Leaderless Consensus Research Articles

Dynamic Relative Output-Feedback Consensus for Multi-Agent Systems Subject to Actuator Saturation

This paper deals with the problem of leaderless consensus control for a class of non-introspective linear multi-agent systems (MASs) subject to input saturation and external disturbances. A novel dynamic relative output-feedback saturated consensus control protocol is proposed, which utilizes not only relative system outputs but also relative controller states from neighboring agents for distributed feedback control. With this new controller structure, the associated control synthesis conditions that guarantee optimal disturbance attenuation performance are fully characterized as linear matrix inequalities (LMIs) using a complete form of Lyapunov function matrix, which can be solved efficiently via convex optimization. The proposed approach unifies the designs for both continuous-time and discrete-time MASs. Two application examples are used to demonstrate effectiveness and usefulness of the proposed results.

Nonlinear PI Control for High-Order Agents With Unknown High-Frequency Gain Signs Under Switching Topologies

Existing results on dealing with unknown high-frequency gain signs (UHFGSs) mainly adopt the Nussbaum-type functions. A new kind of control algorithms with nonlinear PI functions are presented to cope with UHFGSs. It is rigorously proven that the proposed algorithms with properly selected nonlinear PI functions can guarantee consensus for high-order multi-agent systems (MASs) under switching topologies with uniformly quasi-strongly $\delta $ -connected graphs (UQSGs). Furthermore, we also investigate the output leaderless consensus of heterogeneous agents with UHFGSs. Finally, the numerical examples are illustrated to show the validity of the proposed results.

Recent advances in distributed adaptive consensus control of uncertain nonlinear multi-agent systems

So far, distributed adaptive consensus problems for uncertain nonlinear multi-agent systems have not yet been extensively studied. Compared with centralised adaptive control, some new challenges need to be well addressed, for examples, (i) how to reach asymptotically consensus tracking with directed topology condition, by using totally distributed adaptive control strategies; (ii) how to ensure globally uniform boundedness of closed-loop systems while achieving leaderless consensus with semi-positive definite Laplacian matrix; (iii) how to maintain system performance while effectively reducing the communication burden among connected agents. This paper is mainly devoted to report some recent advances in distributed adaptive consensus control. Besides, some interesting research topics which are worthy of further investigation will also be discussed.

Output feedback consensus control for fractional-order nonlinear multi-agent systems with directed topologies

This paper is devoted to the output feedback consensus control problem for a class of nonlinear fractional-order multi-agent systems (MASs) with general directed topologies. It is worth noting that the considered fractional-order MASs including the second-order MASs as special cases. By introducing a distributed filter for each agent, a control algorithm uses only relative position measurements is proposed to guarantee the global leaderless consensus can be achieved. Also the derived results are further extended to consensus tracking problem with a leader whose input is unknown and bounded. Finally, two simulation examples are provided to verify the performance of the control design.

Distributed control of higher-order nonlinear multi-agent systems with unknown non-identical control directions under general directed graphs

This paper addresses the leaderless consensus control problem for higher-order nonlinear multi-agent systems with completely unknown non-identical control directions. In contrast to the existing consensus results, we propose a distributed consensus algorithm using only local information available to the individual agent under a general directed graph. Nussbaum-type functions are used to deal with the unknown control directions, and novel auxiliary variables including the estimate of the consensus value are defined and employed in designing the control algorithm to avoid the appearance of multiple Nussbaum-type function terms in the stability analysis. The uncertain dynamics of each agent is approximated by the function approximation technique, and the unknown disturbance and the approximation error are suppressed by introducing an adaptive robust term. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that under the proposed distributed algorithm, the boundedness of all the closed-loop signals and asymptotic consensus can be achieved. Simulation results on pendulum plants are given to verify the theoretical analysis.

Distributed Consensus for Multiple Lagrangian Systems With Parametric Uncertainties and External Disturbances Under Directed Graphs

In this paper, we study the leaderless consensus problem for multiple Lagrangian systems in the presence of parametric uncertainties and external disturbances under directed graphs. To achieve asymptotic behavior, a robust continuous term with adaptive varying gains is added to alleviate the effects of the external disturbances with unknown bounds. In the case of a fixed directed graph, by introducing an integrate term in the auxiliary variable design, the final consensus equilibrium can be explicitly derived. We show that the agents achieve weighted average consensus, where the final equilibrium is dependent on three factors, namely, the interactive topology, the initial positions of the agents, and the control gains of the proposed control algorithm. In the case of switching directed graphs, a model-reference-adaptive-consensus-based algorithm is proposed such that the agents achieve leaderless consensus if the infinite sequence of switching graphs is uniformly jointly connected. Motivated by the fact that the relative velocity information is difficult to obtain accurately, we further propose a leaderless consensus algorithm with gain adaptation for multiple Lagrangian systems without using neighbors' velocity information. We also propose a model-reference-adaptive-consensus-based algorithm without using neighbors' velocity information for switching directed graphs. The proposed algorithms are distributed in the sense of using local information from its neighbors and using no common control gains. Numerical simulations are performed to show the effectiveness of the proposed algorithms.

Saturated input consensus algorithms for perturbed double-integrator systems without velocity measurements

This study addresses the consensus problem of perturbed double-integrator systems. Specifically, we propose consensus algorithms for these systems that simultaneously account for input saturation, lack of velocity information, and existence of time-varying external disturbances; in this sense, we extend some of existing results in the literature. The designs have been developed by means of introduction of auxiliary dynamics for each agent. First, we propose a leaderless consensus algorithm and then deal with the leader–follower consensus and consensus with reference velocity. Sufficient control gain conditions and upper bounds of the consensus errors are derived for each case by considering both bidirectional and unidirectional communication topologies. The effectiveness of the algorithms is evaluated through simulation studies.

Fixed-Time Consensus of Nonlinear Multi-Agent Systems With General Directed Topologies

In this brief, the authors study the fixed-time consensus problem for a class of first-order nonlinear multi-agent systems where the communication topologies are general directed. Both fixed-time tracking consensus and fixed-time leaderless consensus problems are investigated. For the leader–follower situation, the communication topology is only required to contain a directed spanning tree. As for the leaderless situation, the topology is required strongly connected. Simulations are finally provided to verify the effectiveness of the proposed algorithms.

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.

Event-Triggered Control for Semiglobal Robust Consensus of a Class of Nonlinear Uncertain Multiagent Systems

In this note, robust consensus for a class of nonlinear second-order multiagent systems with uncertainties is investigated from an event-triggered control approach. An event-triggered distributed control protocol is designed to achieve semiglobal robust leaderless consensus for directed graphs. To guarantee the feasibility of the proposed scheme, the event-based consensus is converted to an event-based stabilization for analysis. Zeno behavior is avoided under the proposed event-triggered mechanism. The effectiveness of the proposed event-triggered scheme is demonstrated by numerical simulations.

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

ABSTRACTThis paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.

Leaderless consensus control of uncertain multi-agents systems with sensor and actuator attacks

In this paper, the leaderless consensus control of a group of high-order strict feedback nonlinear systems with uncertainties under sensor and actuator attacks is considered. A fully distributed adaptive leaderless consensus control strategy is proposed to deal with the sensor and actuator attacks. Compared with existing results in which the model considered is simple, a strict-feedback nonlinear system is considered in this paper, which makes the problem more challenging. It is shown that all closed-loop signals are uniformly bounded and asymptotic output consensus is achieved in presence of sensor and actuator attacks. Simulations are given to demonstrate the effectiveness of the proposed protocols.

Consensus of multi-agent systems with delayed sampled-data and directed topologies

In this paper, the leader-following and leaderless consensus problem of high-order multi-agent systems on directed graphs are discussed. The delayed sampled outputs are only available data, observer-based output feedback controllers are presented. By constructing appropriate Lyapunov-Krasovskii function and auxiliary integral function to deal with the delayed sampled-data, sufficient conditions are given to ensure the global exponential consensus of the considered systems. We also obtain the upper bounds of the allowable delay and sampling period. Finally, we give the simulation examples to validate the effectiveness of the proposed methods.

Consensus of Multi-Agent Systems With Heterogeneous Input Saturation Levels

In this brief, a consensus problem is investigated for a class of multi-agent systems with input saturation, in which the common assumption in existing related literature that each agent has the same input saturation level is removed. Furthermore, the communication graphs are general directed graphs. New kinds of fully distributed control protocols, depending on only the relative state information, are successfully designed to achieve global state consensus among the agents. Specifically, neither the saturation levels of the neighboring agents nor the information about the global communication topology is involved in the controller design. Both leaderless consensus and leader-following consensus with a dynamic leader are studied. Simulation examples are finally provided to illustrate the theoretical results.

Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling

This paper investigates mean square leaderless consensus of networked nonlinear multi-agent systems. An efficient distributed event-triggered mechanism based on stochastic sampling is introduced to reduce the communication cost and controller updates. The stochastic sampling interval randomly switches between two given values. Mean square consensus criteria for multi-agent systems with strongly connected networks or networks containing directed spanning trees are derived, respectively. Moreover, the case with a special event-triggered weighting matrix and the case without even-triggered strategies are also discussed. Finally, an example is given to verify the theoretical results.

Consensus in Fractional-Order Multi-Agent Systems With Intermittence Sampled Data Over Directed Networks

The leaderless consensus of fractional-order multi-agent systems (FOMASs) by intermittence sampled data control method is investigated in this brief, for which a distributed intermittence sampled data control protocol is presented to reduce the updating rate and working time of controllers. Subsequently, the Laplace transform and the stability theory are utilized to derive some necessary and sufficient consensus criteria that show the relations among the fractional order, sampling period, communication width, coupling strengths, and network topology. What is more, it can be discovered that both the communication width and sampling period have the lower and upper bounds for given networks to attain leaderless consensus. Finally, a numerical simulation example is presented to prove the theoretical results.

Distributed consensus of networked markov jump multi-agent systems with mode-dependent event-triggered communications and switching topologies

This paper investigates the distributed leaderless consensus problem of networked Markov jump multi-agent systems with mode-dependent switching topologies. Specifically, a novel mode-dependent sampling and event-triggered communication strategy is proposed to reduce the network burden with less conservatism. Based on model transformation and constructing the mode-dependent Lyapunov-Krasovskii functional, sufficient consensus criteria are first established. Then, the desired event triggering function parameters and the controller gains are designed in terms of linear matrix inequalities (LMIs). In the end, an illustrative example is provided to verify the effectiveness of our proposed consensus method.

On leaderless consensus of fractional-order nonlinear multi-agent systems via event-triggered control

The consensus problem of fractional-order multi-agent systems is investigated by eventtriggered control in this paper. Based on the graph theory and the Lyapunov functional approach, the conditions for guaranteeing the consensus are derived. Then, according to some basic theories of fractional-order differential equation and some properties of Mittag–Leffler function, the Zeno behavior could be excluded. Finally, a simulation example is given to check the effectiveness of the theoretical result.

Distributed Cooperative Control of Multiple Hybrid Energy Storage Systems in a DC Microgrid Using Consensus Protocol

Hybrid energy storage system (HESS) consisting of battery and supercapacitor (SC) is an effective approach to alleviate voltage stability problems brought by the fluctuation of renewable resources in a dc microgrid. This paper proposes a novel distributed control scheme for multiple HESSs based on a leaderless consensus protocol to realize the power splitting between batteries and SCs and thus regulate the dc bus voltage. Without assigning leaders among the batteries and SCs, each SC or battery has equal priority in participating in voltage or state of charge (SOC) regulation using only neighboring information exchange instead of global communication. This distributed approach makes the system robust against any physical failure or communication fault only if the remaining communication network is connected. Consensus for the state variable associated with the battery SOC, the SC terminal voltage, and the dc average bus voltage are all achieved in this scheme, and thus the voltage quality and the energy storage lifetime can be improved. In addition, the small-signal stability of a four-HESS system is investigated, and the impact of the control parameters on the system is analyzed. Simulations and experimental studies are conducted to demonstrate the effectiveness of the proposed control scheme in an islanded dc microgrid.

Adaptive Distributed Consensus Control of One-Sided Lipschitz Nonlinear Multiagents

This paper addresses the leaderless consensus control for a network of multiagent systems with the one-sided Lipschitz and quadratic inner-boundedness nonlinear dynamics. A distributed dynamic consensus protocol as a function of relative state feedback of the neighboring agents with edge-based adaptive coupling weights is designed for an undirected communication graph to achieve asymptotic consensus among the nonlinear agents. Further, an extension of the proposed consensus protocol in the presence of external disturbance is devised to ensure the ${L_{2}}$ stability of the consensus error. This paper is less conservative and more general owing to its application to the systems with large Lipschitz constants and to a broad class of the nonlinear systems. In comparison to the previous consensus control schemes, the proposed approach can be employed to design consensus protocols for the one-sided Lipschitz systems with unknown communication topology. This feature enables the fully distributed consensus control as the communication graph information is not required for the consensus protocol design. Simulation results for a network of six mobile agents are provided to demonstrate the effectiveness of proposed consensus schemes in the absence or presence of an external disturbance.