Bound Of Delay Research Articles

Delay‐dependent stability of a class of stochastic delay systems driven by G‐Brownian motion

This study discusses delay-dependent stability of a class of stochastic delay systems driven by G-Brownian motion in the sublinear expectation space. With the help of the degenerate Lyapunov functional, the mean square exponential stability and quasi-sure exponential stability criteria for stochastic delay systems driven by G-Brownian motion are established and an explicit upper bound of time delay is derived. In particular, for the delay-free case, the corresponding sufficient conditions are also obtained. Here, the stability conditions are directly related to the coefficients of the stochastic delay systems and are different from the existing stability conditions which are presented in terms of the G-Lyapunov function. Some examples are introduced to illustrate the delay-dependent stability criteria.

Abel lemma‐based finite‐sum inequality approach to stabilization for 2‐D time‐varying delay systems

AbstractThe problem of delay‐dependent stability is concerned for two‐dimensional discrete‐time systems with interval time‐varying delays in this paper. Choosing a Lyapunov functional with the upper bound and lower bound of delays, considering all terms in the difference and using two‐dimensional Abel lemma‐based finite‐sum inequalities, a new delay‐dependent stability criterion in terms of linear matrix inequality is derived for two‐dimensional discrete‐time systems. Then, based on the delay‐dependent stability criteria, a state feedback control problem and a dynamic output feedback control problem are considered to realize the stability control for the two‐dimensional discrete‐time system. Finally, it is shown through four numerical examples that the stability criterion can provide a larger admissible maximum upper bound with less decision variables than the stability criterion using two‐dimensional Jensen inequalities approach.

Distributed formation‐containment control with Euler‐Lagrange systems subject to input saturation and communication delays

SummaryThis paper is concerned with the problem of formation‐containment on networked systems, with interconnected systems modeled by the Euler‐Lagrange equation with bounded inputs and time‐varying delays on the communication channels. The main results are the design of control algorithms and sufficient conditions to ensure the convergence of the network. The control algorithms are designed as distributed dynamic controllers, in such a way that the number of neighbors of each agent is decoupled from the bound of the control inputs. That is, in the proposed approach the amplitude of the input signal does not directly increase with the number of neighbors of each agent. The proposed sufficient conditions for the asymptotic convergence follow from the Lyapunov‐Krasovskii theory and are formulated in the linear matrix inequalities framework. The conditions rely only on the upper bound of delays and on a subset of the controller parameters, but they do not depend on the model of each agent, which makes it suitable for networks with agents governed by distinct dynamics. In order to illustrate the effectiveness of the proposed method we present numerical examples and compare with similar approaches existing in the literature.

Wafer sojourn time fluctuation analysis for time-constrained dual-arm multi-cluster tools with activity time variation

ABSTRACT In semiconductor manufacturing systems, a time-constrained multi-cluster tool should be scheduled such that a wafer stays in a process chamber in a given time range to satisfy a wafer residency time constraint. In practice, activity time is subject to variation. It could lead to some fluctuation of wafer residency time in a process chamber. Hence, it is crucial to analyze how wafer residency time varies with activity time variation. This issue is especially challenging for multi-cluster tools. This work focuses on determining the exact upper bound of wafer sojourn time delay resulted from activity time variation for dual-arm multi-cluster tools. After discussing their dynamic behaviours, it presents a two-level real-time operational architecture and a real-time control policy. Based on them, this work derives for the first time an efficient algorithm to calculate the exact upper bound of wafer sojourn time delay in a process chamber. As a result, engineers can test whether a given schedule is feasible. Several examples of industrial significance are used to demonstrate the application of the proposed approach.

Robust stability and stabilization of networked control systems with stochastic time-varying network-induced delays

This paper investigates the robust stability analysis and state feedback controller design of networked control systems (NCSs). A stochastic network-induced delay in given interval with known lower and upper bounds is considered. Therefore, the NCS is modeled as linear system with probabilistic time-varying delay distribution. Then, the Lyapunov-Krasovskii functional (LKF) is formulated using probabilistic informations of both lower and upper bounds of the time-varying network-induced delay, and Wirtinger-based integral inequalities are used to estimate the accuracy of the resulting time derivatives and also to reduce conservatism by introducing some new cross terms. Afterwards, stability condition based on [Formula: see text] disturbance attenuation level is expressed in terms of a set of linear matrix inequalities (LMIs), and Finsler’s lemma is used to relax it by adding slack decision variables and decoupling the systems matrices from those of Lyapunov-Krasovskii. This procedure makes the state feedback controller design as simple as a variables change. Finally, a maximum allowable upper bound of the network-induced delay and state feedback controller gains are calculated by resolving the above relaxed LMIs’ convex optimization problem. Practical numerical examples are provided to validate the proposed approach; the results show that the negative effects of the unpredictable network-induced delays are compensated and the stability of NCSs with high disturbance attenuation level is guaranteed. A comparative study with other results in recent researches is also given and the superiority of the proposed method in terms of robustness and conservatism reduction is shown.

State bounding for discrete-time switched nonlinear time-varying systems using ADT method

This article deals with the state bounding problem for discrete-time switched nonlinear time-varying systems with multiple time delays and bounded disturbances. With the aid of the average dwell time method and a technique used in positive systems, we put forward new criteria such that all solutions of the system exponentially converge to a ball under the designed average dwell time (ADT) switching, where the given ADT does not depend on the upper bound of delays. Simulation and numerical examples are presented to illustrate the validity of our results.

Robust backstepping control of uncertain nonlinear systems with unknown time-varying input delay

A robust compensator is developed for a class of strict-feedback uncertain nonlinear systems with additive disturbance and unknown time-varying input delay. The compensator is composed of a Proportional-Integral (PI) control and delay compensation term based on a finite integral of the past control values. The sufficient inequality conditions on controller gains and upper bound of input delay are derived using a Lyapunov-based stability analysis by choosing suitable L-K functionals, which guarantee a global uniformly ultimately bounded (GUUB) tracking result. Simulation results show the performance and robustness of controller for different values of time-varying input delay.

Ecological Cooperative Adaptive Cruise Control for a Heterogeneous Platoon of Heavy-Duty Vehicles With Time Delays

To deal with energy crisis and environmental issues, higher fuel economy standards and more stringent limitations on greenhouse gas emissions for ground vehicles have been made. Ecological cooperative adaptive cruise control (Eco-CACC) has been considered as an effective solution to decrease the fuel consumption and greenhouse gas emissions of a platoon of vehicles, and this article proposes an Eco-CACC strategy for a heterogeneous platoon of heavy-duty vehicles with time delays. The proposed Eco-CACC strategy consists of distributed control protocols for the following vehicles and a new model predictive controller for the leading one. Firstly, after the distributed control protocols are designed based on the neighboring vehicle information, the sufficient conditions that guarantee the internal stability and string stability are derived, and the upper bound of the time delays under controller parameters is also obtained. Secondly, assuming the vehicle platoon as a rigid body with followers staying at desired positions, the new model predictive controller is designed in order to further improve the overall fuel economy of vehicle platoon. Simulations are conducted to validate the sufficient conditions of internal stability and string stability, and to explore the fuel saving performance of the proposed control strategy. The simulation results demonstrate that, compared with the benchmark, the proposed Eco-CACC strategy can significantly improve the fuel economy of heterogeneous platoon.

Event-triggered Consensus Control of Multi-agent Systems with Nonuniform Communication Delays via Reduced-Order Observers

This paper studies a consensus problem for linear multi-agent systems (MASs) over directed communication networks with nonuniform time-varying delays. To overcome the limited computing and storage resources, a distributed control scheme is designed for each agent by using the event-triggered strategy. At the same time, a reduced-order observer is put forward in the controller design when only the relative output measurement is available. The communication network model with nonuniform time-varying delays is more challenging than the fixed delays or non-delays in the literature. Theoretical analysis is provided to show that the proposed control scheme can guarantee the consensus of MASs, with Zeno-behavior excluded and the upper bound of time delay obtained. A numerical example is provided to illustrate the feasibility and effectiveness of the theoretical results.

On 3D simultaneous attack against manoeuvring target with communication delays

This article investigates the simultaneous attack problem of multiple missiles against a manoeuvring target with delayed information transmission in three-dimensional space. Based on the kinetic model of the missiles, the problem is divided into three demands: the velocity components normal to line-of-sight converge to zero in finite time, the component of motion states along line-of-sight should achieve consensus and converge to zero. The guidance law is designed for each demand and by theoretical proof, the upper bound of delay which can tolerate is presented and the consensus error of the relative distances can converge to a small neighbourhood of zero. And simulation example presented also demonstrates the validity of the theoretical result.

Formation Control of High-Order Swarm Systems With Time-Varying Delays and Switching Interconnections

The paper investigates the formation control problem for high-order linear swarm systems with limited communications such as time-varying delays and switching interconnections. Firstly, the problem description is given including the dynamics of high-order swarm systems, formation protocol and the definitions of formation maintenance and tracking. Secondly, four formation conditions are derived: the former three are related to formation function, reference trajectory, auxiliary functions and network topology; the fourth one is equivalent to the stability of N-1 time-delay systems. In order to get lower conservative criteria, the Free-weighting Matrices(FWM) approach is employed to analyze the stabilization problem. Finally, the allowance upper bound of delays is calculated through solving the feasible linear matrix inequalities (LMIs). Numerical examples and simulation results are given to demonstrate the effectiveness and benefit on reducing conservativeness of the proposed method.

Distributed Optimization for Aggregative Games Based on Euler-Lagrange Systems With Large Delay Constraints

This article investigates an aggregative game based on Euler-Lagrange systems subject to time-varying communication delays. First, a distributed algorithm is put forward to try to find the Nash equilibrium by the deliberated group of Euler-Lagrange systems with “small” delay and “large” delay. Second, we illustrate the convergence of two circumstances, separately. The first circumstance derives the upper bound of delays for guaranteeing globally exponential convergence, and the other obtains globally exponential convergence, even in some restrictions on “large” delays. Finally, a numerical example is used to show the effectiveness and superiority of proposed method.

Delay Bound Optimization in NoC Using a Discrete Firefly Algorithm

The delay bound in system on chips (SoC) represents the worst-case traverse time of on-chip communication. In network on chip (NoC)-based SoC, optimizing the delay bound is challenging due to two aspects: (1) the delay bound is hard to obtain by traditional methods such as simulation; (2) the delay bound changes with the different application mappings. In this paper, we propose a delay bound optimization method using discrete firefly optimization algorithms (DBFA). First, we present a formal analytical delay bound model based on network calculus for both unipath and multipath routing in NoCs. We then set every flow in the application as the target flow and calculate the delay bound using the proposed model. Finally, we adopt firefly algorithm (FA) as the optimization method for minimizing the delay bound. We used industry patterns (video object plane decoder (VOPD), multiwindow display (MWD), etc.) to verify the effectiveness of delay bound optimization method. Experiments show that the proposed method is both effective and reliable, with a maximum optimization of 42.86%.

Distributed Optimization for Resource Allocation Problems Under Large Delays

In this paper, a distributed resource allocation problem is investigated based on a continuous-time algorithm in the presence of time-varying communication delays. The considered delays are allowed to take both “large” and “small” delay values in an alternating manner. The “small” delays refer to a class of delays that guarantee the exponential convergence to the optimal solution; otherwise, they are called “large” delays. The existence of “large” delays may affect the behavior of the optimal allocation solution, and the existing algorithms with delays may not be applicable to this kind of “large” delays. To address “large” delay cases, a switched algorithm is first proposed based on switching techniques, and then, such an algorithm is modeled as switched delay systems. Second, by adopting the Lyapunov functional theory, the upper bound of delays is first derived to guarantee the exponential convergence to the optimal solution under “small” delays, and then, a delay-dependent sufficient condition is obtained to ensure exponential convergence of the proposed algorithm based on some restrictions on “large” delays. Finally, we adopt an IEEE 118-bus practical example to show the effectiveness of the proposed algorithm.

Model-Based Periodic Event-Triggered Control Strategy to Stabilize a Scalar Nonlinear System

This article focuses on the problem of stabilizing a scalar continuous-time nonlinear system under bounded network delay and process noise. In order to save the feedback network's bandwidth, a model-based periodic event-triggered control policy is utilized to maintain longer intersampling intervals, which are at least as long as the sampling period of periodic policies. Furthermore, the event-triggering condition is only checked intermittently at fixed time instants, i.e., the sampling time instants. Without acknowledgment (ACK), the updating of nominal models at the sensor and at the controller are asynchronous. The two cases, where the network delay is either less than the sampling period or larger than the sampling period, are investigated. In comparison with periodic sampling methods, our scheme can make full use of the received data packets, particularly their sampling time instant information, which yields a lower occupied bit rate while guaranteeing the desired input-to-state stability. Note that the obtained bit rate conditions are only related to the Lipschitz parameter, the bound of network delay, the number of quantization bits, and the sampling period. The bounded process noise will not incur any increase of the stabilizing bit rate under the proposed strategy.

Global tracking of nonlinear systems with simultaneous unknown time‐varying state and input delays

SummaryThis paper presents the design of a robust control law for a class of nonlinear dynamical systems subjected to parametric uncertainty and simultaneous unknown, variable state and input delays. A novel controller is developed, which consists of a filtered tracking error and the integral of previous values of control input where the limits of integration are dependent on the known bound of the input delay. Lyapunov‐Krasovskii functionals–based stability analysis guarantees a global uniformly ultimately bounded tracking result where sufficient conditions on controller gains and maximum allowable delay are derived. The performance and robustness of the controller are evaluated by simulation on a two‐link robot manipulator for different combinations of time‐varying state and input delays.

Sampling-based cooperative adaptive cruise control subject to communication delays and actuator lags

This paper studies a sampling-based cooperative adaptive cruise control (CACC) problem under communication delays and actuator lags. To deal with this problem, a new sampled control framework for each following vehicle is established, in which the time-varying communication delays and actuator lags are involved. By the proposed framework, an effective sampled control law for the CACC systems is given with the leader–predecessor following communication topology. In order to guarantee inner vehicular stability, the Lyapunov–Krasovskii function method is applied to obtain the sufficient condition for the existence of a controller by using state transformation. Furthermore, additional string stability conditions are complemented by considering the upper bound of delays. A useful controller design algorithm is given to ensure inner stability and string stability simultaneously. A numerical example is given to illustrate the effectiveness of controller design methodology of CACC systems.

Stability Criteria for Systems with Multiple Probabilistic Intervals Time-varying Delay

The problem of stability for systems with multiple probabilistic intervals time-varying delay is investigated in this paper. First, it is assumed that the probability distributions of the time-varying delay falling into three intervals are known in prior. Two random variables obeying Bernoulli distributions, respectively, are introduced to characterize the probability of the time-varying delay taking values in three intervals. An equivalent new model including the existing ones as its special cases is given. Second, an appropriate Lyapunov-Krasovskii functional is constructed by exploiting more information of delay. Third, based on Lyapunov stability theory, several delay-distribution-dependent stability criteria are derived in the form of linear matrix inequalities by employing Reciprocally convex technique and Generalized Finsler's lemma. which can provide a larger upper bound of delay compared with the existed ones. Finally, a well-known numerical example is given to show the effectiveness of the proposed method.

Event-Triggered $H_{\infty}$ Filtering for Discrete-Time T–S Fuzzy Systems via Network Delay Optimization Technique

This paper is concerned with the problem of ${H_{\infty }}$ filter design for discrete-time Takagi–Sugeno (T–S) fuzzy systems under an event-triggered (ET) communication mechanism. A partition method is adopted to overcome the asynchronous problem of the premise variables caused by introducing ET mechanism. The delay segmentation approach is used to deal with the network delay caused by network transmission, and new sufficient conditions are constructed to optimize the upper bound of network delay by combining each segments of the delay with the piecewise Lyapunov–Krasovskii functional. Moreover, it is shown that, for the considered discrete-time T–S fuzzy systems, using the nonsegmentation method, the results obtained by using the delay segmentation approach can be reduced to the existing results. Finally, an illustrative example is provided to show the advantages of the proposed design method.

Modified-transformation-based networked controller for offshore platforms under multiple outloads

In the paper, we study the problem of vibration control for offshore platform in nonideal network environment under wave and current forces based on the modified transformation. We consider the wave and current synchronously and give a dynamical system for the outside loads. The problem of time delay, packet dropouts and disordering due to nonideal network are taken into account. In the networked control model, two buffers output the received packets according to time stamps and upper bound of time delay. Based on a transformation, we reduce the time delay system into an equivalent delay-free system. Taking the nonideal network communication conditions into account, we design a modified transformation based on the past time data, wave and current loads, and received packets through network at current time. The networked controller is presented to depress the vibration of structure in nonideal network communication environment based on the modified transformation. An algorithm is given to simplify the computation of control law by recurrence. The system stability under presented networked controller is analyzed based on Lyapunov functional. Through the simulation results and comparison with other networked controllers, we can see that the presented controller can reduce the oscillation of offshore platform effectively.