This study addresses the cluster consensus problem for generic linear heterogeneous multi-agent systems. The main purpose of this study is to unveil how agents confront the effects of intra-cluster couplings and inter-cluster couplings, and reach cluster consensus. For the semi-heterogeneous case, where agents in the same cluster have identical dynamics, cluster consensus is achieved if each agent suppresses the inter-cluster couplings. For the heterogeneous case, where all agents have different dynamics, cluster consensus is achieved if each agent confronts both inter-cluster and intra-cluster couplings. Two kinds of control protocols using relative output errors are designed for the heterogeneous case. For both semi-heterogeneous and heterogeneous cases, design procedures are provided to construct controllers to satisfy the relation between the dynamics of agents and the communication graph, which ensure cluster consensus. Finally, numerical examples are provided to verify the theoretical results.

In this study, the problem of synchronised trajectory tracking for a network of multi-input–multi-output (MIMO) non-minimum phase (NMP) systems is addressed under a switching communication topology. First, an approach to convert the original system equation into a normal form is proposed, where a coordinate transformation matrix is introduced. Then, a control solution is developed, which is made up of a distributed observer network to generate an estimate of the reference system, a causal stable inversion to estimate the bounded state reference and feedforward term, and a local state-trajectory tracker to achieve simultaneously asymptotic output tracking and internal dynamics stabilisation. Finally, the solution is applied to the synchronised flight-path angle and velocity tracking problem of a network of F-16 aircraft, and further compared with the classic proportional–integral–derivative control-based approach used in many real-life applications. Simulation results demonstrate the effectiveness of the proposed solution, as well as the performance advantages owing to a systematic consideration of the NMP property.

In this study, the problem of designing a stochastic optimal controller for sampled-data systems whose sampling interval is subjected to a certain probability distribution is addressed. To design the controller, the Kronecker product operation and the Vandermonde matrix were introduced. A design method of the stochastic optimal controller is proposed. It is shown that the controller guarantee that the closed-loop system has exponentially mean square stability. Finally, the simulation results illustrate the effectiveness and practicability of the proposed method.

This study is concerned with observer design and observer-based output feedback control for a fractional reaction diffusion (FRD) system with a spatially-varying (non-constant) diffusion coefficient by the backstepping method. The considered FRD system is endowed with only boundary measurable and actuation available. The contribution of this study is divided into three parts: first is the backstepping-based observer design for the FRD system with non-constant diffusivity, second is the output feedback controller generated by the integration of a separately backstepping-based feedback controller and the proposed observer to stabilise the FRD system with non-constant diffusivity, and the last is the Mittag–Leffler stability analysis of the observer error and the closed-loop FRD systems. Specifically, anti-collocated location of actuator and sensor is considered in the stabilisation problem of this system with Robin boundary condition at and the boundary feedback controller for Dirichlet actuation at . By designing an invertible coordinate transformation to convert the observer error system into a Mittag–Leffler stable target system, the observer gains are obtained. They are used to design the output feedback control law for stabilising the closed-loop system. Finally, a numerical example is shown to validate the effectiveness of the authors' proposed method.

The authors propose an adaptive robust control approach for the levitation control of non-linear maglev vehicle with state constraint. The system contains non-linear and (possibly) time-varying uncertainty, which is supposed to be bounded. In order to prevent the undesirable collision, the airgap between suspended chassis and guideway should be restrained in a specified range for safety concerns. Furthermore, the maglev vehicle does not satisfy the (global) matching condition. The authors propose a three-step state transformation approach to transform the maglev vehicle to an interconnected uncertain system. After that, the robust control is proposed based on the transformed system, and the adaptive law is constructed to emulate the total system uncertainty. The adaptive robust control is able to ensure the system performance (uniform boundedness and the uniform ultimate boundedness) of uncertain maglev vehicle. In addition, the airgap can be confined within the specified range.

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.

This work studies the cooperative tracking problem for high-order non-linear multi-agent systems under a directed communication topology. The state and input of the leader are bounded. Distributed adaptive non-linear protocols based on the relative states of neighbouring agents are proposed, which can ensure the states of the followers converge to the state of the leader under the assumption that the directed communication topology contains a spanning tree with the root node being the leader agent. The distinctive features of this work are that the authors do not put Lipschitz restrictions (globally Lipschitz or Lipschitz-like condition) on non-linear functions and the adaptive protocols here can be implemented in a fully distributed fashion without using any global information (such as the knowledge of eigenvalue information of the Laplacian matrix associated with the whole communication topology). The effectiveness of the proposed distributed controller is illustrated by simulating a flexible joint system.

In this study, an integrated fault tolerant preview tracking control framework is proposed based on reduced-order simultaneous state and fault estimation, robust preview control and fault signal compensation. In general, this work consists of three key design parts. Firstly, the analysis and synthesis conditions of a novel reduced-order simultaneous state and fault estimator are given based on the equivalent model reconstruction and optimisation of the parametric solution. Note that such a reduced-order design method can avoid traditional output equation reduction requirement, and has a wider application scope. Secondly, the robust preview tracking control policy is constructed by integrating state-feedback, preview action, and integral operation. Relying on augmentation modelling technique, a linear quadratic preview control design problem is transformed into an equivalent augmented state-feedback control design problem. Thirdly, the fault compensation is achieved by using estimated fault to accommodate fault influence. These involved designs are performed at the optimisation level, and thus guarantee the robust tracking performance of closed-loop systems. The effectiveness of the above conclusions is finally verified via two case studies.

This study develops distributed neuro-adaptive control protocols for synchronisation of leader–follower multi-agent systems (MASs) with non-linear dynamics in non-strict-feedback form. The communication graph is assumed to be directed, and the agents are considered heterogeneous. The leader's dynamics are also assumed non-linear, and the state derivative of the leader is unknown to its immediate followers. The well-known command filtered backstepping approach, presented for single-agent systems in the literature, is extended to the synchronisation of MASs with non-strict-feedback non-linear dynamics. This obviates the requirement of computing the th-order derivatives of the local neighbourhood synchronisation error at the step of the design. The number of adaptive tuning laws and consequently the complexity of the neuro-adaptive design is reduced by estimating only a positive scalar related to unknown non-linear dynamics of each agent. An auxiliary system is then introduced into the control design to compensate for the discrepancy between designed and saturated control signals. The proposed distributed control protocol guarantees that all signals in the closed-loop system are cooperatively semi-globally uniformly ultimately bounded, and the consensus error for all agents converge to a small neighbourhood of the origin. Finally, a simulation example demonstrates the effectiveness of the proposed control scheme.

This study investigates a continuous sliding mode tracking problem for robot manipulators under the presence of parametric uncertainty and external disturbances. A chattering-free integral terminal sliding mode control scheme is first proposed by integrating an integral terminal sliding surface with an observer. Lypaunov stability theory is employed to prove the global finite-time tracking of robotic system. The appealing advantages of the proposed controller are that it is easy to implement with the continuous sliding mode control featuring chattering-free, fast transient and high steady-state tracking precision. Extensive simulations on two degree of freedoms (DOFs) are presented to demonstrate the effectiveness and improved performance of the proposed approach.

A class of persistent monitoring problems in one-dimensional space with the aid of multi-agent systems, which is formulated as an optimisation problem of minimising a novel performance metric is studied. The concept of the monitoring index is introduced in the performance metric to describe the importance of different targets in the space due to the requirements of the monitoring task. Based on a given class of moving trajectories, an optimal control approach is used to minimise the performance metric of monitoring space. After some model transformation, the infinitesimal perturbation analysis method is used to design the gradient-based algorithm, aiming to find the optimal trajectories, where the monitoring index exhibits the effect on the monitoring time for different targets. Numerical simulations are represented to demonstrate the performance of the algorithm and reveal the effectiveness of the monitoring index.

This study focuses on the stability analysis and design of output feedback controllers for a non-linear discrete-time switched system with uncertain subsystems. The considered system involves time-varying delay, non-linear terms, and affine parametric uncertainties. The main goals of this study are first to derive sufficient conditions to guarantee the stability of the unforced switched system and then, to construct two stabilising output feedback controllers (static and dynamic) to stabilise the closed-loop system with considering arbitrary switching signals. In this regard, based on switched Lyapunov functions, an appropriate Lyapunov–Krasovskii functional is constructed to establish the sufficient conditions; these conditions depend only on the upper bounds of the time-delay and uncertain parameters. Furthermore, in the proposed method, the admissible bound of time-delay and the maximum non-linearity of subsystems could be calculated. Finally, numerical examples are provided to verify the theoretical results.

This study is concerned with the finite-time stability of non-linear systems with impulsive effects due to logic choice. Firstly, we introduce a class of non-linear systems with logic-induced impulses and it generalises the model established in Suo and Sun (2015). Then, based on semi-tensor product technique, several criteria for finite-time stability for the system are given. Finally, two numerical examples are provided to illustrate authors' results.

This study investigates the problem of input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive time-varying delayed systems. Some Lyapunov–Krasovskii-type criteria on ISS and iISS which are effective for destabilising impulses and stabilising impulses are derived from advanced linear dissipation inequalities under average impulsive interval constraints. The conditions which require the coefficients of the linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be constants in the existing results on ISS/iISS of impulsive delayed systems are weakened. In this study, with the aid of the notions of uniformly exponentially stable function and average impulsive interval, the results allow the coefficients of the developed linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be time-varying functions which can take both positive and negative values, and the impulsive intervals of an impulsive sequence are allowed to have arbitrarily small lower bound and enough big upper bound simultaneously. Two examples are presented to illustrate the effectiveness of the results.

Synchronisation behaviours emerge from the interaction of oscillators. This study addresses the problem of almost sure exponential synchronisation for networked harmonic oscillators over switching communication networks. The coupling protocol relies on only the sampled velocity data and is periodical intermittent interactions over networks described by directed graphs subject to Markovian jumping. Next, the leader–following coupling protocol is proposed in order to approach a desired synchronisation trajectory. By using the stability theory of stochastic differential equations, some sufficient conditions are established to guarantee synchronisation in the almost sure sense. The almost sure exponential synchronisation can be achieved even when the coupling network and strength are switched between enabling and disabling the system to achieve complete synchronisation. Some numerical simulations are presented to illustrate the effectiveness of the theoretical results.

This study addresses the group controllability of continuous-time multi-agent systems. The problem is investigated in the leaderless framework where the whole group is consisted of a number of dynamic agents with autonomous capability, which can complete the large-scale complex task through local interaction and can be divided into some subgroups. This study concentrates on the group controllability problems of continuous-time multi-agent systems, gives the general definition of the group controllability, and establishes group controllability criteria. Sufficient and necessary conditions are derived for the group controllability of continuous-time multi-agent systems. Finally, the numerical example and simulations are given to illustrate the theoretical results.