This study deals with the output stationary average consensus problem for heterogeneous linear multi-agent systems with unknown parameters under undirected or balanced directed networks. The output stationary average consensus means that the outputs of agents reach an agreement on the average of their initial outputs. Each agent is modelled as an unknown linear system of any order (which might extensively vary between the agents) with the relative degree one or two. The agent in the network has only access to its own output and the relative outputs of its neighbours. Based on a direct model reference adaptive control scheme, a novel decentralised adaptive output consensus protocol is proposed to ensure that the output of each agent converges to the output of its reference model, as well as reaching output stationary average consensus. Finally, an illustrative example is presented to better highlight the merit of the proposed protocol.

This study deals with the problem of fault detection (FD) for linear discrete time-varying (LDTV) systems by combining the parity space-based method with the stationary wavelet transform (SWT). For the purpose of achieving good FD performance and simultaneously reducing the online computational burden resulted by high parity space order, SWT on residual signal is the first step in this study. This allows the formulation of residual generation as the selection of wavelet basis for SWT and the design of time-varying parity space vectors in a framework of multiscale optimisation. A recursive algorithm is developed for the computation of optimal parity space vectors and, based on this, a bank of residual signals can be obtained. Moreover, a weighted multiscale residual evaluation strategy is presented to detect the occurrence of a fault. The major contribution of the study lies in the development of a recursive design of SWT aided parity space vectors, which delivers an improvement of FD performance for a lower parity space order and an easy online implementation. A numerical example is demonstrated to illustrate the effectiveness of the proposed method.

ARMAX models are widely used in control engineering for both system description and control design. They can accurately describe a large class of real processes with relatively low complexity, but do not take into account observation errors, which can be particularly important in applications like filtering and fault diagnosis. Due to the intrinsic dependence in ARMAX process output, a single outlier may contaminate multiple data entries and completely spoil the conventional least-squares estimate. In this study, the authors develop a novel Moving Horizon Estimator that is not only robust to outliers but also able to reveal outliers. By utilising the fact that outliers are extreme errors that occur infrequently, the estimation problem is formulated as a least-squares optimisation problem with outliers explicitly modelled and regularised with -norm to induce sparsity. A coordinate descent-based solver is developed to obtain iterative algorithms with guaranteed convergence and closed-form solution available to each coordinate sub-problem per iteration. Due to the explicit modelling of outlier vectors, the impact of an outlier on multiple time instants can be estimated and mitigated. Simulation tests demonstrate that the proposed algorithm can effectively cope with outliers, even for the case when the commonly used Huber's M-estimation approach breaks down.

The authors investigate the dynamic modelling problem and the active vibration control design problem for a flexible Timoshenko robotic manipulator in this study. For the practical robotic manipulator, the authors analyse the dynamic characteristic considering the shear deformation and elastic deflection of the flexible arm link and describe this flexible system with a coupled partial differential equation and ordinary differential equations (PDE–ODEs) model. Furthermore, the authors design the active vibration control and disturbance observers to solve the vibration problem of the flexible robotic manipulator under the external disturbances, namely, to reduce the shear deformation and the deflection of the flexible Timoshenko link. Besides, the manipulator is driven to track the given angular position with an active angular controller, simultaneously. The effectiveness of the designed vibration control laws is analysed by the theoretical analysis and verified by the numerical simulation.

This study considers the problem of disturbance estimation and fault detection for positive systems. Depending on the occurrences of disturbance and/or faults on positive systems, the authors use two types of observer structures and provide design strategies for reliable estimation of states, disturbance, and faults. Although various positive observers have been designed for positive systems, they fail to estimate the states in presence of unknown inputs. To realise simultaneous estimation of states and unknown inputs for positive systems, a special type of unknown input observer (UIO) called positive UIO (PUIO) is introduced and an linear matrix inequality (LMI) based approach is provided to make its design possible. The authors also show that simultaneous states and sensor fault estimation can be solved by a conversion scheme through a positive filtering process of the output. This allows to convert the sensor fault as an unknown input and employ the PUIO design. Finally, the problem of robust fault detection for positive systems is formulated and solved by combining the capability of UIO with proportional–integral (PI) observer. This integrated observer (PIUIO) decouples the unknown input disturbance through its UIO part while allowing PI part to estimate the fault. Several examples are constructed to support the theoretical results.

This study considers the parameter identification problem of a pseudo-linear autoregressive moving average system (i.e. linear-in-parameter autoregressive output-error ARMA systems), whose disturbance is an ARMA process. By means of the filtering technique, a filtering-based gradient iterative (F-GI) algorithm and a filtering-based least squares iterative (LSI) algorithms are presented for enhancing the estimation accuracy. Furthermore, a filtering-based decomposition LSI algorithm is derived for improving the computational efficiency. The key is to use the hierarchical identification principle, to apply the data filtering technique for identification, and to replace the unknown terms in the information vectors with their estimates. Compared with the F-GI algorithm, the filtering-based LSI algorithm and the filtering-based decomposition LSI algorithm have faster convergence rates. The simulation results indicate that the proposed algorithms are effective.

This study is concerned with the problem of achieving exponential convergence and Lyapunov stability with respect to time-varying time-delay for switched systems with quantised measurements. Here the controller under the influence of time-delay is designed by quantised sampling signals to stabilise the continuous-time switched systems. The difficulty of this study lies in how to design a quantisation rule ensuring the unsaturation of quantiser under the coupling effect of switching uncertainty and time-delay uncertainty. To this aim, a virtual system is introduced to update observer states and facilitate stability analysis. Furthermore, by restraining the upper bound of the sampling interval, all the situations discussed are divided into three categories, under which, the authors study the distinguishments of system states and observer states at delay time to acquire quantisation rule and quantiser properties at the sampling time. Within this setup, the upper bound of the system states and thus the stability of the closed-loop systems are obtained. The authors at last give an illustrative example to show the usefulness of the proposed framework for stability analysis of some classes of switched systems.

The main goal of this study is to introduce a new polynomial fuzzy model-based structure for a class of marine systems with non-linear and polynomial dynamics. The suggested technique relies on a polynomial Takagi–Sugeno (T–S) fuzzy modelling, a polynomial dynamic parallel distributed compensation and a sum-of-squares (SOS) decomposition. The new proposed approach is a generalisation of the standard T–S fuzzy models and linear matrix inequality which indicated its effectiveness in decreasing the tracking time and increasing the efficiency of the robust tracking control problem for an underactuated surface vessel (USV). Additionally, in order to overcome the USV control challenges, including the USV un-modelled dynamics, complex nonlinear dynamics, external disturbances and parameter uncertainties, the polynomial fuzzy model representation is adopted. Moreover, the USV-based control structure is formulated in terms of SOS conditions. Unlike the conventional approaches, the proposed approach can be easily implemented in the real-time and applied to a reasonably wide class of non-linear systems. Finally, the extensive studies and hardware-in-the-loop simulations are presented, which prove the effectiveness of the novel proposed method.

This study presents a rigorous mathematical framework for the global asymptotic synchronisation of memristive neural networks comprising multiple time-varying delays (MTVDs) through sampled-data control. First, a novel Lyapunov–Krasovskii functional (LKF) is constructed with some new terms, which can fully capture the information on lower and upper bounds of each MTVD. Second, extended convex combination method is presented, which can successfully solve the combination of MTVDs. Third, based on the LKF and employing the extended convex combination technique, synchronisation criterion is derived. In comparison with existing results, the established criterion is more appropriate since it fully utilises the lower and upper bounds of each MTVD. Finally, simulation results are presented to validate the theoretical models.

This study investigates the stochastic suppression and stabilisation of non-linear hybrid delay systems with general one-sided polynomial growth condition and decay rate. Given an unstable non-linear hybrid delay system with general one-sided polynomial growth condition, the authors introduce two independent Brownian noise and perturb this system into stochastic hybrid delay system . It is shown that the non-linear diffusion term may suppress the potential explosion of hybrid delay system. Under a stronger condition, another linear diffusion term will make the perturbed stochastic hybrid delay system is almost surely stable with general decay rate.

To cope with load disturbance often encountered when performing identification tests on non-linear systems with input delay in industrial applications, a bias-eliminated Hammerstein-type output error (OE) model identification method is proposed in this study. By taking into account the load disturbance response as a time-varying parameter for estimation, two recursive least-squares (RLS) identification algorithms is established to estimate the Hammerstein-type model parameters and the time-varying disturbance response. A one-dimensional searching approach is adopted to determine the integer-type delay parameter by minimising the fitting error of output response. Moreover, an auxiliary OE model is constructed to ensure consistent estimation under stochastic noise. In addition, two adaptive forgetting factors are introduced into the proposed RLS algorithms to enhance the estimation convergence on the model parameters and the disturbance response. Asymptotic properties of parameter estimation are analysed along with a proof, in particular for unbiased estimation against a constant disturbance. Two illustrative examples are given to demonstrate the effectiveness of the proposed identification method.

This study investigates the stabilisation problem for a class of discrete-time two-dimensional (2D) switched systems. Here the 2D systems mean that the state evolves following two independent directions, which are usually represented as horizontal states and vertical states. The considered systems are represented by Roesser model and incorporate both stable and unstable modes. Based on a switching signal regulation approach, which restricted the switching number as well as the running time ratio between the unstable and stable modes, the exponential stability condition is established for the 2D switched systems with synchronous switching. Besides, solving the proposed stabilisation results in linear matrix inequality form, the stabilising controller gains can be obtained. Moreover, considering the time delay in the controllers when the switching occurs, the proposed results are extended to the stabilisation problem for the 2D switched systems under asynchronous switching. A numerical example further demonstrates the validity of the developed results.

This study investigates the asymptotic swarm stabilisation of fractional-order swarm systems in the presence of two different kinds of model uncertainties and external disturbances while the upper bound of the uncertainties is a linear function of pseudo-states norms with unknown coefficients. To this end, first a fractional-integral sliding manifold is constructed and then an adaptive-robust sliding mode controller is designed to guarantee the asymptotic swarm stability in a fractional-order linear time-invariant swarm system. The stability analysis of the proposed control system is done based on the Lyapunov stability theorem. Using the proposed controller, the coefficients of the upper bound function of the uncertainties are estimated by adaptive laws. Simulation results are provided to show the effectiveness of the proposed controller.

In this study, the author investigates controllability of discrete-time bilinear systems by using invariant sets. An invariant set defined in this study is a set on which the system is invariant, namely for any initial state that belongs to the set, the system cannot be steered away from this set. If a system is controllable, then it has no invariant set in its state space other than the state space itself. Invariant sets are thus closely related to controllability. By studying the invariant sets of discrete-time bilinear systems, the author first presents a necessary and sufficient condition for controllability of the systems in dimension two, which covers a classical result under the same condition. Then the author considers the high-dimensional systems and improve the recent results on controllability by relaxing a condition concerning invariant sets, where more general controllability criteria are derived. Finally, examples are given to illustrate the obtained results.

This study addresses mean-square stability of networked control system with state quantisation process and suffers random packet losses. A logarithmic quantiser is applied in order to decrease the possibility of the packet loss phenomenon. Also, the quantisation process is designed as event driven so that the quantisation is only performed when necessary. It is shown that stability in mean-square sense is achieved if a series of LMI conditions are valid. Simulations are finally performed to show the effectiveness of the results of the theoretical analysis.

This brief study investigates the synchronisation of undirected coupled harmonic oscillators by using a sampled-data control strategy. In the absence of measured velocity information, each of the networked oscillators can only obtain the measurements of the position states relative to its neighbours at the sampling moments. A distributed protocol based on the sampled relative position measurements at a series of time instants is proposed for the coupled harmonic oscillators. Necessary and sufficient conditions for achieving synchronisation are analytically established in virtue of the graph theory, matrix analysis theory and Schur stability theory of cubic polynomials. Theoretical results indicate that the explicit range that contains all the desirable sampling periods is uniquely determined by the largest eigenvalue of the Laplacian matrix associated with the network graph and the position gain of the harmonic oscillators. An effective simple iterative method is then developed to calculate the range in which the desirable sampling periods fall. Finally, numerical simulations are performed to illustrate the correctness of the theoretical results and effectiveness of the proposed protocol.

This study investigates an asynchronous switching state feedback control problem for discrete impulsive switched delay systems with average dwell time. A novel time-varying multi-Lyapunov–Krasovskii functional approach is adopted to establish the control synthesis conditions that guarantee the exponential stability of the closed-loop systems. The relation between the upper bound of asynchronous switching delay and the stability conditions is also explicitly given, and the overall conservativeness of the stability results is improved over the existing results. A numerical example is provided to illustrate the effectiveness of our theoretical results, where the comparison with the existing results demonstrates significant improvement using the proposed method.

Both state-based and observer-based output feedback event-triggered controls for continuous-time switched linear systems are studied. An improved event-triggered sampling mechanism is adopted in feedback control, under which Zeno behaviour can be easily excluded in sampling process. Meanwhile, it is shown that the closed-loop switched system is stable in the sense of global uniform boundedness satisfying an average dwell time condition. A numerical example is finally given to verify the developed results.

A robust continuous control for tracking a step reference signal without any overshoot and arbitrarily small rise time is proposed for a linear multivariable system. Integral sliding mode technique with the super-twisting sliding mode is used to make the control robust against the matched disturbances with bounded derivatives. Moore's eigenstructure assignment is used to compute nominal control part of the integral sliding mode technique which makes the system output to track the step reference with arbitrarily small rise time and without any overshoot under some mild assumptions. The efficacy of the proposed control is validated using simulation results on benchmark quadruple tank model.

In this study, a delay-dependent memory state-feedback controller for linear systems with input time-delay in the presence of external disturbance has been investigated. At first, a new formula is introduced to obtain the prediction vector from the system dynamics and then by using this formula, the effect of input time-delay on the original delayed system is reduced. To guarantee the prescribed disturbance attenuation level of the closed-loop system, Lyapunov theory and linear matrix inequality (LMI) approaches are used. In the case of feasibility, sufficient LMI conditions provide the stabilising gain of the predictor-based controller. To illustrate the effectiveness of the proposed method, it is applied to a quarter-car model of an active suspension system considering the actuator time-delay.