This study is concerned with the output-based resilient event-triggered control for networked control systems (NCSs) subject to denial of service (DoS) attacks, where ‘resilient’ is interpreted as that the NCSs can tolerate a larger time delay with a certain degree of performance degradation when there are DoS attacks. Otherwise, the NCSs run with performance. In order to characterise DoS attacks, an additional positive term which implies the effects of DoS attacks is imposed on the pre-designed triggering condition. By considering the fact that only partial output measurements can be obtained, the output-based security performance analysis as well as an output feedback controller design under the proposed event-triggered strategy is conducted with Lyapunov–Krasovskii method and linear matrix inequalities technique. At last, the simulation results show that the designed controller is resilient to DoS attacks with less dependent on the transmission packets while sacrificing some control performance.

In this study, the sliding mode control problem is investigated for a class of discrete-time systems with fading measurements. The channel fading is modelled as the Rice fading model to characterise the fading phenomenon via wireless sensor network. An integral-like sliding surface involving fading parameters is first constructed. And then, a sliding mode controller is designed by using fading measurements and channel parameters. It is shown that the state trajectories can be driven to the neighbourhood around the specified sliding surface and the stochastic stability with prescribed performance can be attained. Finally, a numerical example is provided.

This study presents two recursive parameter and state estimation algorithms for state-space systems, considering the process noises and observation noises. Based on the Kalman filter and hierarchical identification principle, the authors propose a Kalman filtering-based hierarchical generalised stochastic gradient algorithm to jointly estimate the parameters and states of observability canonical state-space systems. With the aim of achieving more accurate parameter estimation, they present a Kalman filtering-based hierarchical multi-innovation generalised stochastic gradient algorithm by utilising a range of available data and more information at each recursion. Finally, the effectiveness of the proposed algorithms is validated through a numerical simulation example.

The stability of two one-link flexible arms for grasping and orientation control of an object is studied. Flexible arms are modelled by Euler–Bernoulli beam model and the overall system is represented by a hybrid partial differential equation (PDE)–ordinary differential equation (ODE) model. The authors' primary concern is the stability analysis of this hybrid PDE–ODE model. In particular, they use the frequency domain method and prove the exponential stability of this system under their previously proposed boundary controller. In addition, they discuss the robustness of the closed-loop system with respect to the several disturbances including disturbances distributed over the arms and disturbances acting at boundaries. Finally, simulation results are presented to investigate the theoretical results.

A study on the simultaneous state and fault estimation for non-linear discrete-time stochastic systems subjected to unknown disturbances is presented. The augmented system approach, system reformation using the state-dependent coefficient (SDC) factorisation, and unknown input filtering method are integrated to simultaneously estimate the state of the system and actuator and/or sensor faults. To achieve this aim, the non-linear system with faults and unknown disturbances is first transformed into an equivalent augmented system by using delayed measurements and the SDC factorisation. Next, within the SDC factorised linear-like augmented system and inspired by the robust two-stage Kalman filter, a novel multi-step estimator named as the robust simultaneous state and fault estimator is proposed to yield a robust state and fault estimation with a multi-step delay. Moreover, a novel real-time state estimator is designed based on the proposed hybrid fault reconstruction model in order to address the inherent time-delay problem. A comparison of the performance of the proposed filters with those of existing methods from the literature is demonstrated using a non-linear two-link manipulator system with friction forces acting simultaneously at each joint.

This study deals with the problem of state bounding for positive singular discrete-time systems with time-varying delay and bounded disturbances. First, the authors derive some new conditions for the existence of componentwise bounds of the state vector of the systems without disturbances. Then, in the case of systems with bounded disturbances, they obtain a sufficient condition for the existence of componentwise ultimate bounds. Since the conditions are given in terms of the spectral radius of the system matrices, they can check them easily and compute directly the smallest componentwise ultimate bound. In addition, the problem of state bounding for positive time-varying singular systems is also investigated in this study. Finally, numerical examples are provided to illustrate the effectiveness and advantages of their results.

This study investigates the discretisation effects of the zero-order holder (ZOH) on DC–DC buck converters under the direct ON/OFF control of sliding mode (SM), and the two core issues of stability and periodicity for the discrete system are focused on. The optimal parameter for the SM controller is first given on the basis of stability and response speed in the continuous-time domain, following its ZOH discretisation. Restricted by the existence condition of discrete SM, the guaranteed stability is investigated and compared with that of the continuous system in the phase plane, proving that the sampling time of ZOH affects its stability region. Meanwhile, the periodic dynamics, including the system state and the symbolic sequence of switching control law, is further studied via analysing the steady limit cycle of state in phase plane; and the existence condition of multi-periodicity is also deduced. Innovatively this study establishes the influence relationship of the periodic dynamics with the performances of the steady-state error of output voltage and switching frequency. Simulation and experiment results are presented to validate the theoretical and practical value of the proposed research.

This study investigates the consensus problem for general linear multi-agent systems with unknown external disturbances. Both the leaderless and the leader–follower consensus problems are considered. By using the absolute output information of each agent, the local states and external disturbances of each agent can be estimated by an extended state observer. Then, by using the relative estimated states and disturbance estimation, the continuous controller can be designed in a fully distributed fashion, which ensures that the consensus error of general linear multi-agent systems converges to zero eventually with the complete disturbance rejection. Moreover, when the absolute output information of each agent is not available, it is shown that the consensus problem can be solved by using only relative output information of neighbouring agents but only the part of the disturbances that affect the common trajectories will be rejected. Finally, simulation examples are given to demonstrate the effectiveness of the proposed protocols. Compared with the previous related works, fully distributed consensus disturbance rejection protocols are developed based on node-based adaptive design and edge-based adaptive design, which require neither global information of the communication graph nor the prior knowledge of the disturbance model.

When dealing with fractional order systems, perturbations in differentiation orders arise frequently due to issues with floating point arithmetics, or due to imprecisions of various order estimation algorithms. This study establishes new results regarding stability/instability of fractional systems with perturbed differentiation orders, knowing the related properties of their unperturbed counterparts. First of all, starting from a point in the space of differentiation orders, sufficient stability/instability conditions of all systems with differentiation orders varying along a line segment with a prescribed direction are established. Then, a continuation procedure is developed allowing computation of the maximum perturbation (along some given direction) which guarantees that the number of zeros in the closed right-half plane of the characteristic function remain unchanged. Finally, sufficient conditions are established guaranteeing stability/instability of all systems having differentiation orders within a domain. The established results allow concluding on the stability of incommensurate fractional transfer functions. They are illustrated by a number of examples, including an experimental one.

The concept of wave-based control (WBC) has been around for about two decades. It is designed primarily for controlling the end-point motions of one-dimensional lumped mass flexible chains. The systems under consideration are, therefore, severely underactuated. Typical control objective for such systems is a point-to-point motion without unwanted residual oscillations. These oscillations, however, become troublesome especially for the lightly damped cases. The only way to attenuate them is to ‘shape’ the control input. For this WBC concept considers a set of hypothetical (forward and backward) motion waves, which combine to form the actual motions. This document critically investigates wonderful properties of WBC which are claimed over the years and presents a completely new mathematical and rigorous treatment of the method. We rectify several misconceptions, especially on the level of a priori knowledge which is required on the system dynamics. Second, the authors present a novel step-by-step procedure to design a WBC law which ultimately leads to a number of opportunities for future explorations. Finally, the necessary and sufficient conditions in system parameter space for the stability of WBC are rigorously elucidated for the first time in the literature to the best of our knowledge.

This study puts forward a hybrid backstepping-boundary iterative learning control (B-BILC) to tackle vibration problem for an Euler–Bernoulli beam system subjected to an unknown external disturbance. Based on Lyapunov's synthesis method, a backstepping term and an iterative term are designed to reduce the vibration and attenuate the effects of the unknown boundary disturbance under the consideration of model property. With the proposed B-BILC scheme, the uniform boundedness of the closed-loop system state and the convergence of the system output are proved via Lyapunov theory. Simulations are provided to show the effectiveness of the proposed scheme and demonstrate that B-BILC yields better performance compared to the Proportion–Derivative-BILC (PD-BILC).

This study investigates the optimal event-triggered sliding mode control (SMC) problem for discrete-time non-linear systems with actuator saturation. A differential-type sliding surface function outperforming the traditional linear version is constructed for the considered system. In order to save the communication resource, a state-dependent event-triggered scheme is designed to determine whether the current state should be transmitted or not automatically. An optimal version is designed to further decrease the computational cost. A Jacobian matrix is introduced to handle the non-linear function error resulting from the implementation of the event-triggered scheme. Combining the above techniques and the Lyapunov stable theory, time-dependent sufficient conditions are developed to guarantee that the sliding mode dynamics are stable and satisfy the desired disturbance attenuation performance. Moreover, time-independent sufficient criteria are presented to obtain the desired performance of the sliding mode dynamics by employing some inequalities. Based on the derived time-independent conditions, sufficient conditions are provided to compute the gain for the sliding surface. A sliding mode controller with adaptive law is designed to guarantee that the trajectories of the saturated control system can be driven onto the predefined sliding manifold. Finally, simulation results are given to illustrate the effectiveness of the proposed control strategy.

This study investigates the robust recursive identification problem for Wiener non-linear systems with non-stationary disturbance and measurement white Gaussian noise. Non-stationary disturbances cannot be eliminated by conventional statistical strategy. To overcome such problem, the non-stationary disturbance signal is modelled as a dynamic parameter with a small change rate which is to be estimated step. Utilising the forgetting factor (FF) and the auxiliary model strategy, a discrete-time recursive least-squares algorithm is designed by augmenting the parameter vector and the information vector. To facilitate the steady asymptotic convergence of the time-invariant system parameters and the dynamic tracking ability of the disturbance, two adaptive FFs are proposed to construct a new matrix FF scheme that is used to update the covariance matrix. Moreover, several asymptotic convergence conditions are also derived based on the stochastic statistical theory under persistent excitation condition. Finally, one illustrative example with non-stationary disturbance is employed to show the effectiveness and advantages of the proposed algorithms.

This study presents a multiobjective optimisation applied to the gear shifting fuzzy control of a vehicle equipped with an automated manual transmission (AMT), aiming to improve acceleration performance and reduce engine fuel consumption and emissions. An Adaptive-Weight Genetic Algorithm was employed to find optimum fuzzy membership functions, according to the input and output ranges, and also optimum control rules with their respective weights. The vehicle behaviour is represented by longitudinal dynamics simulations developed in Simulink/Matlab^™ interface, associated with the ADVISOR^™ fuel converter block, that provides the engine emissions and fuel consumption. These simulations were based on the FTP-75 emissions test procedure, that considers cold and hot phases of the driving cycle evaluating the engine transient operation as a function of the catalyst efficiency during the warm-up period. The optimum fuzzy control with the best trade-off among the optimisation criteria presented 19.72% fuel saving associated with 12.90% hydrocarbon, 29.20% carbon monoxide and 17.02% nitrogen oxides emissions reduction and an acceleration performance improvement when compared to a standard gear shifting procedure for a manual controlled gearbox. Moreover, the optimised fuzzy gear shifting control, improves the relationship between fuel consumption and emissions significantly, when compared to another optimum AMT control based on speed limits only.

In this paper, the problem of cooperative control of robotic sensor networks (RSNs) for monitoring dynamic pollutant plumes in two-dimensional (2D) space is studied. The pollutant plume propagation dynamics is governed by a 2D advection-diffusion partial differential equation (PDE), and the plume front is modelled by a level set with a pre-specified threshold value. Distributed consensus Luenberger-type PDE observers are first constructed using local concentration measurements from the RSNs for unanimous estimate of the dynamic concentration field over the entire spatial domain. With the aid of the distributed consensus observers, a leaderless cooperative control scheme is then developed for the RSNs to monitor the dynamic plume front expansion. It is proved using the Lyapunov stability method and set stability concept that the proposed cooperative control scheme guarantees tracking of the dynamic plume front expansion and coverage of the plume front. Extensive numerical simulation results demonstrate the effectiveness and merit of the proposed cooperative control scheme.

In this study, a new observer for a class of non-linear single input/single output systems is proposed. This observer is based on a modulating function with time/output dependent coordinates transformation which transforms the original system into a like-type observer canonical form. In the new coordinates, the initial conditions are annihilated. This property permits to construct a fast convergent deadbeat observer activated after an time delay chosen in order to avoid the singularity of the transformation at the initial time . The finite-time convergence of the observer is established, i.e. it is shown that the estimation error is bounded in finite time. The proposed observer is used in an output feedback controller design. Using the already established results on the output feedback stabilisation of non-linear input-affine systems, the separation principle is addressed here and the authors show that output feedback controller guarantees under certain conditions the stability of the closed-loop system. Two numerical examples are given to illustrate the effectiveness of the proposed observer-based output feedback controller.

In this study a decentralised event-based scheme is proposed to synchronise the spacecraft's attitudes during their convergence toward the desired attitude, in the presence of disturbance. To achieve this goal, decentralised integral-based triggering mechanisms are introduced which not only reduce the data transmission among the spacecraft efficiently but also guarantee a minimum inter-event time for each triggering module. Moreover, a design procedure is given to find the control gains and triggering conditions parameters properly. Finally, simulation results are provided to show the effectiveness of the system.

This study first addresses an extended asynchronous switching control issue resulting from switching delay and false alarm for a family of switched positive systems. Based on a new set of switching signals superior to the average dwell time switching, the state-feedback controller is designed to guarantee the positivity and global asymptotic stability for the closed-loop system. In addition, the corresponding sufficient condition formulated in terms of linear programming problem is derived. Different from the previous works, the authors' established results further relax the restriction that all subsystems must be stabilisable in the normal-running period with matched controller, and allow the increase of the Lyapunov function in the switching delay period, false alarm period, normal-running period with matched controller and all switching instants. Finally, a numerical example with practical considerations is used to show the effectiveness and potential of the proposed theories.

Parameter convergence is desirable for adaptive control as it enhances the overall stability and robustness properties of the closed-loop system. In existing online historical data (OHD)-driven parameter estimation schemes, all OHD are exploited to update parameter estimates such that exponential parameter convergence is ensured under a condition of sufficient excitation which is strictly weaker than the traditional persistent excitation (PE) condition. However, the exploitation of all OHD not only results in possible unbounded adaptation but also loses the flexibility of handling slow time-varying uncertainties. In this brief, a novel OHD-driven parameter estimation scheme that exploits only partial OHD is presented to improve parameter convergence and is incorporated with direct adaptive control to construct a composite learning control strategy. The proposed approach guarantees exponential parameter convergence under a condition of interval excitation which is also strictly weaker than the PE condition while eliminating the drawbacks of existing OHD-driven parameter estimation schemes. Numerical results have verified the effectiveness and superiority of the proposed approach.

This study proposes an interval estimation method of actuator fault for linear discrete-time system. An augmented descriptor system, which is equivalent to the original system, is formulated by letting the actuator fault term be an auxiliary state. Then, an fault estimation observer is constructed to attenuate the effect of unknown but bounded disturbances and measurement noise. By using interval analysis technique, the interval estimation of actuator fault can be obtained. Finally, a DC servo-motor example is given to show the effectiveness and superiority of the proposed method.