Second-order group consensus for multi-agent systems via pinning leader-following approach

This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control. The network topology is assumed to be directed and weakly connected. The pinning consensus protocol is designed according to the agent property, that is, the inter-act agent and the intra-act agent. Some consensus criteria are proposed to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.     

Dissipative consensus problems for multi-agent networks via sliding mode control

In this paper, dissipative consensus problems are discussed for multi-agent networks. Firstly, sufficient conditions are proposed to ensure $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Then, by designing an integral-type sliding surface function, a controller is obtained and the corresponding sufficient conditions are given to guarantee $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Moreover, the sliding mode control law is formulated such that multi-agent networks drive onto the predefined surface in finite time. Finally, an example is given to illustrate the effectiveness of the obtained results.     

Static group synchronization of second-order multi-agent systems via pinning control

This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples.     

Finite-time stochastic boundedness for Markovian jumping systems via the sliding mode control

The finite-time stochastic boundedness (FTSB) via the sliding mode control (SMC) approach is analyzed for Markovian jumping systems (MJSs) with time-delays. First, an integral switching surface is constructed. And to make sure the reachability of the sliding mode surface in a finite-time, an SMC law is designed. In addition, the delay-dependent criteria for FTSB are obtained over the reaching phase and the sliding motion phase. Furthermore, in line with linear matrix inequalities (LMIs), sufficient conditions are provided to guarantee the FTSB of systems over the whole finite-time interval. Lastly, an example is given to indicate the validity of the proposed approach.     

Finite-time consensus control for a class of multi-agent systems with dead-zone input

This paper investigates a finite-time consensus issue for non-affine pure-feedback multi-agent systems with dead-zone input. Compared with the existing results on multi-agent systems, finite-time consensus problem of non-affine multi-agent systems is proposed for the first time. Based on the backsteppting technique, adaptive finite-time consensus control scheme is presented. With the help of this strategy, adaptive virtual variables, adaptive laws and the actual controller are designed to guarantee that the consensus errors converge to a small scale of the origin in finite time. Finally, a practical example is applied to verify the feasibility of the proposed method.     

Asynchronous consensus of multi-agent systems via variable period intermittent control with heterogeneous pulse-modulated function

Most existing consensus control in multi-agent systems (MASs) require agents to update their state synchronously, which means that some agents need to wait for all individuals to complete the iteration before starting the next iteration. To overcome this bottleneck, this paper studied asynchronous consensus problems of second-order MASs (SOMASs) with aperiodic communication. An asynchronous pulse-modulated intermittent control (APIMC) with heterogeneous pulse-modulated function and time-varying control period, which can unify impulsive control and sampled-data control, is proposed for the consensus of SOMASs. A time-varying discrete system is constructed to describe the evolution of the sample values of position and velocity of the SOMAS. Then, by the analysis tools from the stochastic matrix and the properties of the Laplace matrix of graph, some effective conditions are obtained to show the relationship between the convergence of the controlled SOMASs and the control parameters. Finally, a 300-node SOMAS whose topology is a random geographic network is included to verify the feasibility of the proposed control and the correctness of the theoretical analysis.     

Dynamic event-triggering sliding mode resilient control for multi-agent systems

The consensus problem for a multi-agent system (MAS) is investigated in this paper via a sliding mode control mechanism subject to stochastic DoS attack, which may occur on each transmission channel independently and randomly according to the Bernoulli distribution. A distributed dynamic event-triggered strategy is implemented on the communication path among agents, where dynamic parameters are introduced to adjust the threshold of event-triggered condition. After that, a distributed sliding mode controller is proposed for ensuring the stochastic consensus of the MAS. Meantime, a minimization problem is solved to obtain the correct controller gain matrix. At last, a numerical example is shown to demonstrate the presented results.     

Predefined-time practical consensus for multi-agent systems via event-triggered control

This paper studies the predefined-time practical consensus problem for multiple single-integrator systems through event-triggered control. A new kind of time-varying functions is firstly proposed. Then, new event-triggered control inputs as well as triggering conditions are designed on the basis of the time-varying function and the local broadcasted states. In particular, the control scheme is fully-distributed because no global information of the system and the communication topology is needed. Furthermore, the consensus analysis is presented based on a sufficient condition for predefined-time practical stability. It illustrates that practical consensus can be ensured with a completely pre-specified time. Besides, the exclusion of Zeno behavior at all the time instants is addressed. Numerical results verify the validity of the obtained control method.     

Distributed disturbance observer based consensus control for linear multi-agent systems with mismatched disturbances

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws.     

Observer-based event-triggered sliding mode control for delayed systems with unknown disturbances

This paper develops the observer-based event-triggered sliding mode control strategy for delayed systems involving unknown disturbances. This strategy comprises a triggering rule which can effectively save resources and an observer-based control law which can drive the states of delayed systems into the practical sliding mode band in some finite time. Some sufficient conditions coupled with this control strategy are proposed to guarantee the robust performance of the delayed systems. Significant outcome of this strategy is that it can be applied to the case in which the disturbances are unmeasured or unknown. Finally, two numerical examples and its simulations are presented to show the performance of the systems and effectiveness of this control strategy.     

Finite-time tracking using sliding mode control

Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In this paper, we consider a general class of fully actuated mechanical systems described by Euler–Lagrange dynamics and the class of underactuated systems represented by mobile robot dynamics that are required to reach and maintain the desired trajectory in finite time. An approach known as the terminal sliding mode control (TSMC) involves non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time thus ensuring finite-time tracking. The main advantage of this control scheme is in fast converging times without excessive control effort. Such controllers are known to have singularities in some parts of the state space and, in this paper, we propose a method of partitioning the state space into two regions where the TSMC is bounded and its complement. We show that the region of bounded TSMC is invariant and design an auxiliary sliding mode controller predicated on linear smooth sliding surface for the initial conditions outside this region. Furthermore, we extend these results to address TSMC for underactuated systems characterized by the mobile robot dynamics. We demonstrate the efficacy of our approach by implementing it for a scenario when multiple dynamic agents are required to move in a fixed formation with respect to the formation leader. Finally, we validate our results experimentally using a wheeled mobile robot platform.     

Finite-time general function consensus for multi-agent systems over signed digraphs

This paper solves the finite-time consensus problem for discrete time multi-agent systems (MASs) where agents update their values via linear iteration and the interactions between them are described by signed digraphs. A sufficient condition is presented that the agents can reach consensus on any given linear function of multiple initial signals in finite time, i.e., there exists an eventually positive Laplacian-based matrix associated with the underlying graph. We prove that the linear iterative framework “ratio consensus” developed for unsigned graphs in the literature can be extended to the computation for signed graphs with appropriate modifications. Our method weakens the limitation of the iterative framework on the “marginal Schur stability” of the weight matrix without increasing the computational complexity. Reaching average consensus on unsigned graphs as in the literature is regarded as a special case of our algorithm. Two illustrative examples are presented to demonstrate the correctness of the proposed results.     

Fixed-time consensus for stochastic multi-agent systems with discontinuous dynamics via quantized control

In this study, the fixed-time consensus (FDTC) for stochastic multi-agent systems (MASs) with discontinuous inherent dynamics is investigated via quantized control. Firstly, an improved lemma for fixed-time (FDT) stability is derived and several more precise estimations for settling time (SLT) are gained by using certain special functions. Secondly, a more general MAS containing discontinuous inherent dynamics and stochastic perturbations is considered, which is closer to practical life. Thirdly, to overcome the limitation of communication, two kinds of quantized control protocols are designed. Besides, in the light of the graph theory, non-smooth analysis, fixed-time (FDT) stability and stochastic analysis theory, some sufficient conditions are put forward to achieve FDTC of MASs. Finally, the validity of the derived theoretical results is testified by two numerical examples.     

Leader-following consensus for multi-agent systems with actuator faults via adaptive event-triggered control

In this paper, the leader-following consensus problem is investigated by event-triggered control for multi-agent systems subject to time-varying actuator faults. Firstly, for a case of the leader without control input, a distributed event-triggered fault-tolerant protocol is proposed with the help of adaptive gains. Secondly, the proposed protocol is developed by an auxiliary nonlinear function to compensate the effect of the leader’s unknown bounded input. It is shown that under the both obtained protocols the tracking errors converge to an adjustable neighborhood around the origin, meanwhile the Zeno behavior is avoided. Moreover, the protocols are fully distributed in sense that any global information associated with the network is no longer utilized. Finally, numerical examples are presented to show the validity of the obtained protocols.     

Mean-square consensus of heterogeneous multi-agent systems with communication noises

This paper addresses the mean-square consensus problems of continuous-time heterogeneous multi-agent systems with communication noises. First, in order to attenuate the communication noises, time-varying consensus gains are applied in the consensus algorithm. Then, by using the tools of algebraic graph theory and stochastic analysis, sufficient conditions for the mean-square consensus are given for the cases with and without a leader. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithms.     

Reachable set control for singular systems with disturbance via sliding mode control

The problem of the reachable set (RS) control of sliding mode control (SMC) for a class of singular systems with or without time-varying delay under zero initial conditions is studied. The purpose is to get an RS boundary containing all states of the system by designing an SMC. Firstly, singular systems with or without time-varying delay are decomposed into slow and fast subsystems by using the decomposition approach. Then, the augmented Lyapunov functional is built utilizing the decomposed state vector. The SMC is designed based on the exponential reaching criterion, resulting in the corresponding closed-loop control system (CLCS) construction. As a consequence, an RS criterion is constructed by employing the inequality scaling approach and the free-weighting matrix in conjunction with the linear matrix inequality (LMI). Finally, the validity and primacy of the results are provided by two numerical and practical examples.     

Event-triggered consensus for second-order multi-agent systems with sampled position data via impulsive control

In this paper, the sampled-data-based event-triggered (SDBET) consensus problem of second-order multi-agent systems (MASs) with sampled position data is studied via impulsive control. Firstly, two kinds of SDBET impulsive control protocols are proposed, both of which employ sampled position data only. Secondly, a novel SDBET transmission scheme is designed to ensure the maximum length of triggering intervals exists, which can be regulated by the parameters in the triggering function. Also, the Zeno behavior is naturally excluded under the SDBET transmission scheme. And by using the designed SDBET impulsive control scheme, consensus of second-order MASs can be achieved with lower transmission and control updating frequency than using the periodical impulsive control scheme. Thirdly, sufficient conditions on the communication topology, the length of triggering intervals and control gains are derived to achieve SDBET consensus. It is also shown that to achieve consensus, both the maximum and minimum lengths of triggering intervals should be restricted. Also, a practical method for calculating the sampling period and other triggering parameters is given to ensure that the length of the triggering interval does not exceed the given range, and the SDBET transmission scheme is truly realized. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.     

Finite-time leaderless consensus control of a group of Euler-Lagrangian systems with backlash nonlinearities

In this paper, we consider the finite-time leaderless consensus control of a group of Euler-Lagrangian systems with backlash nonlinearities. A finite time distributed continuous control scheme is proposed for the multi-agent systems. It is shown that the output of the Euler-Lagrangian systems reach consensus within finite time. Transient performances in terms of convergence rate is also analyzed. Finally simulation results are carried out to verify the effectiveness of the proposed schemes.