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In recent works, exact and nonstandard finite difference schemes for scalar first order linear delay differential equations have been proposed. The aim of the present work is to extend these previous results to systems of coupled delay differential equations X ′ ( t ) = A X ( t ) + B X ( t − τ ) , where X is a vector, and A and B are commuting real matrices, in general not simultaneously diagonalizable. Based on a constructive expression for the exact solution of the vector equation, an exact scheme is obtained, and different nonstandard numerical schemes of increasing order are proposed. Dynamic consistency properties of the new nonstandard schemes are illustrated with numerical examples, and proved for a class of methods.

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.

In this study, the problem of finite‐time feedback stabilisation for switched linear input‐delay systems with saturating actuators is addressed by virtue of the comparison‐function‐like method. Finite‐time state feedback stabilisation is discussed and controllers are designed to make the closed‐loop systems finite‐time stable. Moreover, for the case that the states are unmeasured, observers are constructed to estimate the unavailable states and the observer–controller compensator strategy is proposed. Based on the results proposed in this study, information of transient performance of the controlled switched systems can be obtained and bounds of system trajectory are estimated. An example is employed to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The additional threshold of a mixed event‐triggering mechanism (ETM) makes it impossible to guarantee the requirement of asymptotic stability. As a consequence, it is necessary to investigate input‐to‐state practically stable (ISpS) which is a mild stability property. In this study, the authors firstly model the closed‐loop event‐triggered control system as a delayed linear parameter‐varying (LPV) systems with a mixed ETM and parameter uncertainty. Then, a co‐design condition in a sense of ISpS of controller gain and trigger parameters for the delayed LPV systems is obtained by employing the parameter‐dependent Lyapunov–Krasovskii functionals and congruent transformation method. Moreover, based on the obtained co‐design condition in a sense of ISpS, an optimisation algorithm for the tradeoffs between resource utilisation and robustness of the closed‐loop system is further proposed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The leader‐following guaranteed‐performance consensus problems for second‐order multi‐agent systems with and without communication time delays are investigated, where a guaranteed performance function is proposed to consider the consensus regulation performance. For the case without the time delay, the coupling gain and pinning strength are carefully considered. When the time delays exist in the communication, we find that the inequality (Seuret and Gouaisbaut) cannot be used to investigate the consensus problems proposed in the study since the obtained conditions cannot be satisfied. Therefore, Jensen's inequality and Newton–Leibniz formula, which can solve this issue well, are introduced. By using the state space decomposition approach, linear matrix inequality and Lyapunov stability theory, some sufficient conditions are derived for achieving the guaranteed performance consensus. Moreover, the upper bound of the performance function is determined. Finally, two examples are shown to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

The main objective of this study is to increase the power system oscillation damping in the presence of wind farms using flexible alternating current transmission systems (FACTS) devices and predictive control. The desired design is conducted to coordinate static synchronous compensator–static synchronous series compensator and rotor side converter in doubly‐fed induction generator (DFIG). This design is done to compensate for the DFIG reactive power and increase power system oscillation damping in the presence of uncertainties in the wind turbine. The method proposed for coordinated design was based on the network predictive control (NPC) so that it could improve damping, and compensate for the time delays in sending wide area signals. In fact, NPC is based on generalised predictive control (GPC) which has the ability to compensate for time delays using model identification method. Using MATLAB software, the simulation results were conducted on a 16‐machine and 69‐bus power system under different scenarios; and the ability of NPC is well proven compared with GPC and the classic method of wide area controller. [ABSTRACT FROM AUTHOR]

This paper addresses the design of conventional sliding mode and super-twisting controls for the uncertain system with state delay to achieve the improved transient response. To ensure the stable sliding motion two approaches are proposed. In the first approach, LMI conditions using Lyapunov-Krasovskii functional are derived to guarantee the stability of the sliding motion. In the second approach, we propose the sliding mode control based on a nonlinear switching functional, with which the sliding motion is governed by delay-free dynamics. Effectiveness of the proposed design approaches are shown through numerical simulation of reheat power system. [ABSTRACT FROM AUTHOR]

We develop a predictor-based adaptive cruise control design with integral action (based on a nominal constant time-headway policy) for the compensation of large actuator and sensor delays in vehicular systems utilizing measurements of the relative spacing as well as of the speed and the short-term history of the desired acceleration of the ego vehicle. By employing an input–output approach, we show that the predictor-based adaptive cruise control law with integral action guarantees all of the four typical performance specifications of adaptive cruise control designs, namely, 1) stability, 2) zero steady-state spacing error, 3) string stability, and 4) non-negative impulse response, despite the large input delay. The effectiveness of the developed control design is shown in simulation considering various performance metrics. [ABSTRACT FROM AUTHOR]

In this study the authors are concerned with the effect of noise on the solutions of a class of non‐linear delay systems. The systems under investigation are non‐linear without linear growth condition requirement, which makes the analysis difficult to ensure the existence and uniqueness of solutions. The authors first introduce a set of new non‐linear growth conditions with delays, and then provide the existence and uniqueness of solutions as well as some properties of the solutions. The new condition only requires the knowledge of the coefficient of the highest term, which is much easier to check in practice than the traditional conditions. Finally, an example is given to show the effectiveness and potential of theoretic results obtained. [ABSTRACT FROM AUTHOR]

This study presents a new approach to decompose singular time‐delay systems (STDSs) in a way that they can be transformable to normal time‐delay systems (TDSs) with a lower order. Necessary and sufficient conditions are provided to determine which STDSs can be transformed to TDSs. Also, a stabilisation method is provided to stabilise the system, while the time delay in the system can belong to several distinct intervals or even everywhere. The proposed method is non‐fragile towards controller parameters. This method also reveals one of the many applicable situations of the proposed decomposition. The effectiveness of the proposed method is illustrated through some examples. [ABSTRACT FROM AUTHOR]

Cooperative teleoperation combines two traditional areas of robotics, that is, teleoperation and collaborative manipulation. Cooperative telerobotic systems consist of multiple pairs of master and slave robotic manipulators operating in a shared environment. The most common control frameworks for nonlinear systems, that is, Proportional Derivative (PD) controllers, possess considerable deficiency in contact motion. In this paper, a novel control scheme is proposed for a nonlinear bilateral cooperative teleoperation system with time delay. In addition to position and velocity signals, force signals are employed in the control strategy. This modification significantly enhances the poor transparency when the slave robots are in collision with the environment. To cope with external forces measurement, a modified force estimation algorithm is proposed to estimate human and environment forces. The closed loop stability of the nonlinear cooperative teleoperation system with the proposed control scheme is investigated using the Lyapunov theory. The main achievement of this research is the stability of the closed loop cooperative teleoperation system in the presence of estimated operator and environmental forces. In addition, it is theoretically and experimentally proved that force reflection occurs and transparency is improved at the same time. Experimental results demonstrate the efficiency of the presented control strategy in free motion as well as when the slave robots are in contact with the environment. [ABSTRACT FROM AUTHOR]

Most of the existing controller tuning methods are based on accurate system model and sensitive to some inevitable uncertainties and unmeasurable disturbance. Aiming at this problem, a thorough robustness analysis on a typical kind of fractional‐order (FO) delay system has been made in this study. A kind of robust FO proportional and derivative controller is proposed based on phase and gain margins. The tuning methods are demonstrated under different circumstances, namely there is gain variation, time constant variation, order variation or even multiple parameters variations in system transfer function. Simulation results show that the closed‐loop control system with the proposed controller can achieve both robustness and satisfactory dynamic performance, and outperform the conventional proportional–integral–derivative controller in all cases. [ABSTRACT FROM AUTHOR]

To suppress disturbances in uncertain tracking control systems with an input‐delay, a disturbance predictor based on a high‐order generalised extended‐state observer is devised in this study. A smooth enough approximation of the disturbance is first made, then the approximation ahead of delay‐time is predicted. The construction of the disturbance predictor is based on a truncated Taylor polynomial. To facilitate the analysis and design of the closed‐loop control system, control gains for the nominal plant are designed in advance. Then the stability analysis for the closed‐loop system is conducted, which yields a robust stability condition. As the disturbance predictor takes into consideration the influence of the input‐delay, the presented method enables the enhancement of the disturbance‐rejection performance. Finally, comparisons of the developed method with major methods in this field are conducted to validate the developed method and to demonstrate its advantages. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Control of air–fuel ratio (AFR) plays a key role in the minimisation of the carbon dioxide and harmful pollutant emissions and maximisation of fuel economy. An inherent time‐varying delay existing in lean‐burn spark ignition (SI) engines is a major challenge for the AFR control. Herein an unstable internal dynamics with a parameter dependent system caused by time delay is established to represent a dominating feature of AFR. The proposed control scheme, LPV‐based fuzzy control technique, combines the features of LPV and fuzzy control to deal with the unstable internal dynamics of an AFR system with external disturbances and a high level of uncertainty in system parameters. Based on the desired error dynamics, an LPV dynamic error consisting of the unstable state and the AFR tracking error is determined. Subsequently, the proposed fuzzy control algorithm through a look‐up table is used to stabilise the LPV dynamic error. Then, the tracking error moves along the desired error dynamics towards zero. The system stability is assured via Lyapunov stability criteria. Finally, the simulation results demonstrate the effectiveness and robustness of the proposed control scheme under different operating conditions. Also, compared with the baseline controller, i.e. proportional–integral controller with Smith predictor, demonstrates its superiority. [ABSTRACT FROM AUTHOR]

In this report, based on the Caputo definition of fractional derivatives we will obtain the Euler-Lagrange equations for two classes of the generalization of delay fractional variational problems depending on indefinite integrals (DFVPIs). On the other hand, we consider the problems with isoperimetric and holonomic constraints. The direct Rayleigh-Ritz method is applied for solving DFVPIs for the first time. In the present method, the Legendre multiwavelet functions with support of Rayleigh-Ritz have been used to give the best approximate solution for the problem. [ABSTRACT FROM AUTHOR]

We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily First-In/First-Out (FIFO). This means that the input signals can be reordered. The feedback law uses the current delay value in the prediction. It does not exactly compensate for the delay in the closed-loop dynamics but does not require to predict future delay values, contrary to the standard prediction technique. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic stabilization of the system state, that is, robust delay compensation, providing that the average ℒ 2 -norm of the delay time-derivative over some time-window is sufficiently small and that the average time between two discontinuities (average dwell time) is sufficiently large. [ABSTRACT FROM AUTHOR]

Self‐excited milling vibrations represent an important problem in the manufacturing industry. This study presents an out‐of‐process analysis based on the Lyapunov–Krasovskii approach which provides operational guidelines for the proper selection of the cutting parameters to guarantee a stable vibration‐free process. The proposed approach considers a time‐delay two degree of freedom model and takes advantage of some useful tools of the control theory developed for time‐delay systems such as the descriptor method and the Bessel–Legendre inequalities. [ABSTRACT FROM AUTHOR]

In this study, a delay‐dependent memory state‐feedback H∞ 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. [ABSTRACT FROM AUTHOR]

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 x˙(t)=f(x(t),x(t−τ(t)),r(t),t) with general one‐sided polynomial growth condition, the authors introduce two independent Brownian noise and perturb this system into stochastic hybrid delay system dx(t)=f(x(t),x(t−τ(t)),r(t),t)dt+h(x(t),r(t),t)dB1(t)+g(x(t),r(t),t)dB2(t). It is shown that the non‐linear diffusion term g(x(t),r(t),t) may suppress the potential explosion of hybrid delay system. Under a stronger condition, another linear diffusion term h(x(t),r(t),t) will make the perturbed stochastic hybrid delay system is almost surely stable with general decay rate. [ABSTRACT FROM AUTHOR]

A robust fault‐tolerant controller design for a class of two‐dimensional discrete‐time systems with mixed actuator faults, stochastic uncertainties and non‐linear perturbation in delayed states is proposed in this study. The authors' aim is to investigate the stochastic stabilisation issue with an adequate level of an extended dissipative performance index where the considered system contains failures occurring among the pre‐specified subset of actuators with admissible uncertainties. More precisely, the considered stochastic system uncertainties are assumed to follow mutually uncorrelated Bernoulli distributed sequences along with their probability rules. Furthermore, a practical actuator fault model consisting of both linear and non‐linear fault terms is proposed. By utilising some inequalities and extended dissipativity theory, the authors develop a robust stochastic stability criterion of the addressed system in the linear matrix inequality framework. Lastly, a simulation example is provided to verify the correctness and significance of the designed fault‐tolerant control strategy. [ABSTRACT FROM AUTHOR]

The class of strict-feedback systems enjoys special properties that make it similar to linear systems. This paper proves that such a class is equivalent, under a change of coordinates, to the wider class of feedback linearisable systems with multiplicative input, when the multiplicative terms are functions of the measured variables only. We apply this result to the control problem of feedback linearisable nonlinear MIMO systems with input and/or output delays. In this way, we provide sufficient conditions under which a separation result holds for output feedback control and moreover a predictor-based controller exists. When these conditions are satisfied, we obtain that the existence of stabilising controllers for arbitrarily large delays in the input and/or the output can be proved for a wider class of systems than previously known. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of state/fault estimation and active fault-tolerant control (AFTC) design for time-delay descriptor fuzzy systems subject to external disturbances and actuator faults. Using Takagi-Sugeno fuzzy models, an adaptive fuzzy observer is proposed to achieve system state and actuator fault estimation simultaneously. According to Lyapunov functional method, design and analysis conditions of the resulting closed-loop delayed descriptor system are formulated in terms of linear matrices inequalities (LMIs). Observer and controller gains are computed by solving a set of LMIs in only one step and then used to both estimate the unmeasured states and actuator faults in AFTC context. Numerical examples are provided to show the merit and the conservativeness of the proposed approach in comparison with the existing methods by considering various types of actuator faults. [ABSTRACT FROM AUTHOR]

A new closed-form equation for stability analysis of a haptic device is presented using frequency response function analysis via continuous time model of the system. Desired impedance of the virtual environment (VE), time delay, and zero-order hold are considered, beside the continuous model of the haptic device. The developed equations provide critical virtual damping and stiffness of the VE versus the mass and viscous friction of the haptic device, sampling time, and time delay. Unlike prior work in this field, the developed equations are valid without any limitation on the values of the time delay and virtual damping. It is shown that they cover available well-known equations in literature for special cases of small values of virtual damping and time delay. The resulting equations are of practical usefulness in many fields, such as surgery simulation for avoiding instability during virtual tool interaction with high-stiffness VEs. The proposed analytical derivation can also be used for studying the effect of operator, sensors, actuator dynamics, and velocity filtering. Simulation and experimental results on the KUKA light weight robot show that the proposed criterion can accurately predict the stability boundaries. [ABSTRACT FROM PUBLISHER]

Summary: In this paper, new sufficient stability conditions for the asymptotic stability of time‐delay systems are presented using the quadratic separation approach. The time‐delay system is modeled as an interconnected closed‐loop system involving a linear transformation and delay‐dependent functions, representing the uncertainties brought by the delay. Those complex‐valued functions are then embedded into adequate norm‐bounded uncertainties, which lead to several stability results. The novelty of this approach relies on the introduction of new dedicated functions that are built in accordance to the Bessel inequality. They allow us to model the system as an uncertain feedback system and to control the accuracy of the inequality. Then, a sequence of linear matrix inequality conditions is proposed, which tends to the analytical bounds for both delay‐dependent stability and delay range stability, at least on examples. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new observer design method for nonlinear systems with large transport delays. The new observer design is a generalization of the PDE-based backstepping-like observer design approach. First developed for delayed linear systems, this approach relies on a modelling of the output time-delay by a 1st order hyperbolic equation, leading to an ODE–PDE representation of the system, and on coordinate transformations of the innovative system. The major technical challenge, that is faced in the generalization of the approach to nonlinear systems, consists in making it applicable in the case of an arbitrarily large time-delay D . This issue is presently coped with by redesigning the cascade observer method to fit ODE–PDE systems. A new class of observers is thus obtained involving a set of cascaded high-gain state observers and output predictors. The latter are defined by PDEs that provide estimates of the system future outputs y ( t + x ) for all x ∈ [ 0 , D ] . The exponential stability of the observer is proved using a set of Lyapunov functionals and its performances are illustrated by simulation. [ABSTRACT FROM AUTHOR]

Unknown time delay poses a significant challenge to the design of networked motion control systems. Moreover, modeling uncertainties, mechanical disturbance, and sensor noise coexist with time delay in such systems, which makes the controller synthesis even more challenging. It has been proven effective to model the time delay as fictitious disturbance so that a disturbance observer (DOB) can be employed to cancel the negative effect of time delay. In this brief, a new double DOB (DDOB) design is proposed by adding one more DOB into the control system to handle actual external disturbance and enable satisfactory tracking performance. Design considerations of the baseline controller and the two DOBs are illustrated, and robust stability analysis is provided to handle modeling uncertainties. A real-time wireless communication protocol, RT-WiFi, is integrated with a DC motor to examine the performance of the proposed DDOB by simulations and experiments. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of linear parameter-varying (LPV) dual-rate system identification with slow-rate output data corrupted by random measurement delays. The local approach is used, and the LPV model is built through convex combination of several local linear models with time-varying weights. The dual-rate sampled data often exist in industry, and the measured output data are inevitably corrupted by random measurement delays. In order to handle random measurement delays and dual-rate sampled data in LPV system identification, the statistical description of the identification problem is established based on the presented output-interpolated LPV dual-rate model, and then, the proposed algorithm to estimate all the unknown model parameters, real output data, and measurement delays are derived in the generalized expectation–maximization algorithm scheme. One simulation example and a practical chemical process are used to verify the efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

In recent years, networked distributed control systems (NDCS) have received research attention. Two of the main challenges that such systems face are possible delays in the communication network and the effect of strong interconnections between agents. This paper considers an NDCS that has delays in the communication network, as well as strong interconnections between its agents. The control objective is to make each agent track efficiently a reference model by attenuating the effect of strong interconnections via feedback based on the delayed information. First, the authors assume that each agent knows its own dynamics, as well as the interconnection parameters, but receives information about the states of its neighbors with some communication delay. The authors propose a distributed control scheme and prove that if the interconnections can be weakened and if the communication delays are small enough, then the proposed scheme guarantees that the tracking error of each agent is bounded with a bound that depends on the size of the weakened interconnections and delays, and reduces to zero as these uncertainties reduce to zero. The authors then consider a more realistic situation where the interconnections between agents are unknown despite the cooperation and sharing of state information. For this case the authors propose a distributed adaptive control scheme and prove that the proposed scheme guarantees that the tracking errors are bounded and small in the mean square sense with respect to the size of the weakened interconnections and delays, provided the weakened interconnections and time delays are small enough. The authors then consider the case that each agent knows neither its dynamics nor the interconnection matrices. For this case the authors propose a distributed adaptive control scheme and prove that the proposed scheme guarantees that the tracking errors are bounded and small in the mean square sense provided the weakened interconnections and time delays are small enough. Finally, the authors present an illustrative example to present the applicability and effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

We analyze the oscillatory dynamics of a time-delayed dynamical system subjected to a periodic external forcing. We show that, for certain values of the delay, the response can be greatly enhanced by a very small forcing amplitude. This phenomenon is related to the presence of a Bogdanov–Takens bifurcation and displays some analogies to other resonance phenomena, but also substantial differences. [ABSTRACT FROM AUTHOR]

In this paper, a new Multiple Model Adaptive Control (MMAC) is proposed to control of the satellite antenna position with time varying input delay. Selecting of adequate delay estimation method and weighting algorithm using delay estimation error are features of proposed controller. Input delay can be effect on the performance of the closed loop system and if delay time is unknown and time varying, the closed loop system will probably be unstable. At these cases, delay time must be identified to adopt control signal. It is assumed that upper bound of the delay time is known. Delay time is divided into several small bounds and then an adequate PI controller is designed for each bound to guarantee closed loop system performance and stability. In the on-line mode, delay time is identified by adequate estimation algorithm and the control signal is constructed by a weighted sum of the designed controllers output. Control signals weights are a function of the absolute error between the estimated and the average delay time in each bound. Performance of the proposed method and stability of closed-loop system is assessed using several simulations of the system. Simulation results confirm the effectiveness of the proposed algorithm with respect to conventional PI controller. [ABSTRACT FROM AUTHOR]

This study investigates the optimal filter for Markov jump linear (MJL) system with multiple delayed modes and observations, in which the data losses are introduced naturally and the Markov chains are assumed to be known up to the present time. To deal with the mode and observation delays, a reorganised observation sequence is defined. Moreover, the optimal filter problem is transformed into one of the delay‐free system which is just with jumping parameters and multiplicative noises. An optimal MJL filter is presented based on the mean squared method, where the filter gains are determined by solving a set of generalised coupled Riccati difference equations based on a set of coupled Lyapunov equations. Alternatively, an optimal stationary MJL filter is developed, where the filter gains are derived by solving a set of generalised coupled algebraic Riccati equations based on coupled algebraic Lyapunov equations. It can be shown that the difference Riccati equations developed in the former filter converge to the stationary ones under appropriate conditions. [ABSTRACT FROM AUTHOR]

Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analyzing the impedance presented by the circuit at a well-chosen node without internal access to the simulator. If any of the poles of this impedance lie in the complex right half-plane, the circuit is unstable. The classic way to detect unstable poles is to fit a rational model on the impedance. In this paper, a projection-based method is proposed which splits the impedance into a stable and an unstable part by projecting on an orthogonal basis of stable and unstable functions. When the unstable part lies significantly above the interpolation error of the method, the circuit is considered unstable. Working with a projection provides one, at small cost, with a first appraisal of the unstable part of the system. Both small-signal and large-signal stability analysis can be performed with this projection-based method. In the small-signal case, a low-order rational approximation can be fit on the unstable part to find the location of the unstable poles. [ABSTRACT FROM AUTHOR]

In this paper, we use a mathematical model of a inventory system with time-varying delivery delay and three control systems in order to compare their properties for the goods flow optimization problem in the inventory systems. Structures of the chosen control systems are based on mathematical discrete equations: a periodic inventory system with adaptive maximal inventory level and perpetual inventory system with adaptive order quantity level as well as the methods proposed by the authors in previous works based on the Smith predictor. The selection of the control systems parameters is done by solving optimization tasks for a specific scenario of time-varying market demand using a genetic algorithm in Matlab/Simulink. In this article, we mainly want to compare which of the control structures is able to achieve a high service level with maintaining of a given inventory maximal level in response to assumed consumer demand scenario. [ABSTRACT FROM AUTHOR]

This paper considers the cluster synchronisation of coupled delay reaction-diffusion systems (DRDSs). First, in light of the technique of matrix representation, we turn the cluster synchronisation of coupled DRDSs into the asymptotical stability of a transformed system. Based on this transformation and by virtue of the Lyapunov-Krasovskii functional method, we provide the sufficient conditions that ensure the cluster synchronisation for DRDSs with constant delay. The effects of spatial domain on the cluster synchronisation is shown by these sufficient conditions. Then, we deal with time-varying delay systems with reaction-diffusion term. The criterion of cluster synchronisation is presented and a brief proof is given. Finally, numerical examples are carried out to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this study, the problem of output regulation with passive performance control is investigated for a class of switched stochastic delay systems by using an average dwell time approach. It is assumed that the system under consideration is subject to the existence of time delays in both states and the regulators switching signal which causes asynchronous switching between candidate regulators and subsystems. By construction of a Lyapunov–Krasovskii (L–K) functional, sufficient conditions for the existence of the corresponding regulators are derived from the cases where the states are measurable and unmeasurable, respectively. Then, a switching signal is designed based on the upper bounds of the time delays. Finally, simulation examples are provided to illustrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis. [ABSTRACT FROM AUTHOR]

This study addresses the distributed economic dispatch problem for DC microgrids when time‐varying delays are present in communication networks. A novel distributed algorithm is proposed, and the proposed controller contains a distributed generation cost optimisation module and a voltage regulation module. The cost optimisation module is aimed to realise cost optimisation by driving the incremental cost rate of every distributed generator to be equal. In the voltage regulation module, a distributed synchronisation algorithm is used to restore the global average voltage. After the effect of the communication delay on the system stability is analysed, the robust stability criticality under load changes is obtained by using linear matrix inequality. The performance of the proposed scheme is validated through simulations and experimentally. [ABSTRACT FROM AUTHOR]

For nonlinear systems, we develop a PDE-based predictor-feedback control design, which compensates actuator dynamics, governed by a transport PDE with outlet boundary-value-dependent propagation velocity. Global asymptotic stability under the predictor-feedback control law is established assuming spatially uniform strictly positive transport velocity. The stability proof is based on a Lyapunov-like argument and employs an infinite-dimensional backstepping transformation that is introduced. An equivalent representation of the transport PDE/nonlinear ODE cascade via a nonlinear system with an input delay that is defined implicitly through an integral of the past input is also provided and the equivalent predictor-feedback control design for the delay system is presented. The validity of the proposed controller is illustrated applying a predictor-feedback “bang–bang” boundary control law to a PDE model of a production system with a queue. Consistent simulation results are provided that support the theoretical developments. [ABSTRACT FROM AUTHOR]

An integral–proportional derivative (I–PD) control strategy for integrating plus time‐delay processes is proposed. The proposed scheme consists of an inner PD loop and an outer I‐loop for taking care of the servo as well as the regulatory action. Explicit formulas for tuning of the proposed controller are derived in terms of gain margin, phase margin and critical gain. Moreover, pole‐placement and frequency loop‐shaping design methods are also explored for designing the I–PD controller. Simulation results show the superiority of the proposed I–PD controller over conventional P/PI/PID ones for integrating processes. The design is also validated through experiments on a temperature control process. [ABSTRACT FROM AUTHOR]

This study addresses the networked control problem for event‐triggered systems with quantisation effect and actuator fault. A new type of finite‐level dynamic logarithmic quantiser is proposed here. Firstly, when the actuator is subjected to deterministic fault and time delay occurs in the network between the sensor and the controller, stability analysis and stabilisation of the system are accomplished. Secondly, suppose the actuator is subjected to stochastic fault and there is packet dropout in the network between the sensor and the controller, the asymptotic stability of the system is analysed, and a mean‐square feedback controller is designed. Finally, simulation studies are made to verify the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

The authors investigate input‐to‐state stabilisation for a general non‐linear system with input delay and disturbance. With an infinite‐dimensional backstepping transformation, the original system is transferred to a target system. A delay‐compensating and disturbances attenuating control law is designed for this kind of non‐linear systems. Stability of the target system is first proved by constructing a Lyapunov functional. Equivalence of norms for original and target system is deduced. Further, input‐to‐state stabilisation for the original system under the delay‐compensating control law is drawn. [ABSTRACT FROM AUTHOR]