Input Time Delay Research Articles

Couple-Group Consensus: A Class of Delayed Heterogeneous Multiagent Systems in Competitive Networks

This paper discusses the couple-group consensus issues of a class of heterogeneous multiagent systems containing first-order and second-order dynamic agents under the influence of both input and communication delays. In distinction to the existing works, a novel distributed coordination control protocol is proposed which is not only on the foundation of the competitive interaction between the agents but also has no virtual velocity estimation in the first-order dynamics. Furthermore, without the restrictive assumptions existing commonly in the related works, several sufficient algebraic criteria are established for the heterogeneous systems to realize couple-group consensus asymptotically. The obtained conclusions show that the achievement of the systems’ couple-group consensus intimately relates to the coupling weights between the agents, the systems control parameters, and the input time delays of the agents, while communication time delays between the agents are irrelevant to it. Finally, several simulations are illustrated to verify the effectiveness of the obtained theoretical results.

Mixed control for discrete‐time systems with input delay

This study is concerned with the mixed H 2 / H ∞ control problem under an open-loop information pattern with input delay. Compared with the delay-free case, one of the main difficulties is the non-causality caused by the time delay in the control input. The mixed H 2 / H ∞ control problem is reformulated as a leader–follower game and the Stackelberg strategy based on the maximum principle is introduced to deal with this. By introducing two co-states to capture the future information and one new state to capture the past effects, the problem can be addressed. The controllers are designed by solving the symmetric and decoupled Riccati equations. Necessary and sufficient conditions that guarantee the existence and uniqueness of the solution are proposed in this study.

Couple-group consensus for discrete-time heterogeneous multiagent systems with cooperative–competitive interactions and time delays

Abstract We investigate couple-group consensus problems for a class of discrete-time heterogeneous systems consisting of first-order and second-order agents under the influence of communication and input time delays. A novel consensus protocol is designed by utilizing cooperative and competitive interactions among agents, so that we solve the couple-group consensus problems casting off a conservation condition of in-degree balance which widely exists in relevant articles. Based on frequency-domain analysis and matrix theory, some sufficient conditions are derived to ensure the achievement of group consensus in some cases, and the upper bound of input time delays are consequently estimated. The results show that the achievement of couple-group consensus is closely relate to the coupling weights between the agents, the control parameters of the systems, the sampled information of discrete-time systems as well as the agents’ input time delays, while it is irrelevant to communication delays. Finally, we provide several simulations to illustrate the correctness of the theoretical results.

Asynchronous output feedback dissipative control of Markovian jump systems with input time delay and quantized measurements

This paper considers dynamic output-feedback control for Markovian jump systems with input mode-dependent interval time delay and quantized measurements. The transitions of the considered system and the desired output feedback controllers are considered to be asynchronous. The transition probabilities of output feedback controllers are allowed to be known, uncertain, and unknown. The main purpose of this paper is to design an asynchronous output feedback controller for Markov jump systems so that the closed-loop system is stochastically stable and achieves strict (Q,S,R)−α dissipativity. A sufficient condition is developed using Lyapunov functional approach. The controller gains are derived by solving a set of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the developed techniques.

Predictor-Based Extended-State-Observer Design for Consensus of MASs With Delays and Disturbances

In this paper, we study output feedback leader-follower consensus problem for multiagent systems subject to external disturbances and time delays in both input and output. First, we consider the linear case and a novel predictor-based extended state observer is designed for each follower with relative output information of the neighboring agents. Then, leader-follower consensus protocols are proposed which can compensate the delays and disturbances efficiently. In particular, the proposed observer and controller do not contain any integral term of the past control input and hence are easy to implement. Consensus analysis is put in the framework of Lyapunov-Krasovskii functionals and sufficient conditions are derived to guarantee that the consensus errors converge to zero asymptotically. Then, the results are extended to nonlinear multiagent systems with nonlinear disturbances. Finally, the validity of the proposed design is demonstrated through a numerical example of network-connected unmanned aerial vehicles.

Stabilization for Schrödinger equation with a distributed time delay in the boundary input

Abstract In this study, the stabilization problem for Schrödinger equation with distributed input time delay is considered. The main idea of solving the stabilization problem is transformation. The original time delay system is firstly transformed into the undelayed system, and then the feedback control law which can stabilize the undelayed system is found. Finally, we prove that the feedback control law can also exponentially stabilize the time delay system.

A Stackelberg strategy for continuous-time mixed H2/H∞ control problem with time delay

This paper is concerned with the mixed H2/H∞ control with linear continuous time system and time delay. To deal with this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The leader’s control strategy minimizes the cost function which is in H2 norm and the follower’s control strategy maximizes the cost function which is in H∞ norm. The main technique of this paper is deal with the noncausal relationship of the variables caused by time delay in the control input by introducing two costates to capture the future information and one state to capture the past information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended state space expression, the explicit expression of the strategy is obtained.

Developing steady and dynamic ORP models for mercury emissions control in power plants using WFGD operating data

The oxidation-reduction potential (ORP) is highly related to Hg re-emission in wet flue gas desulfurization (WFGD) systems in coal-fired power plants. Developing an accurate model that describes the ORP characteristics is beneficial to achieve the operation optimization of the WFGD system and Hg re-emission reduction. In this paper, steady and dynamic ORP models were reported based on the least squares support vector machine (LSSVM) technique and using operating data acquired from a coal-fired power plant. For the steady model, input parameters consisted of flue gas flow, flue gas temperature, inlet SO2 concentration, oxidation air flow, recycle pump currents, and slurry feed flow. For the dynamic model, in addition to the parameters listed above, time delays of these parameters were also considered in the modeling scheme. Both models achieved high accurate predictions. Model sensitivity analysis was conducted to investigate the influence of the input parameters and time delays on ORP. Results show that the parameters are adequate to describe the characteristics of the ORP. In addition, parametric time delays play an important role to represent the dynamic characteristics of the ORP. These models can be extended to design process control strategy and conduct the ORP operation optimization of the WFGD system in power plants to mitigate Hg re-emission from the scrubber.

Guaranteed cost consensus for second-order multi-agent systems with heterogeneous inertias

In this paper, the guaranteed cost consensus problem for second-order multi-agent systems with directed topology is considered, in which each agent has a heterogeneous inertia and control gain. The distributed control protocols with the absolute and relative velocity dampings are proposed, respectively. In each kind of protocol, both the communications with and without the input time delay are also considered. By introducing the auxiliary variables and using Lyapunov stability theory, some sufficient conditions are given to achieve the consensus. Moreover, the upper bounds of the guaranteed cost functions are obtained. Finally, some simulation examples are presented to show the effectiveness of the proposed approaches.

Tracking control of uncertain time delay systems: An ADRC approach

This article deals with the control of a class of robotic systems with constant input time delay through the Active Disturbance Rejection paradigm, by means of Generalized Proportional Integral observers. The system is represented as a linear perturbed system, whose lumped disturbance input is estimated and then compensated by an Extended State Observer-Based Control, which is implemented on a predictor scheme for the time delay compensation. A complete Lyapunov Krasovskii functional was used to perform the stability analysis, leading to an ultimate bound trajectory tracking error. The proposal is tested and validated on a two degrees of freedom robotic manipulator.

Realization of Nonlinear Time-Delay Input–Output Equations

In this letter the problem of transforming a nonlinear multi-input multi-output time-delay control system, described by a set of higher order functional differential equations relating system inputs and outputs, into a set of first order functional differential equations, is studied. The globally linearized system equations are described in terms of polynomials in a delay operator and derivative operator. The Euclidean left division of polynomials is used to compute the basis of a certain free submodule of differential 1-forms. The integrability of the submodule is proved to be necessary and sufficient for the solvability of the problem.

Underactuated Stratospheric Airship Trajectory Control Using an Adaptive Integral Backstepping Approach

This paper deals with trajectory tracking control for an underactuated stratospheric airship in the presence of model uncertainties and external disturbances. An adaptive integral backstepping trajectory control is designed from the underactuated airship nonlinear dynamics model. The proposed controller has a two-level structure. A low-level controller based on nonlinear adaptive integral backstepping method stabilizes the attitude and velocity of the airship, whereas a high-level controller performs guidance and trajectory tracking task. Two underactuated cases of zero lateral control force and zero roll moment input are studied. Meanwhile a control allocation component based on active set with weight least square algorithm is put into the low-level controller, to find the optimal control surfaces and thrust inputs under constraints of actuator saturation. By using Lyapunov theory the closed-loop trajectory control system is proven to be globally asymptotically stable. Finally, simulation results show that the proposed adaptive integral backstepping controller can follow the reference even in the presence of parametric uncertainties and external disturbances and time delay inputs.

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

SummaryIn this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.

Input Time Delay Margin in Event-Triggered Consensus of Multiagent Systems.

In this paper, the event-triggered consensus problem of multiagent systems with input time delay is investigated. First, the normal event-triggered control scheme containing the input time delay is introduced to reduce the number of communication. Then the following results are achieved: 1) the procedure of setting parameters is carefully formulated for the event-triggered control scheme; 2) the precise input time delay margin is calculated for the event-triggered consensus of the multiagent systems; 3) a more general condition of constructing event-triggered functions is derived to exclude the Zeno behavior; 4) the self-triggered control scheme is further applied to avoid the continuous measurement; and 5) the observer-based control scheme is also utilized to tackle the problem of unmeasurable state. Finally, the correctness and the effectiveness of these results are demonstrated by numerical simulations.

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

SummaryThe global stabilization problem for a class of stochastic time‐delay nonlinear systems with stochastic‐input‐to‐state‐stable–like conditions is investigated. Different from the existing results, the nonlinear growing conditions are more general, and the existences of the state and input time delays make the work more challenging in the control design and stability analysis. By introducing an appropriate gain‐scaling method and using a homogeneous domain control strategy, a delay‐independent controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability. Examples are given to show the validness of the proposed method.

A hybrid elman neural network predictor for time series prediction

Artificial Neural Networks have become popular in the world of prediction and forecasting due to their nonlinear nonparametric adaptive-learning property. They become an important tool in data analysis and data mining applications. Elman neural network due to its recurrent nature and dynamic processing capabilities can perform the prediction process with a good range of accuracy. In this paper an Elman recurrent Neural Network is hybridised with a time delay called a tap delay line for time series prediction process to improve its performance. The Elman neural network with the time delay inputs is trained tested and validated using the solar sun spot time series data that contains the monthly mean sunspot numbers for a 240 year period having 2899 data values. The results confirm that the proposed Elman network hybridised with time delay inputs can predict the time series with more accurately and effectively than the existing methods.

Block-oriented identification of non-linear systems with input time delay in presence of measurement noise: a Laguerre–neural network approach

This paper proposes an approach for identification of non-linear dynamic systems with input time delay into the block-oriented Wiener model in the presence of measurement noise. The model comprised a linear dynamic subsystem (LDS) at the input side that is cascaded with a non-linear static subsystem (NSS). The LDS comprised Laguerre filters, whereas the NSS is constructed using committee neural networks (CNNs). The Laguerre filter compensates for the input time delay, whereas the CNN finds an appropriate non-linear mapping between its input and output with the useful property of the measurement noise attenuation. The parameters of the Laguerre filters as well as those of the CNN are determined using offline training algorithms. In order to find the optimal values of the weights of the CNN, a noise analysis is conducted. The proposed method is applied to a simulated continuous-stirred tank reactor (CSTR) with input time delay and measurement noise. The results indicate substantial benefits of the proposed method compared with the similar methods proposed in the literature for system identification.

Further results on adaptive state feedback stabilization for a class of stochastic feedforward nonlinear systems with time delays

This paper further discusses the state feedback stabilization for stochastic high-order feedforward nonlinear systems with input time delay. By constructing the appropriate Lyapunov–Krasovskii functional, and using the variable transformation technique and the homogeneous domination idea, a state feedback controller is designed to ensure that the closed-loop system will be globally asymptotically stable in probability. Finally, an example is given to verify the effectiveness of the obtained analytical results.

Discrete-Time Predictor Feedback for Consensus of Multiagent Systems With Delays

This note develops a discrete-time predictor feedback control scheme for continuous-time multiagent systems with input and communication time delays. With measurement of locally available relative state signals among neighbored agents, the controller is able to achieve consensus for a large variety of linear open-loop agent dynamics, including exponentially unstable systems. Moreover, the new design can deal with arbitrarily large time delays in some special scenarios. The feature of discrete-time and relative state measurement substantially saves implementation cost compared with the existing methods in the literature. Numerical simulation demonstrates the effectiveness of the proposed theoretical design.

The stability analysis of nonlinear switched systems with time delay in input and states with stable and unstable subsystems

Time delay and sampling appear in many industrial systems. It is irrefutable that applying measurement delay with controls can cause the sampling of control laws with the delay in the behavior of nonlinear control systems. As a result, in this paper, the stability of nonlinear time varying switched system with time delay in the input and the states of the system is studied in two modes by a new Lyapunov Krasovskii functional (LKF). Firstly, if all subsystems of the proposed nonlinear switched system with time delay are stable. Then, if some of the subsystems of the proposed switched system are unstable. This paper is organized in two steps. In the first step, the upper bound for the time delay under sufficient conditions in the nonlinear systems with time delay in input and states is obtained. In this step, the Uniformly Globally Asymptotic Stability is proved for nonlinear systems with the presence of time delay. In the second step, with a proper Lyapunov Krasovskii functional, the global exponential stability of the proposed switched system is proved. Also, finally a proper observer is designed for our proposed switched system in two stable and unstable modes.