Time-varying Communication Delays Research Articles

Observer-based input-to-state stabilization of networked control systems with large uncertain delays

We consider output-feedback predictor-based stabilization of networked control systems with large unknown time-varying communication delays. For systems with two networks (sensors-to-controller and controller-to-actuators), we design a sampled-data observer that gives an estimate of the system state. This estimate is used in a predictor that partially compensates unknown network delays. We emphasize the purely sampled-data nature of the measurement delays in the observer dynamics. This allows an efficient analysis via the Wirtinger inequality, which is extended here to obtain exponential stability. To reduce the number of sent control signals, we incorporate the event-triggering mechanism. For systems with only a controller-to-actuators network, we take advantage of continuously available measurements by using a continuous-time predictor and employing a recently proposed switching approach to event-triggered control. For systems with only a sensors-to-controller network, we construct a continuous observer that better estimates the system state and increases the maximum output sampling, therefore, reducing the number of required measurements. A numerical example illustrates that the predictor-based control allows one to significantly increase the network-induced delays, whereas the event-triggering mechanism significantly reduces the network workload.

Event-triggered consensus control for leader-following multi-agent systems with time-varying delays

In this paper, we perform the delay robustness analysis of an event-triggered consensus protocol for a leader-following multi-agent system with time-varying communication delays, and focus on designing the consensus protocol as well as event-triggering conditions in order that all followers can track the state of the leader at low communication/controller-updating costs. The leader has unidirectional communication connections to at least one follower. The local communication structure among followers is characterized by an undirected connected graph. It is shown that the maximum allowable time delay depends on the largest eigenvalue of the interaction graph Laplacian, event-checking period and one protocol parameter. The relationship between the maximum allowable time delay and the change rate of time delays is also characterized. Finally, numerical examples are given to demonstrate the effectiveness of the proposed consensus protocol.

Task-Space Synchronization of Networked Mechanical Systems With Uncertain Parameters and Communication Delays

This paper addresses the adaptive synchronization problem of networked mechanical systems in task space with time-varying communication delays, where both kinematic and dynamic uncertainties are considered and the information flow in the networks is represented by a directed graph. Based on a novel coordination auxiliary system, we first extend existing feedback architecture to achieve synchronization of networked mechanical systems in task space with slow-varying delays. Given that abrupt turns arise for the delays sometimes, we then propose a delay-independent adaptive synchronization control scheme which removes the requirement of the slow-varying condition. Both of the two control schemes are established with time-domain approaches by using Lyapunov-Krasovskii functions. Simulation results are provided to demonstrate the effectiveness of the proposed control schemes.

Group Consensus of Second-Order Dynamic Multi-Agent Systems with Time-Varying Communication Delays and Directed Networks

AbstractThis paper studies the group consensus problem for second-order multi-agent dynamic systems with time-varying delays, where the agents in a network may reach one more consistent values asymptotically. The fixed network topology is in case of being directed and weakly connected. Based on algebraic graph theory and Lyapunov function approach, we propose some sufficient conditions for reaching group consensus. All the results are presented in the form of linear matrix inequalities(LMIs). A simulation example is provided to demonstrate the effectiveness of the theoretical analysis.

Decentralized attitude synchronization tracking control for multiple spacecraft under directed communication topology

This paper studies the attitude synchronization tracking control of spacecraft formation flying with a directed communication topology and presents three different controllers. By introducing a novel error variable associated with rotation matrix, a decentralized attitude synchronization controller, which could obtain almost global asymptotical stability of the closed-loop system, is developed. Then, considering model uncertainties and unknown external disturbances, we propose a robust adaptive attitude synchronization controller by designing adaptive laws to estimate the unknown parameters. After that, the third controller is proposed by extending this method to the case of time-varying communication delays via Lyapunov–Krasovskii analysis. The distinctive feature of this work is to address attitude coordinated control with model uncertainties, unknown disturbances and time-varying delays in a decentralized framework, with a strongly connected directed information flow. It is shown that tracking and synchronization of an arbitrary desired attitude can be achieved when the stability condition is satisfied. Simulation results are provided to demonstrate the effectiveness of the proposed control schemes.

Delay-dependent Stability Analysis of Microgrid with Constant and Time-varying Communication Delays

This article describes the procedure to develop a cyber physical model of a microgrid considering the influence of constant and time-varying communication delays. The microgrid central controller transmits information through an open communication network that imposes certain constraints. One of the major constraints is communication delays, which affect the dynamic performance of the system. These delays may be constant or time varying. The impact of these time delays on the stability is addressed by finding an index called the time-delay margin. This article proposes an analytical method to determine the delay margin of a distributed generation based microgrid with constant and time-varying delays. In the case of constant time delays, the transcendental characteristic equation of the proposed microgrid model is transformed into a polynomial. The real roots of the polynomial coincide exactly with the imaginary roots of the characteristic equation, which decides the delay-dependent stability of the system. For the case of time-varying delays, a sufficient condition that verifies the asymptotic stability of the system is presented in this article. The delay margin values are theoretically calculated for different sets of microgrid central controller gains, and their accuracy is validated by simulation studies.

Piecewise Affine Networked Control Systems

This paper addresses the exponential stability of piecewise affine networked control systems (PWANCS), where a continuous-time piecewise affine (PWA) plant is in feedback with a PWA controller over a communication network. The main contribution of this paper is to propose sufficient Krasovskii-based stability conditions for PWANCS. Furthermore, the problem of finding a lower bound on the maximum network-induced delay that guarantees exponential stability is cast as a convex optimization program in terms of linear matrix inequalities. The network consists of a sample-and-hold device with an unknown and time-varying sampling frequency, and nonideal communication links with data-packet losses and uncertain time-varying communication delays.

Predictor-based networked control under uncertain transmission delays

We consider state-feedback predictor-based control of networked control systems with large time-varying communication delays. We show that even a small controller-to-actuators delay uncertainty may lead to a non-small residual error in a networked control system and reveal how to analyze such systems. Then we design an event-triggered predictor-based controller with sampled measurements and demonstrate that, depending on the delay uncertainty, one should choose various predictor models to reduce the error due to triggering. For the systems with a network only from a controller to actuators, we take advantage of the continuously available measurements by using a continuous-time predictor and employing a recently proposed switching approach to event-triggered control. By an example of an inverted pendulum on a cart we demonstrate that the proposed approach is extremely efficient when the uncertain time-varying network-induced delays are too large for the system to be stabilizable without a predictor.

Consensus of single integrator multi-agent systems with directed topology and communication delays

In this paper, a distributed control scheme has been developed for consensus of single integrator multi-agent systems with directed fixed communication topology for arbitrarily large constant, time-varying or distributed communication delays. It is proved that the closed loop control system can reach consensus with an exponential convergence rate if and only if the topology is quasi-strongly connected. Simulation results are also provided to demonstrate the effectiveness of the proposed controller.

Dynamic output-feedback-based [formula omitted] design for networked control systems with multipath packet dropouts

This paper is devoted to the stability of networked control system with time-varying delays. A dynamic output feedback controller is designed to realize H∞ control of the networked system with the H∞ performance attenuation level γ. Since the frequent occurrence of packet dropouts and communication delays which all could degrade the performance of system or even cause system instability, we consider the networked control system with both input and output packet dropouts and bidirectional time-varying communication delays. Some sufficient conditions are obtained to grantee asymptotic stability of the system in view of Schur complement and singular values decomposition of matrix. Afterwards, intensive analysis is carried out to present the existence of admissible dynamic output feedback controller by applying an appropriate weighting method which introduces slack matrices variables. What is more, a numerical example is presented to illustrate the validity of theoretical analysis.

Distributed power control for DERs based on networked multiagent systems with communication delays

This paper develops a distributed secondary cooperative scheme for the current-controlled PWM inverters (CC-PWMIs) based on networked multiagent systems that can guarantee the accurate power sharing among the distributed energy resource (DER) units in microgrids. With the assumption that the communication networks are local, time-varying, and with low bandwidth, two distributed secondary controllers are designed such that all DERs in the microgrid can share their active and reactive powers accurately on the conditions of both fixed and switching topologies with time-varying communication delays. Moreover, delay-dependent sufficient conditions are obtained by using the Lyapunov–Krasovskii stable analysis method. The proposed controllers, allowing each DER unit to receive the current and active/reactive load information intermittently from its neighboring DERs, are then fully distributed. The effectiveness of the proposed control methodology is verified by the simulation of a low-voltage microgrid test system in the MATLAB/SimPowerSystems Toolbox.

Compensating the Effect of Communication Delay in Client-Server--Based Shared Haptic Virtual Environments

Shared haptic virtual environments can be realized using a client-server architecture. In this architecture, each client maintains a local copy of the virtual environment (VE). A centralized physics simulation running on a server calculates the object states based on haptic device position information received from the clients. The object states are sent back to the clients to update the local copies of the VE, which are used to render interaction forces displayed to the user through a haptic device. Communication delay leads to delayed object state updates and increased force feedback rendered at the clients. In this article, we analyze the effect of communication delay on the magnitude of the rendered forces at the clients for cooperative multi-user interactions with rigid objects. The analysis reveals guidelines on the tolerable communication delay. If this delay is exceeded, the increased force magnitude becomes haptically perceivable. We propose an adaptive force rendering scheme to compensate for this effect, which dynamically changes the stiffness used in the force rendering at the clients. Our experimental results, including a subjective user study, verify the applicability of the analysis and the proposed scheme to compensate the effect of time-varying communication delay in a multi-user SHVE.

Finite interval tracking algorithm for nonlinear multi-agent systems with communication delays

ABSTRACTWe propose an iterative learning control (ILC) tracking strategy to solve the tracking problem of multi-agent systems with nonlinear dynamics and time-varying communication delays. The distributed tracking strategy, in which each tracking agent only utilises its own and neighbours’ information, enables the tracking agents successfully track a maneuvering target in a finite time interval although with presence of time delays. Compared with the existing related work, the quantitative relationship between the boundary of tracking errors and the estimation of time delays is derived. Furthermore, in many practical control problems, identical initialisation condition may not be satisfied, which is called initial-shift problem. Hence, a forgetting factor is introduced to deal with that problem. It is proved that the presented results are effective via conducting numerical examples.

Asynchronous Consensus of Multiple Double-Integrator Agents With Arbitrary Sampling Intervals and Communication Delays

This paper addresses asynchronous consensus problems of multiple double-integrator agents with discontinuous information transmission, where each agent receives its neighbors' state information at discrete instants determined by its own clock. A novel consensus protocol is proposed based on continuous information of each agent itself and sampled information of each agent's neighbors. By using nonnegative matrix theory and graph theory, we prove that the consensus problem is solvable in the asynchronous sampled-data setting without or with time-varying communication delays, if the union of the effective communication topology across any time interval with some given length contains a spanning tree. Remarkably, the sampling intervals and communication delays are allowed to be arbitrarily large yet bounded. By proposing a modified protocol based on the idea of pinning control, we extend the existing result to the desired consensus problem. Numerical examples are finally provided to validate the theoretical results.

L-infinity event-triggered networked control under time-varying communication delay with communication cost reduction

A novel L-infinity event-triggered networked control scheme under time-varying communication delay is proposed. The control objective is to maintain L-infinity input to state stability while minimizing triggering and communication overhead under uncertainties. The event triggering is asynchronous for satisfying each subsystem performance requirement individually, and the event triggering strategy is adaptive to the variable communication delay to reduce the communication cost without degrade of system performance (input to state stability). The relations between the communication delay and the event triggering conditions are investigated and related bounds are derived analytically. An example of electrical power system frequency control task is used to illustrate the effectiveness of the proposed scheme in terms of achieving identical control performance with lower communication overhead.

Consensus of networked multi-agent systems with diverse time-varying communication delays

In this paper, the problem of consensus for discrete-time networked multi-agent systems (NMASs) with a directed topology and diverse time-varying communication delays is investigated. By introducing the networked predictive control scheme, the predictions of states at current time, instead of available outdated states, are exploited to design a distributed consensus protocol, which compensates for communication delays actively. For NMASs with identical linear agents and bounded time-varying communication delays, necessary and sufficient conditions of the consensus are provided. Numerical simulations are given to compare the proposed networked predictive control method with the standard non-predictive way, and demonstrate the effectiveness of theoretical results.

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

This article is concerned with event-triggered fuzzy control design for a class of discrete-time nonlinear networked control systems (NCSs) with time-varying communication delays. Firstly, a more general mixed event-triggering scheme (ETS) is proposed. Secondly, considering the effects of the ETS and communication delays, based on the T-S fuzzy model scheme and time delay system approach, the original nonlinear NCSs is reformulated as a new event-triggered networked T-S fuzzy systems with interval time-varying delays. Sufficient conditions for uniform ultimately bound (UUB) stability are established in terms of linear matrix inequalities (LMIs). In particular, the quantitative relation between the boundness of the stability region and the triggering parameters are studied in detail. Thirdly, a relative ETS is also provided, which can be seen as a special case of the above proposed mixed ETS. As a difference from the preceding results, sufficient conditions on the existence of desired fuzzy controller are derived to ensure the asymptotic stability of the closed-loop system with reduced communication frequency between sensors and controllers. Moreover, a co-design algorithm for simultaneously determining the gain matrices of the fuzzy controller and the triggering parameters is developed. Finally, two illustrative examples are presented to demonstrate the advantage of the proposed ETS and the effectiveness of the controller design method.

Containment consensus with measurement noises and time-varying communication delays**Project supported by the National Natural Science Foundation of China (Grant No. 11102019), the Aeronautical Science Foundation of China (Grant No. 2013ZC72006), and the Research Foundation of Beijing Institute of Technology, China.

In this paper, we consider the containment consensus control problem for multi-agent systems with measurement noises and time-varying communication delays under directed networks. By using stochastic analysis tools and algebraic graph theory, we prove that the followers can converge to the convex hull spanned by the leaders in the sense of mean square if the allowed upper bound of the time-varying delays satisfies a certain sufficient condition. Moreover, the time-varying delays are asymmetric for each follower agent, and the time-delay-dependent consensus condition is derived. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

State consensus for hierarchical multi-agent dynamical systems with inter-layer communication time delay

This paper studies the consensus problem for hierarchical multi-agent dynamical systems with the inter-layer communication time-varying delay. This paper firstly finds a mathematical model for the hierarchical multi-agent dynamical systems with inter-layer communication time-varying delay, and then delay-dependent sufficient conditions are proposed for reaching a consensus based on Lyapunov function approach. A Lyapunov function is introduced to quantify the total disagreement among the nodes of a hierarchical network. All the results are in the form of linear matrix inequalities (LMIs). Simulation results are provided to verify the effectiveness of the proposed condition for agreement in networks with inter-layer communication time-delay.

Four-Channel Teleoperation with Time-Varying Delays and Disturbance Observers

This paper addresses the robust stability of teleoperated systems under the four-channel architecture, affected by time-varying communication delays and using disturbance observers. It is based on our previous work which provides a framework for robust stability against delays with bounded variation and a bounded time-derivative, using structured singular values (SSV). The main new feature here is the inclusion of disturbance observers (DOBs). The DOB concept is well-documented and relevant to many applications, since only position (but not force) measurements are usually available. In this paper, we adapt two DOBs (master and slave) to our generic framework, by representing them as stable, fast filters affected by the uncertainty in the plant modelling. Our main result is an SSV test to verify robust stability. The simulation results confirm the usefulness of this approach.