Leaderless Consensus Control Research Articles

Convex synthesis for optimal ℋ∞ consensus of input-delayed multi-agent systems via dynamic relative output feedback

In this paper, we address the leaderless consensus control problem for a class of linear multi-agent systems (MASs) subject to nonlinear time-varying input delays and unknown external disturbances. The MAS is considered to be non-introspective, meaning that each individual agent is not able to measure the absolute plant state/output of its own but can sense relative information from its neighbours. A novel dynamic relative output-feedback (DROF) controller structure is proposed by leveraging the integral quadratic constraints (IQCs) from robust control theory. This new DROF controller is compelling in the sense that it utilises not only the relative plant outputs, but also the relative controller states and relative IQC-induced dynamics states for distributed feedback control. Based on this, the associated consensus control synthesis conditions that guarantee optimal disturbance attenuation performance in the presence of time-varying input delays are derived and formulated as linear matrix inequalities (LMIs), which can be solved efficiently via convex optimisation. Effectiveness of the proposed theoretical results is demonstrated through simulation studies.

Global smooth leaderless consensus control of high-order nonholonomic chained systems

This paper investigates the leaderless consensus control problem of high-order nonholonomic chained systems. Based on the relationship between state and consensus error, a novel Lyapunov function is defined and is proved positive definite and radially unbounded. The first control law is constructed to make the Lyapunov function non-increasing. The Lyapunov method, graph theory and LaSalle invariance principle are applied to analyse system stability, where some skillful mathematical calculations are conducted to overcome the difficulties caused by nonholonomic constraint and high-order structure, and the explicit expression and the conditions of control parameter matrix are calculated. Then, the second control law is designed by extending the results to the input saturation case. Both of the two controllers are smooth, time-invariant, static, distributed, and able to achieve global asymptotic consensus of nonholonomic chained systems over connected undirected graph. Numerical simulation examples are implemented to demonstrate the effectiveness of the proposed control schemes.

Distributed adaptive leader–follower and leaderless consensus control of a class of strict-feedback nonlinear systems: a unified approach

In this paper, distributed adaptive consensus for a class of strict-feedback nonlinear systems under directed topology condition is investigated. Both leader–follower and leaderless cases are considered in a unified framework. To design distributed controller for each subsystem, a local compensatory variable is generated based on the signals collected from its neighbors. Such a technique enables us to solve the leader–follower consensus and leaderless consensus problems in a unified framework. And it further allows us to treat the leaderless consensus as a special case of the leader–follower consensus. For leader–follower consensus, the assumption that the leader trajectory is linearly parameterized with some known functions as required in most recent relevant literatures is successfully relaxed. It is shown that global uniform boundedness of all closed-loop signals and asymptotically output consensus could be achieved for both cases. Simulation results are provided to verify the effectiveness of our schemes.

Consensus Control for Reactive Power Sharing Using an Adaptive Virtual Impedance Approach

Reactive power sharing among distributed generators (DGs) in islanded microgrids (MGs) presents control challenges, particularly in the mismatched feeder line condition. Improved droop control methods independently struggle to resolve this issue and centralized secondary control methods exhibit a high risk of collapse for the entire MG system under any failure in the central control. Distributed secondary control methods have been recently proposed to mitigate the reactive power error evident in the presence of mismatched feeder lines. This paper details a mathematical model of an adaptive virtual impedance control that is based on both leaderless and leader-followers consensus controls with a novel triangle mesh communication topology to ensure accurate active and reactive power sharing. The approach balances an enhanced rate of convergence with the anticipated implementation cost. A MATLAB/Simulink model with six DG units validates the proposed control performance under three different communication structures: namely, ring, complete, and triangle mesh topologies. The results suggest that leaderless consensus control is a reliable option with large DG systems, while the leader-followers consensus control is suitable for the small systems. The triangle mesh communication topology provides a compromise approach balancing the rate of convergence and the expected cost. The extensibility and scalability are advantages of this topology over the alternate ring and complete topologies.

Adaptive Leaderless Consensus Control of Strict-Feedback Nonlinear Multiagent Systems With Unknown Control Directions

The leaderless consensus problem over strict-feedback nonlinear multiagent systems (MASs) with unknown model parameters and control directions is investigated. The main idea of the existing consensus strategies for strict-feedback nonlinear MASs with unknown control directions is leading agents toward predefined global leaders/exosystems. However, in several missions, agents need to reach autonomous agreement on an a priori unknown quantity for a desired state, and hence the existing results are not applicable in these missions. The main contribution of this article is designing an adaptive leaderless consensus control scheme for strict-feedback nonlinear MASs when agents' control directions are unknown and unidentical. First, we introduce decentralized local error surfaces designed based on each agent position and neighboring agents' positions. We show that as the error surfaces remain bounded and converge to zero, the boundedness of the agents' positions and achieving leaderless consensus in the MAS can be guaranteed. Then, based on the properties of the Nussbaum-type functions, a decentralized backstepping adaptive control law is proposed under which the local error surfaces remain bounded and converge to zero. Finally, the design is more clarified and evaluated via an example.

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.

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.

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.

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.

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.

Neuro-adaptive leaderless consensus of fractional-order multi-agent systems

Leaderless consensus control problem of fractional-order multi-agent systems (FOMASs) with unknown nonlinearities and unknown external disturbances is investigated in this paper. Firstly, based on neural networks, an adaptive control protocol with integer-order dynamics is proposed to approximate the unknown nonlinearities, which is easy to implement in reality. And then, a novel auxiliary Lyapunov function which contains Riemman–Liouvile fractional-order integral is first constructed to verify the effectiveness of the designed control protocol. Moreover, the convergence analysis of FOMASs is finished by taking the Barbalat lemma for the first time. Finally, theoretical results are demonstrated by several numerical simulations.

Robust Semi-Global Leaderless Consensus and Containment Control of Identical Linear Systems with Imperfect Actuators

This paper investigates both the robust semi-global leaderless consensus problem and the robust semi-global containment control problem for a group of identical linear systems with imperfect actuators. The imperfect actuators are characterized by nonlinearities such as saturation and dead zone and there input output relationships are not precisely known. The dynamics of follower agents are also affected by the input additive disturbances. Low-and-high gain feedback consensus protocols are constructed to solve these problems. More specifically, it is shown that robust semi-global leaderless consensus can be achieved over a connected undirected graph and robust semi-global containment control can be achieved when each follower agent has access to the information of at least one leader agent. Numerical simulation illustrates the theoretical results.

Smooth time-invariant control for leaderless consensus of networked nonholonomic systems

This article studies the leaderless consensus control problem of multiple nonholonomic chained systems. Two smooth time-invariant static distributed controllers are derived based on Lyapunov method...

Distributed finite-time leaderless consensus control for double-integrator multi-agent systems with external disturbances

We study the finite-time consensus control of double-integrator multi-agent systems with external bounded disturbances under the fixed leaderless network communication topology. Based on the relative position and the relative velocity information, a novel finite-time consensus protocol is constructed. By using the Lyapnuov finite-time theory, it is shown that the proposed protocol can coordinate the states of agents to guarantee the finite-time consensus under an undirected connected topology. And then we extend the results onto the strongly connected directed communication topology. Importantly, the finite convergence time of the leaderless systems is explicitly presented. Finally, the effectiveness of the results is illustrated by numerical simulation.

Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems

In this paper we consider finite-time leaderless consensus control of multi-agent systems consisting of a group of nonlinear mechanical systems with parametric uncertainties. New adaptive finite time continuous distributed control algorithms are proposed for the multi-agent systems. It is shown that the states of the mechanical systems can reach a consensus within finite time under an undirected graph. Transient performances in terms of convergence rates and time are also analyzed. Finally simulation results illustrate and verify the effectiveness of the proposed schemes.