design of observer-based output feedback consensus protocols in a low-and-high gain feedback framework is proposed for a linear heterogeneous multiagent system, where the unstable zero dynamics of the follower agents is affected by disturbances. Conditions on the graph that represents the connectivity among the agents and on how the disturbances enter the zero dynamics of the follower agents are identified, under which the leader-following almost output consensus can be attained with the proposed protocols. More specifically, the proposed protocols achieve leader-following output consensus to an arbitrarily high level of accuracy, and the effect of the disturbances on the consensus errors is attenuated to an arbitrarily low level.

Secure consensus with partial public protocols

Existing consensus designs require that the information of local control laws is open access. This is undesirable whenever the privacy of local interactions is concerned. In this paper, a different framework of the consensus protocol design with the consideration of authority management of accessing local controllers is provided, by using an edge-based implementation. In the scenario of the proposed designs, each local controller is realized by a parallel connection of a public element and a private element. The public elements are uniform and open access. However, the private elements are allowed to be significant nonuniform and are only known by the pairs of agents who share them. For both continuous-time multi-agent systems and their sampled-data counterparts, we provide the design criterions for the partial public protocols under both static and dynamic public elements, respectively. By exploring the edge sensitivity design approach, it is shown that the consensus can be achieved under the proposed protocols if the private control laws satisfy certain constraints dependent on the public ones and the network topologies. Numerical examples are also provided to illustrate the proposed design criterions.

Consensus control for a class of linear multiagent systems using a distributed integral sliding mode strategy

In this paper, a consensus framework is proposed for a class of linear multiagent systems subject to matched and unmatched uncertainties in an undirected topology. A linear coordinate transformation is derived so that the consensus protocol design can be conveniently performed. The distributed consensus protocol is developed by using an integral sliding mode strategy. Consensus is achieved asymptotically and all subsystem states are bounded. By using an integral sliding mode control, the subsystems lie on the sliding surface from the initial time, which avoids any sensitivity to uncertainties during the reaching phase. By use of an appropriate projection matrix, the size of the equivalent control required to maintain sliding is reduced which reduces the conservatism of the design. MATLAB simulations validate the effectiveness and superiority of the proposed method.

Guaranteed Cost Leaderless Consensus Protocol Design for Fractional-Order Uncertain Multi-Agent Systems with State and Input Delays

This paper addresses the guaranteed cost leaderless consensus of delayed fractional-order (FO) multi-agent systems (FOMASs) with nonlinearities and uncertainties. A guaranteed cost function for FOMAS is proposed to simultaneously consider consensus performance and energy consumption. By employing the linear matrix inequality approach and the FO Razumikhin theorem, a delay-dependent and order-dependent consensus protocol is formulated for FOMASs with input delay. The proposed protocol not only guarantees the robust stability of the closed-loop system error but also ensures that the performance degradation caused by the system uncertainty is lesser than that obtained with other approaches. Two numerical examples are provided in order to verify the effectiveness and accuracy of the proposed protocol.

Event-Triggered Bipartite Consensus in Networked Euler–Lagrange Systems With External Disturbance

This brief presents an even-triggered control framework for networked Euler-Lagrange systems to achieve bipartite consensus even in the presence of external disturbance. In particular, an adaptive protocol with simple distributed updating laws is proposed by combining the disturbance compensator technique. The new event-triggered control algorithm is constructed without utilizing velocity information, which mitigates the cost on distributed bipartite consensus protocol design. Additionally, there is no Zeno behaviors by giving the positive lower bounds of execution intervals. Numerical examples are applied in the end to verify the correctness of theoretical results.

Consensus control of multi-agent systems with P-one-sided Lipschitz

This paper investigates the consensus problem for a class of multi-agent systems with P-one-sided Lipschitz nonlinearity. This nonlinearity offers a significant extension to application range of existing consensus control protocol design methods, which removes the assumption of the quadratic inner-boundedness. To solve this problem, a strongly connected graph topology is applied within the consensus protocol design framework. Moreover, the leader-following scenario is addressed under the graph topology. Under the above objectives, sufficient conditions are employed to yield consensus. Two examples are performed to illustrate the properties.

Formula omitted]-learning algorithm in solving consensusability problem of discrete-time multi-agent systems

This paper solves the consensusability problem for the single-input discrete-time multi-agent system (MAS) over directed graphs by the linear quadratic regulator (LQR) design method. It is proved that the maximum consensus region is exactly the largest gain margin (GM) of LQR. Based on this, the necessary and sufficient condition on consensusability is derived by solving a standard algebraic Riccati equation (ARE). The developed framework permits that the consensusability problem can be solved when the agents’ models are completely unavailable. Q-learning algorithm is employed to compute the maximum consensus region and implement the consensus protocol design. The algorithm runs only on a single agent rather than the intercommunicating MAS hence the unattainable initial admissible protocols are not required. A numerical example is given to illustrate the effectiveness of the developed methods.

A New Switched System Approach to Leader–Follower Consensus of Heterogeneous Linear Multiagent Systems With DoS Attack

This paper investigates the leader-follower robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus of heterogeneous multiagent systems with denial of service attack, where different attack intensities are considered. A switched system model is introduced to model such an attack phenomenon. Then, sufficient conditions to guarantee the solvability of the robust output consensus problem are obtained, and the quantitative relationship between the consensus performance and attack parameter is established. It is shown that the consensus protocol design problem can be transformed into two static output feedback (SOF) control problems. It is also shown that the SOF controller gains can be determined by solving some linear matrix inequalities without the knowledge of the probability information of each attack. Finally, the effectiveness of the control protocol is demonstrated by a simulation study.

Regional Leader-Following Consensus of Generalized One-Sided Lipschitz Multiagents: A Monte Carlo Simulation-Based Strategy

This article addresses the leader-following exponential consensus control problem for generalized one-sided Lipschitz (OSL) multiagents (MAs) using relative-state information under a directed spanning tree. Previous works have accomplished the consensus protocol design for the globally OSL nonlinear MA systems. Unlike the existing results, the proposed strategy employs a less conservative approach in the form of matrix inequalities and convex routines by assuming that the nonlinear MAs satisfy the OSL condition in a local region by relaxing the so-called quadratic inner-boundedness constraint. A novel algorithm is provided to incorporate the value of generalized OSL constant and to consider the regional consensus protocol computation via Monte Carlo simulations, based on uniform random numbers. The proposed approach is fully automatic, easily solvable, and presented for the consensus control of generalized (locally) OSL nonlinear systems for the first time. The proposed approach also studies the criteria for the exponential consensus convergence rate for attaining a faster convergence of the consensus error. Furthermore, the developed consensus protocol for the generalized OSL systems is then extended for the case of switching topologies. The proposed consensus protocol of locally OSL nonlinear MA systems can also be employed to the global OSL nonlinear MA systems as a special case for attaining the local performance. The effectiveness of the proposed approach is verified by the leader-following consensus of eight moving agents and a practical application of F-18 aircraft.

Consensus Protocol Design for Leader-Following Multi-Agent Systems With Stochastic Sampling Information

Abstract This paper studies a consensus protocol design for leader-following multi-agent systems (MASs) via stochastic sampling information. Unlike traditional sampled-data control, this paper is focused on the stochastically varying sample intervals with a given probability by the Bernoulli distribution. Based on the Lyapunov–Krasovskii functional and reciprocally convex technique, the sufficient conditions are derived for the stochastic sampled-data protocol design of the error system, which guarantees that the following agent's states can reach an agreement on the leader's state. Finally, the numerical examples are provided to demonstrate the effectiveness of the developed theoretical results.

The variant d-path Laplacian based consensus protocols for networked harmonic oscillators

In this paper, we address the consensus protocol design problem of the networked harmonic oscillators interacting through a directed graph with peer pressure from the perspective of the output information, in which the peer pressure is in the expression of the variant d-path Laplacian. For networked harmonic oscillators without time delay, sufficient conditions in terms of coupling strength are given, while for networked harmonic oscillators with time delay, sufficient conditions in the term of coupling strength and the upper bound on the time delay are proposed. Finally, simulation examples are provided to verify the theoretical results.