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This paper describes consensus control of multi-agent systems (MAS) with input and communication delay in the frequency domain. Each agent of MAS is a linear continuous-time system. The considered linear dynamic model of each agent involves multiple input delays. An H 2 controller is proposed for optimal performance and robustness of the MAS. The internal stability approach is employed to compute the H 2 controller and the performance index of the overall MAS. A sufficient criterion is derived for gain and delay margin to reach convergence. The simulation paradigm shows the effectiveness of the proposed control scheme. • This paper studies the consensus problem in multi-agent systems with delays. • The proposed algorithms have been analyzed in the frequency domain. • The homogenous linear dynamic model of each agent involves multiple input delays. • The internal stability is used to design the proposed controller. • Sufficient criteria are obtained for gain and delay margins. [ABSTRACT FROM AUTHOR]

For leader-following multiagent systems with input saturation, the existing protocols use a low gain feedback approach to achieve semi-global consensus. The main drawback of this approach is the ineffective utilization of the actuator potential, resulting in bad performance. To improve the transient performance of the consensus tracking, this paper proposes a gain scheduled approach for multiagent systems subject to the saturator saturations. A novel kind of scheduler-based protocols are proposed, which consists of state feedback controllers with time-varying gain and parameter schedulers. The role of the controllers is to achieve the consensus tracking, while the schedulers can accelerate this consensus progress by enlarging the gain parameter. To remove the dependence of the schedulers on global information, a minimum-value-based consensus algorithm is put forward, with idea of driving all values of agents throughout the network to their minimum value. Its implementation is guaranteed by the network-topology connectivity. Finally, our approach is further extended to the case where the leader’s control input is nonzero, time-varying, and bounded. The discontinuous protocol and its continuous approximation counterpart are designed, yielding the exact- and quasi-consensus tracking, respectively. Simulation results verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

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]

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]

Cooperative output regulation is a general framework, which considers output synchronisation, homogenisation and disturbance rejection simultaneously. To be an extension, this study divides the lumped disturbance into two parts, namely, local disturbance which is slow‐varying, mismatched and non‐linear, and global disturbance generated by an autonomous linear system. Generalised extended state observers (GESOs) are constructed to estimate the local states, the local disturbances and the global disturbance simultaneously. Observer‐based controllers are designed to realise cooperative output regulation in the presence of mismatched uncertainties. In control design, a linear matrix inequality‐based design methodology is proposed to get the exponentially convergent GESO with guaranteed decay rate. A simulation example is then shown to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the authors investigate distributed model predictive control for polytopic uncertain systems subject to actuator saturations and packet dropouts with time‐varying probabilities in controller‐to‐actuator channels. For the sake of less computational efforts and a flexible system structure, the global system is decomposed into several lower‐dimensional subsystems and the subsystems optimise a global performance function in parallel. A novel augmented distributed controller model is proposed to describe both the actuator saturations and packet dropouts in one unified expression by adopting a stochastic variable taking the value 1 or 0 with time‐varying probabilities and accordingly a new result is obtained. By placing the saturated linear feedback law into the convex hull of a group of linear feedback laws, the distributed controller for each subsystem is obtained from the solution of the convex optimisation problem involving linear matrix inequalities. A numerical example is supplied to demonstrate the effectiveness of the developed techniques. [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]

This paper addresses the feedback stabilization problem for Markov jump linear systems with quantized control input. A simple but powerful input controller for eliminating the input quantization in Markov jump linear systems is used. The proposed mode-dependent input controller comprises two parts: the linear part and the nonlinear part, where the linear part determines the fundamental characteristics of the systems, and the nonlinear part eliminates the effect of the input quantization. The stability is analyzed in detail for both the discrete-time and continuous-time Markov jump linear systems with input quantization. The sufficient conditions and the specific mode-dependent input controller to guarantee the stability of the systems are obtained. Numerical examples are given to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]