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The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays.

A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.

The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

The purpose of this manuscript, a state feedback gain depends on the optimal design of fractional order PID controller to time-delay system is established. In established optimal design known as advanced cuttlefish optimizer and random decision forest that is combined performance of random decision forest algorithm (RDFA) and advanced cuttlefish optimizer (ACFO).

The proposed ACFO uses the concept of crossover and mutation operator depend on position upgrading to enhance its search behavior, calculational speed as well as convergence profile at basic cuttlefish optimizer.

Fractional order proportional-integrator-derivative (FOPID) controller, apart from as tuning parameters (kp, ki and kd) it consists of two extra tuning parameters λ and µ. In established technology, the increase of FOPID controller is adjusted to reach needed responses that demonstrated using RDFA theory as well as RDF weight matrices is probable to the help of the ACFO method. The uniqueness of the established method is to decrease the failure of the FOPID controller at greater order time delay method with the help of controller maximize restrictions. The objective of the established method is selected to consider parameters set point as well as achieved parameters of time-delay system.

In the established technique used to evade large order delays as well as reliability restrictions such as small excesses, time resolution, as well as fixed condition defect. These methods is implemented at MATLAB/Simulink platform as well as outcomes compared to various existing methods such as Ziegler-Nichols fit, curve fit, Wang method, regression and invasive weed optimization and linear-quadratic regression method.

The model for digitally controlled three-phase pulse width modulation (PWM) boost rectifiers is a sampled data model, which is different from the continuous time domain models presented in previous studies. The controller, which is tuned according to the model in continuous time domain and discretized by approximation methods, may exhibit some unpredictable performances and even result in unstable systems under some extreme situations. Consequently, a small-signal discrete-time model of digitally controlled three-phase PWM boost rectifier is required. The purpose of this paper is to provide a simple but accurate small-signal discrete-time model of digital controlled three-phase PWM boost rectifier, which explains the effect of the sampling period, modulator and time delays on system dynamic and improves the control performance.

Based on the Laplace domain analysis and the waveforms of up-down-count modulator, the small signal model of digital pulse width modulation (DPWM) in the Laplace domain is presented. With a combination of state-space average and a discrete-time modeling technique, a simplified large signal discrete time model is developed. With rotation transformation and feed-forward decoupling, the large-signal model is decoupled into a single input single output system with rotation transformation. Then, an integrated small signal model in the Laplace domain is constructed that included the time delay and modulation effect. Implementing the modified z-transform, a small-signal discrete-time model is derived from the integrated small signal model.

In a digital control system, besides the circuit parameters, the location of pole of open-loop transfer function is also related to system sampling time, affecting the system stability, and the time delay determines the location of the zero of open-loop transfer function, affecting the system dynamic. In addition to the circuit parameters discussed in previous literature, the right half plane (RHP) zero is also determined by the sampling period and the time delay. Furthermore, the corner frequency of the RHP zero is mainly determined by the sampling period.

The model developed in this paper, accounting for the effect of the sampling period, modulator and time delays on the system dynamic, give a sufficient insight into the behavior of the digitally controlled three-phase PWM rectifier. It can also explain the effect of sampling period and control delay time on system dynamic, accurately predict the system stability boundary and determine the oscillation frequency of the current loop in critical stable. The experimental results verify that the model is a simple and accurate control-oriented small-signal discrete-time model for the digitally controlled three-phase PWM boost rectifier.

The purpose of this paper is to investigate the effect of time delay on the ability of a human operator to complete a task with a teleoperated mobile‐robot using two systems, two different ways of interacting with the mobile‐robots and several different environments.

Teleoperators are observed completing a series of tasks using a joystick to control a mobile‐robot while time delays are introduced to the system. They sit at a computer and view scenes remotely on a screen. Cameras are either mounted on the robot or mounted externally so that they view both the environment and robot. Teleoperators complete the tests both with and without sensors. One robot system uses an umbilical cable and one uses a radio link.

In simple environments, a teleoperator may perform better without a sensor system to assist them but as time delays are introduced then there are more failures. In more complicated environments or when time delays are longer, then teleoperators perform better with a sensor system to assist. Teleoperators may also tend to perform better with a radio link than with an umbilical connection.

Teleoperated systems rely heavily on visual feedback and experienced operators. This paper investigates the effect of introducing a delay to the delivery of that visual feedback.

The paper suggests that in simple environments with short time delays then the amount of sensor support should be small but in more complicated environments or with longer delays then more sensor support needs to be provided.

Results from imposing time delays on a teleoperated mobile‐robot are presented. Effects on the task of different ways of viewing activity on a computer display are presented, that is with cameras mounted on the robot or cameras mounted externally to view both the environment and robot. Results from using sensors to assist teleoperators are presented. The paper suggests that the amount of sensor support should be varied depending on circumstances.

The purpose of this paper is to concern the design of a robust model predictive controller for distributed networked systems with transmission delays.

The overall system is composed of a number of interconnected nonlinear subsystems with time-varying transmission delays. A distributed networked system with transmission delays is modeled as a nonlinear system with a time-varying delay. Time delays appear in distributed systems due to the information transmission in the communication network or transport of material between the sub-plants. In real applications, the states may not be available directly and it could be a challenge to address the control problem in interconnected systems using a centralized architecture because of the constraints on the computational capabilities and the communication bandwidth. The controller design is characterized as an optimization problem of a “worst-case” objective function over an infinite moving horizon.

The aim is to propose control synthesis approach that depends on nonlinearity and time varying delay characteristics. The MPC problem is represented in a time varying delayed state feedback structure. Then the synthesis sufficient condition is provided in the form of a linear matrix inequality (LMI) optimization and is solved online at each time instant. In the rest, an LMI-based decentralized observer-based robust model predictive control strategy is proposed.

The authors develop RMPC strategies for a class of distributed networked systems with transmission delays using LMI-Based technique. To evaluate the applicability of the developed approach, the control design of a networked chemical reactor plant with two sub-plants is studied. The simulation results show the effectiveness of the proposed method.

This paper aims to provide a precise tracking control scheme for multi-input multi-output “MIMO” nonlinear systems with unknown input time-delay in industrial process.

The predictive control scheme based on multi-dimensional Taylor network (MTN) model is proposed. First, for the unknown input time-delay, the cross-correlation function is used to identify the input time-delay through just the input and output data. And then, the scheme of predictive control is designed based on the MTN model. It goes as follows: a recursive d-step-ahead MTN predictive model is developed to compensate the influence of time-delay, and the extended Kalman filter (EKF) algorithm is applied for its learning; the multistep predictive objective function is designed, and the optimal controlled output is determined by iterative refinement; and the convergence of MTN predictive model and the stability of closed-loop system are proved.

Simulation results show that the proposed scheme is of desirable generality and capable of performing the tracking control for MIMO nonlinear systems with unknown input time-delay in industrial process effectively, such as the continuous stirred tank reactor (CSTR) process, which provides a considerably improved performance and effectiveness. The proposed scheme promises strong robustness, low complexity and easy implementation.

For the limitations of proposed scheme, the time-invariant time-delay is only considered in time-delay identification and control schemes. And the CSTR process is only introduced to prove that the proposed scheme can adapt to practical industrial scenario.

The originality of the paper is that the proposed MTN control scheme has good tracking performance, which solves the influence of time-delay, coupling and nonlinearity and the real-time performance for MIMO nonlinear systems with unknown input time-delay.

This paper aims to use a new design approach based on a Lagrange mean value theorem for the stabilization of multivariable input‐delayed system by linear controller.

The delay‐dependent asymptotical stability conditions are derived by using augmented Lyapunov‐Krasovskii functionals and formulated in terms of conventional Lyapunov matrix equations and some simple matrix inequalities. Proposed design approach is extended to robust stabilization of multi‐variable input‐delayed systems with unmatched parameter uncertainties. The maximum upper bound of delay size is computed by using a simple optimization algorithm.

A liquid monopropellant rocket motor with a pressure feeding system is considered as a numerical design example. Design example shows the effectiveness of the proposed design approach.

The proposed approach can be used in the analysis and design of the uncertain multivariable time‐delay systems.

The paper has a great potential in the stability analysis of time‐delay systems and design of time‐delay controllers and may openup a new direction in this area.

The purpose of this paper is to discuss the properties of transparency and excitability of positive linear time‐invariant systems under internal point delays.

The problem is solved by combining the algebraic conditions for positivity, excitability, and transparency for the case of linear and time‐invariant dynamic systems in the presence of discrete lags.

It is shown that the excitability independent of delay is guaranteed if an auxiliary delay‐free system is excitable. Necessary and sufficient conditions for excitability and transparency are formulated in terms of the parameterization of the dynamics and control matrices, and equivalently, in terms of strict positivity of a matrix of an associate system obtained from the influence graph of the original system. Such conditions are testable through simple algebraic tests involving moderate computational effort.

The practical implications mainly rely on some biological and medical problems where delays are present by nature, excitability means the activation of all the state components under positive controls after a short time in the sense that it cannot remain identically zero. In the same way, it relays on the activation of all the output components under zero controls and non‐negative initial conditions.

The paper extends the concepts of excitability and transparency to dynamic systems with point time‐lags which are very common in nature and some practical problems.

The purpose of this paper is to design a model-based bilateral teleoperation method to improve the feedback force and velocity/position tracking for robotic-assisted tasks (such as palpation, etc.) under constant and/or varying time delay with environment dynamic property. Time delay existing in bilateral teleoperation easily destabilizes the system. Proper control strategies are able to make the system stable, but at the cost of compromised performance. Model-based bilateral teleoperation is designed to achieve enhanced performance of this time-delayed system, but an accurate model is required.

Viscoelastic model has been used to describe the robot tool-soft tissue interaction behavior. Kevin-Boltzmann (K-B) model is selected to model the soft tissue behavior due to its good accuracy, transient and linearity properties among several viscoelastic models. In this work, the K-B model is designed at the master side to generate a virtual environment of remote robotic tool-soft tissue interaction. In order to obtain improved performance, a self perturbing recursive least square (SPRLS) algorithm is developed to on-line update the necessary parameters of the environment with varying dynamics.

With fast and optimal on-line estimation of primary parameters of the K-B model, the reflected force of the model-based bilateral teleoperation at the master side is improved as well as the position/velocity tracking performance. This model-based design in the bilateral teleoperation avoids the stability issue caused by time delay in the communication channel since the exchanged information become position/velocity and estimated parameters of the used model. Even facing with big and varying time delay, the system keeps stably and enhanced tracking performance. Besides, the fast convergence of the SPRLS algorithm helps to track the time-varying dynamic of the environment, which satisfies the surgical applications as the soft tissue properties usually are not static.

The originality of this work lies in that an enhanced perception of bilateral teleoperation structure under constant/varying time delay that benefits robotic assisted tele-palpation (time varying environment dynamic) tasks is developed. With SPRLS algorithm to on-line estimate the main parameters of environment, the feedback perception of system can be enhanced with stable velocity/position tracking. The superior velocity/position and force tracking performance of the developed method makes it possible for future robotic-assisted tasks with long-distance communication.

Computerising inventory control procedures is usually an attempt to gain better control over stock availability. The effectiveness of the procedures depends on the time delays imparted by such events as order processing and delivery. Through these time delays, much of a finished goods physical distribution system is linked together through the inventory control procedures. Changing the length of any one time element through changes in inventory stocking rules, order processing methods or selected transportation services impacts on the economics of the entire physical distribution system. Little is understood about the effects of time change in such complex systems. In this article, the actual computer inventory control procedures of a chemical company were computer simulated. Physical distribution system design decisions and their associated time delay effects were explored by interrogating the model. Surprising effects were discovered, some of them being counter‐intuitive to what simple theory would predict. Management guidelines were provided as to the system‐wide economic consequences of change in individual elements of a physical distribution system.