Presence Of Time-varying Delays Research Articles

A delay-dependent anti-windup compensator for wide-area power systems with time-varying delays and actuator saturation

In this paper, a delay-dependent anti-windup compensator is designed for wide-area power systems to enhance the damping of inter-area low-frequency oscillations in the presence of time-varying delays and actuator saturation using an indirect approach. In this approach, first, a conventional wide-area damping controller is designed by using H&#x221E output feedback with regional pole placement approach without considering time-varying delays and actuator saturation. Then to mitigate the effect of both time-varying delays and actuator saturation, an add-on delay-dependent anti-windup compensator is designed. Based on generalized sector conditions, less conservative delay-dependent sufficient conditions are derived in the form of a linear matrix inequality &#x0028 LMI &#x0029 to guarantee the asymptotic stability of the closed-loop system in the presence of time-varying delays and actuator saturation by using Lyapunov-Krasovskii functional and Jensen integral inequality. Based on sufficient conditions, the LMI-based optimization problem is formulated and solved to obtain the compensator gain which maximizes the estimation of the region of attraction and minimizes the upper bound of L2-gain. Nonlinear simulations are performed first using MATLAB &#x002F Simulink on a two-area four-machine power system to evaluate the performance of the proposed controller for two operating conditions, e.g., 3-phase to ground fault and generator 1 terminal voltage variation. Then the proposed controller is implemented in real-time on an OPAL-RT digital simulator. From the results obtained it is verified that the proposed controller provides sufficient damping to the inter-area oscillations in the presence of time-varying delays and actuator saturation and maximizes the estimation of the region of attraction.

Affine formation maneuver tracking control of multiple second-order agents with time-varying delays

This paper considers an affine maneuver tracking control problem for leader-follower type second-order multi-agent systems in the presence of time-varying delays, where the interaction topology is directed. Using the property of the affine transformation, this paper gives the sufficient and necessary conditions of achieving the affine localizability and extends it to the second-order condition. Under the $(n+1)$-reachable condition of the given $n$-dimensional nominal formation with $n+1$ leaders, a formation of agents can be reshaped in arbitrary dimension by only controlling these leaders. When the neighboring positions and velocities are available, a formation maneuver tracking control protocol with time-varying delays is constructed with the form of linear systems, where the tracking errors of the followers can be specified. Based on Lyapunov-Krasovskii stability theory, sufficient conditions to realize affine maneuvers are proposed and proved, and the unknown control gain matrix can be solved only by four linear matrix inequalities independent of the number of agents. Finally, corresponding simulations are carried out to verify the theoretical results, which show that these followers can track the time-varying references accurately and continuously.

Estimation and disturbance rejection performance for fractional order fuzzy systems

This paper gives attention to the issues of output tracking and disturbance rejection performance for a class of fractional order Takagi–Sugeno fuzzy systems in the presence of time-varying delay and unknown external disturbances. More specifically, a new configuration of a fractional order modified repetitive controller that incorporates an improved equivalent-input-disturbance estimator and gain fluctuations in its design is proposed to perform disturbance rejection for the addressed system. By introducing a continuous frequency distributed equivalent model and using the Lyapunov–Krasovskii stability theory, a new set of sufficient conditions ensuring robust asymptotic stability of the resulting closed-loop system is obtained in the framework of linear matrix inequalities. Finally, a numerical example is presented to validate the developed theoretical results, where it is shown that the obtained conditions could force the considered system output to exactly track the given any kind of reference signal by compensating the unknown external disturbance.

Adaptive output-feedback synchronisation of electromechanical systems under time-varying communication delays

ABSTRACT This paper deals with the position synchronisation problem for a class of electromechanical systems, which can be represented by Euler–Lagrange equations, where velocities of agents are not measurable. The agents share their position errors and filter-output signals, instead of actual velocity errors, over a directed communication network, in the presence of time-varying delay. Besides, balanced communication topology is also not required. The proposed adaptive control mechanism ensures the position synchronisation among agents, as well as the tracking of each agent to given desired trajectory, under the effects of time-varying communication delay, parametric uncertainty and unknown external disturbance, simultaneously. By employing a classical Lyapunov approach and Lyapunov–Krasovskii functionals, it is concluded that the suggested control structure yields semi-global asymptotic convergence of all closed-loop errors, including synchronisation errors. The simulation results, on a six-marine vessel network system, are presented to validate the feasibility of the proposed control scheme.

Finite-time consensus of input delayed multi-agent systems via non-fragile controller subject to switching topology

Abstract This paper focuses on the problem of finite-time consensus of linear multi-agent systems with input time-varying delay by employing a non-fragile control scheme, where the network topology of the communication process among agents is subject to a switching directed graph. The main intention of this paper is to propose a non-fragile controller design protocol that guarantees the finite-time stability of the resulting closed-loop system even in the presence of time-varying delay in the input channel. Sufficient conditions for the solvability of such a problem are obtained by using the Lyapunov–Krasovskii stability theory, the algebraic graph theory and some integral inequalities. Based on the obtained conditions, an explicit expression of the desired non-fragile control gain matrix is then presented. Finally, an illustrative example is given to exhibit the applicability and effectiveness of the proposed finite-time consensus control design method.

Distributed Receding Horizon Control of Constrained Networked Leader–Follower Formations Subject to Packet Dropouts

A novel receding horizon control scheme is presented in this paper to manage networked leader–follower formation control problems in the presence of time-varying delay and data loss (measurement and feedback packet dropouts) occurrences on the communication and feedback channels. One of the main novelties of the proposed paradigm relies on the use of reachability analysis concepts involving the capability to combine sequences of predecessor sets with polyhedral piecewise state-space partitions. The predecessor sets are here derived offline by taking into account the prescribed state and input constraints, the interconnected nature of the system and the time delay induced by the network latency. They are used online to compute admissible and optimal control actions via a distributed receding horizon computational paradigm. Feasibility, uniformly ultimate boundedness and constraints satisfaction are formally proved regardless of any bounded time delays.

Robust leader-following output regulation of uncertain multi-agent systems with time-varying delay

In this paper, the robust analysis and design of leader-following output regulation for multi-agent systems described by general linear models is given in presence of time-varying delay and model uncertainty. To this aim, a new regulation protocol for the closed-loop multi-agent system under a directed graph is proposed. An important specification of the proposed protocol is to guarantee the leader-following output regulation for uncertain multi-agent systems with both stable and unstable agents. Since many signals can be approximated by a combination of the stationary and ramp signals, the presented results work for adequate variety of the leaders. The analysis and design conditions are presented in terms of certain matrix inequalities. The method proposed can be used for both stationary and ramp leaders. Simulation results are presented to show the effectiveness of the proposed method.

Consensus Tracking for Teleoperating Cyber-physical System

In this paper, we investigate the consensus tracking problem for teleoperating cyber-physical system (TCPS) under time-varying delay and actuator saturation constraints. Due to the introduction of communication network, variable propagation time delays are considered in cyber element. In addition, actuator saturation problem is investigated in physical element, which is caused by the physical restrictions on robots. Then, a novel distributed consensus tracking controller is proposed in the presence of time-varying delay and actuator saturation. Meanwhile, sufficient conditions are provided to show that the consensus tracking controller can stabilize the master-slave TCPS. Finally, simulations and experiments are performed to validate our proposed results. It is shown that the consensus controllers can guarantee the asymptotic stability of single-master-multi-slave TCPS.

Stabilisation for teleoperation systems with sampled-data information feedback

ABSTRACTThis paper considers sampled-data control of bilateral teleoperation systems in the presence of time-varying delay. The assumptions on continuous-time position/force signal transmission are removed and the proposed control strategy is more realistic. By constructing a novel delay-dependent Lyapunov functional, the relationship is established among the control parameters, the delay bounds and the upper bounds of the sampling periods. The tracking performance can be achieved with the designed controller. Simulations and experiments are both provided to verify the effectiveness and benefits of the proposed approach.

Prediction-based control of LTI systems with input and output time-varying delays

The stability of a prediction-based controller is studied in presence of time-varying delays both in the input and in the output. Thanks to the reduction method and a Lyapunov–Krasovskii analysis, stability conditions are derived. A comparison is also made between the single input delay and single output delay cases. It is shown that this method can be applied to stabilize output delay systems without restriction on the delay rate. The results are illustrated numerically on a double integrator.

Design, analysis and performance evaluation of a third order distributed protocol for platooning in the presence of time-varying delays and switching topologies

This paper is concerned with the problem of designing a decentralized consensus protocol for platooning of non-identical vehicles in the presence of heterogeneous time-varying communication delays. The proposed control protocol makes use of a state feedback and to this aim drivetrain dynamics are modeled as third-order linear systems. Necessary and sufficient conditions for convergence and exponential stability, derived by using an appropriate Krasovskii functional, demonstrate the ability of the platoon in reaching the required regime with an exponentially bounded behavior. The proposed LMI-based approach allows to estimate both delay margin and decay rate. Moreover, convergence is proven under switching communication network topologies by means of a Lyapunov-Razumikhin function, and the assessment of a string stable behavior has been also theoretically investigated. High-fidelity simulations with Plexe show the effectiveness of the theoretical results in different driving conditions and in the presence of external disturbances and communication impairment. Different communication channel models are used in the validation stage to further prove robustness of the proposed methodology with respect hard delay and packets losses.

A Wide-Area Damping Controller Considering Network Input and Output Delays and Packet Drop

This paper presents the development of a novel synchrophasor measurement-based wide-area centralized damping controller to improve the stability of a power system in presence of time-varying delay and packet dropout in the communication network. Two different strategies have been adopted to deal with the input and the output delays. In the first strategy, the system output delay has been compensated by predicting the dynamics of the signals. In the second strategy, a wide-area controller, based on delay-range-dependent stability criteria, has been designed for the time-varying delays in the input signals. The network induced delays and the maximum amount of the consecutive packet dropout are assumed to be bounded. The controller parameters are optimally obtained using a trace minimization of certain matrix variables by formulating Linear Matrix Inequalities problem. The system has been identified by applying Prediction-Error-Minimization methodology, and proposing a new type of probing test input-signal. A new methodology has been proposed to obtain the feedback channel latency in real time. The proposed methodology has been simulated on New England 39-bus test system and also validated on a hardware testbed consisting of physical Phasor Measurement Units connected, in feedback loop, to a Real-Time Digital Simulator.

Second-Order Containment Control of Multiagent Systems in the Presence of Uncertain Topologies with Time-Varying Delays

This paper considers the containment control problem of second-order multiagent systems in the presence of time-varying delays and uncertainties with dynamically switching communication topologies. Moreover, the control algorithm is proposed for containment control, and the stability of the proposed containment control algorithm is studied with the aid of Lyapunov-Krasovskii function when the communication topology is jointly connected. Some sufficient conditions in terms of linear matrix inequalities (LMIs) are provided for second-order containment control with multiple stationary leaders. Finally, simulations are given to verify the effectiveness of the obtained theoretical results.

Distributed formation control for teleoperating cyber-physical system under time delay and actuator saturation constrains

Teleoperating Cyber-Physical System (TCPS) is referred as a new generation of networked teleoperating system. Question of how to enable master operator and slavers to collaborate for sensing and control is largely unexplored. This paper is concerned with a distributed formation control problem for multi-slave TCPS under time delay and actuator saturation constraints. We first develop a min-weighted rigid graph based topology optimization scheme to reduce the redundancy of communication links in slavers, such that the information fusion can be simplified in the formation controller design. The sufficient conditions for stability are presented to show that the formation controllers can stabilize the master-slave TCPS in the presence of time-varying delay and actuator saturation constraints. Finally, to show the validity of our proposed result, both simulations and experiments are performed. It is demonstrated that the topology optimization reduces the redundancy of communication links in slave site at the expense of increased convergence time, while the formation controllers guarantee global asymptotic stability of teleoperation systems subjected to time-varying delay and actuator saturation constraints.

Stability Control of Force-Reflected Nonlinear Multilateral Teleoperation System under Time-Varying Delays

A novel control algorithm based on the modified wave-variable controllers is proposed to achieve accurate position synchronization and reasonable force tracking of the nonlinear single-master-multiple-slave teleoperation system and simultaneously guarantee overall system’s stability in the presence of large time-varying delays. The system stability in different scenarios of human and environment situations has been analyzed. The proposed method is validated through experimental work based on the 3-DOF trilateral teleoperation system consisting of three different manipulators. The experimental results clearly demonstrate the feasibility of the proposed algorithm to achieve high transparency and robust stability in nonlinear single-master-multiple-slave teleoperation system in the presence of time-varying delays.

Convergence Rate for Discrete-Time Multiagent Systems With Time-Varying Delays and General Coupling Coefficients.

Multiagent systems (MASs) are ubiquitous in our real world. There is an increasing attention focusing on the consensus (or synchronization) problem of MASs over the past decade. Although there are numerous results reported on the convergence of a discrete-time MAS based on the infinite products of matrices, few results are on the convergence rate. Because of the switching topology, the traditional eigenvalue analysis and the Lyapunov function methods are both invalid for the convergence rate analysis of an MAS with a switching topology. Therefore, the estimation of the convergence rate for a discrete-time MAS with time-varying delays remains a difficult problem. To overcome the essential difficulty of switching topology, this paper aims at developing a contractive-set approach to analyze the convergence rate of a discrete-time MAS in the presence of time-varying delays and generalized coupling coefficients. Using the proposed approach, we obtain an upper bound of the convergence rate under the condition of joint connectivity. In particular, the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients, which have been widely applied in the existing works on this topic. As an application of the main results, we will show that the classical Vicsek model with time delays can realize synchronization if the initial topology is connected.

Bilateral Control of Teleoperation Systems With Time Delay

In this paper, we address the stability and tracking control problem of constant input-based bilateral teleoperation systems in the presence of time-varying delay. The teleoperation algorithm comprises delayed position and position–velocity signals with undelayed position and velocity signals of the master and slave manipulators. An adaptation law is employed locally to learn and compensate uncertain parameters associated with the gravity loading vector of the master and slave manipulators. Lyapunov–Krasovskii functions are employed to derive stability and tracking properties of the position, velocity, and synchronizing error of the master and slave manipulator. These properties are established in the presence of symmetrical and unsymmetrical time-varying delays under constant input interaction forces between human and master manipulator and between environment and slave manipulator. Finally, evaluation results are presented to illustrate the theoretical development of this paper.

Consensus with guaranteed convergence rate of high-order integrator agents in the presence of time-varying delays

This paper aims to study the consensus problem in directed networks of agents with high-order integrator dynamics and fixed topology. It is considered the existence of non-uniform time-varying delays in the agents control laws for each interaction between agents and their neighbours. Based on Lyapunov–Krasovskii stability theory and algebraic graph theory, sufficient conditions, in terms of linear matrix inequalities, are given to verify if consensus is achieved with guaranteed exponential convergence rate. The efficiency of the proposed method is verified by numerical simulations. The simulations reveal that the conditions established in this work outperformed the similar existing ones in all numerical tests accomplished in this paper.

Dynamics of linear delayed systems with decaying disturbances

Dynamical systems in the real world are always subject to various disturbances. This paper studies the dynamics of linear delayed systems with decaying disturbances, both discrete- and continuous-time cases are considered. It is first shown that if an unforced linear system is exponentially stable, then the disturbed system has a dynamical property like exponential stability provided that the disturbance decays at an exponential rate, and has a dynamical property like asymptotic stability provided that the disturbance asymptotically approaches zero. These results are then applied to block triangular systems in the presence of time-varying delays, leading to criteria for checking the stability properties of this class of systems by considering diagonal blocks of system matrices. Particularly, a block triangular system is exponentially stable if and only if each system described by the diagonal blocks of system matrices is exponentially stable. Finally, a numerical example is presented to illustrate the theoretical results.

Generic Approach to Stability Under Time-Varying Delay in Teleoperation: Application to the Position-Error Control of a Gantry Crane

In this paper, we develop a generic approach for modeling a teleoperation setup, as a negative single feedback loop containing a linear time-invariant block and an uncertain time-varying delay. It is not based on specific dynamics of masters and slaves, neither on any control architecture. The main added value of the proposed approach is the possibility of deriving frequency-domain conditions for robust stability in the presence of time-varying delays and parametric uncertainties. To address stability, we choose a primitive result providing a bound of certain delay subsystem. We combine this, with input-output stability criteria and μ-analysis and synthesis techniques, to reach a procedure based on the structured singular value providing less conservative results. Finally, our approach is presented within a suggested flowchart that helps the designer to manage the control parameter ranges and facilitates the gradual achievement of stability, robust stability, and performance properties. As a case study, we consider the Internet-based teleoperation of a gantry crane by means of the position-error control architecture. We have also obtained actual delay bounds appearing with UDP protocol for different Internet locations. Simulation and experimental results confirm the robust performance of the teleoperation system in terms of stability and tracking behavior.