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Based on the improved radial basis function (RBF) neural networks, the distributed three‐dimension formation control scheme in the presence of dynamic uncertainties is studied for non‐linear multi‐agent systems with time delay. A virtual leader which tracks the desired signal is followed by all agents adaptively. Linear reduced‐order observers are designed on the basis of absolute and local state errors of each agent. The local state error and absolute state error are generated between neighbouring agents and each individual agent in formation, respectively. The time delay for each agent in the formation can be offset by designing a Lyapunov function, which can simplify the controller design. To deal with non‐linear dynamic uncertainties and unavoidable disturbance, improved RBF neural networks are employed. In comparison with traditional RBF neural networks, improved RBF neural networks can provide better convergence performance. Subsequently, the formation controller is designed and the stability of the systems is validated by using a new Lyapunov function. Numerical simulation is conducted to demonstrate the effectiveness of the proposed method for non‐linear multi‐agent time‐delay systems. [ABSTRACT FROM AUTHOR]

This study deals with the protocol design for achieving robust global consensus tracking of multi‐agent systems. Agent dynamics are described as general linear systems with actuator saturation and input additive uncertainties and disturbances. Via developing a scheduled low‐and‐high gain design technique, the state feedback protocol is proposed, under which global consensus tracking and disturbance rejection for such systems can be achieved under the mild assumptions on agent dynamics and network topology. This result is further extended to the case of the reduced‐order observer‐based protocol design, with the help of the special coordinate basis approach. Finally, the advantages of the proposed protocols are illustrated by a numerical simulation. [ABSTRACT FROM AUTHOR]

A two‐degree‐of‐freedom consensus scheme is investigated for fractional‐order multi‐agent systems with time delay. The two‐degree‐of‐freedom protocol including the individual controllers and the coupling controllers can realise the global tasks and improve consensus performance. Based on such a protocol, a closed‐loop multi‐input multi‐output framework in frequency domain is established. Then the multi‐agent system is decoupled into several subsystems with respect to the eigenvalues of the Laplacian matrix. For each subsystem, the robust stabilising region of the individual controller satisfying H∞ index is obtained on the basis of the improved D‐partition method. The controller parameters chosen in the region can provide robustness for the individual agent. The parameters of the coupling controller that ensure fast consensus are determined by first deriving the stabilising region and then searching for the fastest consensus speed in the obtained region. The two‐degree‐of‐freedom structure can trade off the consensus performance and disturbance rejection and is applicable to arbitrary‐order multi‐agent systems with time delay including the fractional‐order system and the integer‐order system. The two‐degree‐of‐freedom consensus controller satisfying other performance criteria can also be designed based on the resultant stabilising region. The simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The study addresses the consensus problem of linear time invariant (LTI) multi‐agent systems with constant input delay and matched external disturbances by using relative output information. First, distributed disturbance observers are constructed to estimate the disturbances generated by linear exosystems with unknown initial conditions. Next, a disturbance observer‐based predictor feedback control law is developed for each agent to realise consensus disturbance rejection in the presence of input delay. Then, a linear matrix inequality‐based control design algorithm is given to determine the satisfactory control parameters. It is proved that state consensus can be achieved for both leaderless and leader–follower networks in the presence of large input delay and matched disturbances under the control scheme. Finally, a simulation example is provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This study addresses the distributed H∞ and H2 consensus control problems for multi‐agent systems with general integrator dynamics and undirected topology. First, based on the frequency domain description of linear multi‐agent systems, a sufficient and necessary condition is imposed on each controller to achieve consensus. Second, both H∞ and H2 optimal controllers are computed analytically according to the corresponding performance indices. The novel controllers not only can optimise the reference tracking performance but also has a simple tuning way to trade off the nominal performance and robustness. Finally, by application to the formation control of autonomous surface vessels shows the effectiveness of the proposed two control strategies. [ABSTRACT FROM AUTHOR]

An optimal disturbance rejection controller design method is put forward analytically for the synchronised output regulation of time‐delayed multi‐agent systems (MAS). All kinds of linear MAS can be described by a novel block diagram based on transfer functions in a unified framework. For each subsystem without intercommunication, the optimal output, input and balancing output–input load disturbance rejection controllers are designed independently. A filter is used to be in series with each controller to not only stabilise the whole systems but also achieve a tradeoff between nominal performance and robustness by adjusting a single tuning parameter. The proposed distributed H2 controllers calculated by algebraic solution perform better capacity of disturbance attenuation than the conventional given‐structured protocols. Two simulation examples demonstrate the validity of the new algorithm. [ABSTRACT FROM AUTHOR]

Output regulation is a general framework, for it not only can achieve closed‐loop stability, but also can realise asymptotic tracking and disturbance rejection. Within this framework, the authors consider the containment problem of heterogeneous linear multi‐agent systems with directed graphs. Via dynamic compensator techniques, the containment problem can be converted into cooperative output regulation problem. Moreover, they artfully construct regulation equations, whose solutions are also given. Adaptive protocols are proposed here by assigning a time‐varying coupling weight to each node. Unlike most existing protocols that depend on certain global information, protocols presented in this paper are independent of any global information, and hence are fully distributed. By combining the compensator technique with adaptive control, they propose the distributed dynamic adaptive state feedback and adaptive output feedback protocols for driving followers into the moving convex hull spanned by leaders. The obtained results are applied to the containment control of a network of heterogeneous agents, where the followers are described by mass‐damper spring systems, and the leaders are specified by harmonic oscillators. [ABSTRACT FROM AUTHOR]

This study considers the observer‐based consensus tracking problem of linear multi‐agent systems with input saturation. Existing observer‐based consensus protocols are designed based on an undirected graph, and need global information, such as the network size or eigenvalue information of the Laplacian matrix. In this study, based on only the agent dynamics and the relative outputs of neighbouring agents, an adaptive consensus protocol is proposed by assigning a time‐varying coupling weight to each node, and this protocol is independent of any global information and hence is fully distributed. Under the assumptions that each agent is asymptotically null controllable with bounded controls and detectable, and the topological graph has a directed spanning tree with the leader as the root node, semi‐global observer‐based consensus tracking of multi‐agent systems can be reached despite actuator saturation occurring. The results are applied to consensus tracking control of two‐mass‐spring systems, which are well‐known models for vibration in many mechanical systems. [ABSTRACT FROM AUTHOR]