Proposed Consensus Protocol Research Articles

Adaptive Event-Triggered Consensus of Fractional-Order Nonlinear Multi-Agent Systems

The leader-following consensus of fractional-order nonlinear multi-agent systems is studied in this paper. An adaptive event-triggered control protocol is proposed to achieve the leader-following consensus scheme. By applying Lyapunov stability theory of fractional-order systems and some effective inequality techniques, some sufficient conditions for ensuring the consensus are derived intensively, and the proposed control method can reduce the communication between the agents greatly. Moreover, the Zeno behavior of event-triggered algorithm for multi-agent systems is excluded. Finally, a simulation example is presented to validate the effectiveness of the proposed consensus protocol.

Disturbance observer-based sliding mode control for consensus tracking of chaotic nonlinear multi-agent systems

This paper deals with the finite-time consensus of chaotic MIMO nonlinear heterogeneous multi-agent systems subjected to matched uncertainties and disturbances. This study proposes a consensus protocol utilizing a novel dynamic sliding mode control, ensuring robust performance and chattering attenuation. For this purpose, firstly, a new time-varying nonlinear sliding manifold is introduced that guarantees exponential finite-time stability. Secondly, a novel reaching law is established that ensures fixed reaching time independent of initial conditions. The fixed reaching time enables the specification of the reaching time by considering the problem constraints. Then, a novel terminal disturbance observer is proposed to efficiently estimate the overall effect of uncertainties and disturbances in the finite-time. Finally, an adaptive form of the proposed controller is presented by incorporating the disturbance observer into the proposed sliding mode control. The proposed consensus protocols are applied to a multi-agent system consisting of two well-known chaotic power systems (PMSM and BLDCM). Computer simulations and comparative studies confirm the results of this study in terms of tracking errors and fast convergence.

State-based event-triggered consensus strategy for Takagi–Sugeno fuzzy fractional-order multiagent systems with switching topologies

This article addresses the event-triggered consensus problem for Takagi–Sugeno fuzzy fractional-order multiagent systems with switching topologies. First, to effectively avoid the frequent communication among agents, a state-based event-triggered consensus strategy is designed, which uses the local information from neighboring agents at sampling moments. Then, several sufficient conditions, which rely on the fractional derivative number and time delay information, are presented to guarantee the consensus of fractional-order multiagent systems based on Takagi–Sugeno fuzzy model. Moreover, Zeno behaviors are precluded by proving that the interval length of the two consecutive event-triggering moments for each agent is greater than a positive constant. Finally, some numerical examples are presented, which not only demonstrated the rationality of our proposed consensus protocol but also shown that the presented consensus method based on the designed event-triggered control protocol has the advantage for avoiding communication congestion compared to the existing results.

On designing a distributed event‐triggered output feedback consensus protocol for nonlinear multiagent systems

AbstractIn this article, the leader–follower consensus problem is considered for a class of nonlinear multiagent systems with event‐triggered inputs. A novel time‐varying gain compensator is designed for each follower by only utilizing the output information of the follower and its neighbors. Based on a time‐varying threshold strategy and a directed communication topology, a distributed event‐triggered output feedback controller is designed for each follower. It is proved by the Lyapunov theory that the leader–follower consensus of the multiagent systems is achieved and the Zeno‐behavior is avoided. Compared with the existing results, it is the first time that a time‐varying gain control algorithm is proposed for the multiagent systems subject to event‐triggered inputs. The effectiveness of the proposed consensus protocol is validated by the chemical reactor systems.

Blockchain-Envisioned Trusted Random Oracles for IoT-Enabled Probabilistic Smart Contracts

In modern decentralized Internet-of-Things (IoT)-based sensor communications, pseudonoise-diffusion oracles are heavily investigated as random oracles for data exchange among peer nodes. As these oracles are generated through algorithmic processes, they pass the standard random tests for finite and bounded intervals only. This ensures a false sense of privacy and confidentiality in exchange through open protocol IoT-stacks in public channels, i.e., Internet. Recently, blockchain (BC)-envisioned random sequences as input oracles are proposed about financial applications, and windfall games like roulette, poker, and lottery. These random inputs exhibit fairness, and nondeterminism in SC executions termed as probabilistic smart contracts (PSCs). However, the IoT-enabled PSC process might be controlled and forged through humans, machines, and bot-nodes through physical and computational methods. Moreover, dishonest entities like contract owners, players, and miners can co-ordinate together to form collusion attacks during consensus to propagate false updates, which ensures forged block additions by miners in BC. Motivated by these facts, in this article, we propose a BC-envisioned IoT-enabled PSC scheme, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SaNkhyA</i> , which is executed in three phases. In the first phase, the scheme eliminates colluding dishonest miners through the proposed miner selection algorithm. Then, in the second phase, the elected miners agree through the proposed consensus protocol to generate a stream of random bits. In the third phase, the generated random bit-stream is split through random splitters and fed as input oracles to the proposed PSC among participating entities. In simulation, the scheme ensures a trust probability of 0.38 even at 85% collusion among miners and has an average block processing delay of 1.3 s compared to serial approaches, where the block processing delay is 5.6 s, thereby exhibiting improved scalability. The overall computation and communication cost is 28.48 ms, and 101 bytes, respectively, that indicates the efficacy of the proposed scheme compared to the traditional schemes.

Fully Distributed Dynamic Event-Triggered Semiglobal Consensus of Multi-agent Uncertain Systems with Input Saturation via Low-gain Feedback

This paper investigates the event-triggered consensus problem of multi-agent systems with uncertainties and input saturation. First, a fully distributed robust consensus low-gain feedback control strategy is proposed, in which some global information, such as the communication graph and the scale of network, is not needed. Then, by defining an internal dynamic variable to memory the past state, an adaptive dynamic event-triggering mechanism is proposed, which contributes to reducing the usage of communication resources and also does not rely on any global information. Furthermore, Lyapunov-based consensus analysis results are presented, and it is also formally shown that Zeno behavior can be excluded with the proposed consensus protocols. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Leader–follower consensus of nonlinear time-delay multiagent systems: A time-varying gain approach

In this paper, the leader–follower consensus problem is investigated for feedforward nonlinear time-delay multiagent systems under a fixed directed topology. A novel static low-gain observer is first proposed for each follower by only utilizing the output information of the follower and its neighbor agents. Based on an appropriate state transformation, the distributed output feedback controller with a static gain is then designed for each follower such that the consensus of the multiagent system is achieved. It is however noted that under the static gain controllers, the consensus convergence speed is slow and transient performance leaves much to be desired. To improve performance of the consensus protocol, the distributed output feedback controllers with bounded time-varying gains are further designed. It is shown that the proposed time-varying gain approach plays a significant role in improving the convergence speed and transient performance of the distributed consensus protocol. Through a simulation example, the effectiveness of the proposed consensus protocol is illustrated, and the advantages of the proposed time-varying gain approach are also demonstrated.

Consensus of High-Order Discrete-Time Multiagent Systems With Switching Topology

The communication cost is generally higher for the consensus of high-order multiagent systems than that for low-order multiagent systems. In this paper, two novel distributed protocols are proposed to address the consensus of high-order discrete-time multiagent systems. By the proposed consensus protocols, each agent only needs to transmit the value of a variable to neighbor agents regardless of the order of agent dynamics. Theoretical analysis shows that the proposed protocols guarantee asymptotic consensus of the agent states in different cases of communication graphs, including jointly connected ones. Simulative examples verify the theoretical results and the efficacy of the proposed protocols.

Distributed fixed‐time event‐triggered consensus of linear multi‐agent systems with input delay

AbstractThis article investigates the distributed fixed‐time event‐triggered consensus problem for linear multi‐agent systems with input delay. The Artstein‐Kwon‐Pearson reduction approach is used to convert the delay‐dependent system to a delay‐free one. Based on the delay‐free system, two distributed event‐triggered protocols are designed based on local information exchange to address the leaderless consensus and the leader‐follower consensus problems. In the proposed consensus protocols, both continuous controller updates and continuous communication as well as the Zeno behavior are successfully excluded. Detailed convergence analysis demonstrates that the closed‐loop system is fixed‐time stable regardless of the initial conditions. Finally, some simulation examples are provided to validate the theoretical results.

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.

Autonomous and non-autonomous fixed-time leader–follower consensus for second-order multi-agent systems

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader–follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.

Quantized Consensus of Multiagent Systems by Event-Triggered Control

This paper investigates the quantized consensus problem of general linear multiagent systems (MASs) by event-triggered control. A novel event-triggered distributed control protocol is proposed based on a new dynamic quantizer. Compared with periodical sampling for most existing works on quantized consensus, the proposed event-triggered control approach can significantly save communication and thus energy resource. It is shown that with the proposed distributed control protocol quantized consensus of the concerned MAS can be achieved, and the Zeno behavior and continuous monitoring of the neighbors’ states are avoided. Moreover, it is shown that the required number of the quantization levels of the new quantizer remains small even if the number of the agents in the MAS is large. Three simulation examples are given to illustrate the effectiveness of the proposed consensus protocol.

Leader-following consensus for multi-agent systems with nonlinear dynamics subject to additive bounded disturbances and asynchronously sampled outputs

This paper is concerned with the leader-following consensus problem for a class of Lipschitz nonlinear multi-agent systems with uncertain dynamics, where each agent only transmits its noisy output, at discrete instants and independently from its neighbors. The proposed consensus protocol is based on a continuous-discrete time observer, which provides a continuous time estimation of the state of the neighbors from their discrete-time output measurements, together with a continuous control law. The stability of the multi-agent system is analyzed with a Lyapunov approach and the exponential practical convergence is ensured provided that the tuning parameters and the maximum allowable sampling period satisfy some inequalities. The proposed protocol is simulated on a multi-agent system whose dynamics are ruled by a Chua’s oscillator.

Event-triggered output consensus disturbance rejection algorithm for multi-agent systems with time-varying disturbances

This study investigates the problem of event-triggered output consensus disturbance rejection for multi-agent systems subject to time-varying disturbances. By virtue of the reduced-order generalized proportional-integral observer (GPIO) technique, a new output consensus disturbance rejection protocol is developed based on the measurement outputs. Taking the limited communication bandwidth into account, the multi-agent system closes the loop under the proposed consensus protocol only when a distributed event-triggering mechanism decides to transmit agent’s current output to its neighbors. The proposed output consensus protocol can effectively enhance the robustness against the time-varying disturbances and save the communication resource, since the time-varying disturbances are accurately estimated and compensated. Furthermore, the proposed consensus algorithm does not require continuous communication among the neighboring agents and can successfully avoid the Zeno phenomenon. Finally, the numerical simulation results are presented to verify the effectiveness of the proposed output consensus protocol.

LPV Scheme for Robust Adaptive Output Feedback Consensus of Lipschitz Multiagents Using Lipschitz Nonlinear Protocol

This article addresses the robust nonlinear adaptive consensus protocol design approach, for nonlinear multiagent (MA) systems under external perturbations with Lipschitz dynamics. Based on the existing results of the adaptive protocol using relative output information, a modified robust nonlinear adaptive consensus protocol for MAs is proposed. The Lipschitz nonlinearity in the agents’ dynamics and the adaptive protocol are reformulated using a composite linear parameter-varying (LPV) approach. Our composite LPV reformulation is less restrictive because it utilizes all the properties of Lipschitz functions. Consensus protocol design conditions based on the proposed reformulation of Lipschitz nonlinearities, Lyapunov theory, and the modified nonlinear consensus protocol are derived to attain the exponential consensus. The proposed consensus protocol approach is further extended by providing necessary and sufficient conditions for the straightforward evaluation of the robust adaptive protocol gains. The proposed fully distributed consensus protocol is robust to ensure the consensus error and adaptive gains bounded by eliminating the effect of disturbances. The resultant consensus control scheme reduces conservatism and is feasible for large values of Lipschitz constants. Finally, simulation results are presented for verifying the potency of the developed control strategies.

Discrete-time event-triggered higher order sliding mode control for consensus of 2-DOF robotic arms

This paper proposes a discrete-time event-triggered higher-order sliding mode protocol for the leader-following consensus of Discrete Homogeneous Multi-Agent Systems (DHMAS). The discrete version of the Super-Twisting Algorithm (DSTA) which is one of the most popular algorithm of higher order sliding mode control blended with event-triggered control approach is used to design the protocol. The DSTA algorithm is robust against the uncertainties present in the DHMAS and improve the consensus performance. The event-triggered control approach reduces the usage of power and communication resources due to the intermittent communication with the neighboring agents to achieve consensus. For implementing the proposed consensus protocol, each follower agent of DHMAS monitor for the event-triggering condition as defined in this paper. The sufficient condition for global stability with proposed consensus protocol is also derived to ensure the stable operation of DHMAS. Further, the proposed protocol is implemented on a discrete homogeneous multi-agent system set up comprise of 2-DOF flexible joint robotic arm considering one robotic arm as a leader and others as followers to show the efficacy of the proposed protocol.

Single-Bit Consensus With Finite-Time Convergence: Theory and Applications

In this article, a new consensus protocol based on the sign of innovations is proposed. Based on this protocol, each agent requires only a single-bit of information about its relative state to its neighboring agents. This is significant in real-time applications, since it requires less computation and/or communication load on agents. Using Lyapunov stability theorem, the convergence is proved for networks having a spanning tree. Furthermore, the convergence is shown to be in finite time, which is significant as compared to most asymptotic protocols in the literature. Time-variant network topologies are also considered in this article, and final consensus value is derived for undirected networks. Applications of the proposed consensus protocol in two-dimensional (2-D)/3-D rendezvous task, distributed estimation distributed optimization, and formation control are considered and the significance of applying this protocol is discussed. Numerical simulations are provided to compare the protocol with those existing in the literature.

Robust Leader-Following Consensus of High-Order Multi-Agent Systems in Prescribed Time

This article addresses the distributed prescribed-time leader-following consensus problem for a class of high-order multi-agent systems (MASs) with perturbed nonlinear agents dynamics and where the topology of the network contains a directed spanning tree, with the leader as the root. Prescribed-time consensus means that an agreement state of the MAS is achieved in a preset time, introduced as a parameter of the control law, and this constant settling time is achieved independently of the agents' initial state. The proposed control method exhibits three main advantages: first, to our best knowledge, it is the first time that prescribed-time convergence in a consensus problem is achieved for agents with high-order nonlinear dynamics, using a robust leader-following protocol, which allows an effective rejection of matched disturbances in the agents' model. Second, the proposed controller provides control signals of lower magnitude than existing approaches. Third, the proposed consensus protocol does not have parameters to be adjusted depending on the connectivity of the considered communication graph.

A Blockchain Consensus Protocol Based on Dedicated Time-Memory-Data Trade-Off

A problem of developing the consensus protocols in public blockchain systems which spend a combination of energy and space resources is addressed. A technique is proposed that provides a flexibility for selection of the energy and space resources which should be employed by a player participating in the consensus procedure. The technique originates from the cryptographic time-memory-data trade-off approaches for cryptanalysis. The proposed technique avoids the limitations of Proof-of-Work (PoW) and Proof-of-Memory (PoM) which require spending of only energy and space, respectively. Also, it provides a flexibility for adjusting the resources spending to the system budget. The proposed consensus technique is based on a puzzle where the problem of inverting one-way function is solved employing a dedicated Time-Memory-Data Trade-Off (TMD-TO) paradigm. The algorithms of the consensus protocol are proposed which employ certain unconstrained and constrained TMD-TO based inversions. Security of the proposed technique is considered based on the probability that the honest pool of nodes generate a longer extension of the blockchain before its update, and a condition on the employed parameters in order to achieve desired security has been derived. Implementation of the proposed technique in Go language and its inclusion as an alternative consensus option in Ethereum platform are shown. Implementation complexity and performance of the proposed consensus protocol are discussed and compared with the ones when PoW and PoM are employed.

Consensus of multiagent systems with random switching topologies and its application

SummaryThis paper is concerned on the consensus problem of multiagent systems with random switching topologies, where the dwell time of each topology consists of fixed and random parts. Firstly, the consensus analysis of such multiagent systems is considered by a mode‐dependent Lyapunov function approach, whose conditions are developed in terms of linear matrix inequalities. Then, three kinds of consensus protocols based on random switching topologies are proposed, whose differences are also illustrated. Moreover, all the existence conditions of such consensus controllers are presented with solvable forms, where the dwell times and topology are both included and play important roles. Finally, the proposed consensus protocols are applied to a chemical process to demonstrate the effectiveness of the proposed methods.