Nonuniform Time-varying Delays Research Articles

Distributed observer-based consensus tracking for nonlinear MASs with nonuniform input delays and disturbances

In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.

Distributed H∞ consensus of multiagent systems with nonuniform time-varying communication delays

This article addresses the distributed H∞ consensus control problem of general linear multiagent systems with time-varying communication delays and external disturbances. The communication network is subject to arbitrarily bounded and nonuniform time-varying communication delays. Based on the leader-following control mode, a novel distributed state feedback control protocol is proposed to achieve state consensus over undirected fixed topology while guaranteeing a prescribed disturbance rejection objective. By means of Lyapunov analysis and some inequality techniques, admissible upper bounds of nonuniform time-varying delays and H∞ consensus criteria are acquired. As opposed to the existing result for the similar problem, our result has its distinct advantages in that it can accommodate arbitrarily bounded nonuniform time-varying communication delays, and has greater delay margin and better consensus performance. Moreover, the consensus problem for the multiagent systems over connected undirected switching topology is discussed. Finally, a numerical example is provided to show the effectiveness and superiority of these obtained results.

Consensus Analysis in Multi-agent Systems with Non-uniform Time-varying Delays and Uncertain Topologies

This paper analyzes the consensus problem in a group of networked agents with nonuniform time-varying delays communicating over an uncertain communication network. Time-varying delays are assumed to be associated with each link in a directed communication graph topology. The network topology for information exchange is modeled with communication links subject to bounded multiplicative uncertainties. By using the the Lyapunov–Krasovskii method, delay-dependent consensus conditions are derived in terms of linear matrix inequalities. A numerical simulation is presented to illustrate the accuracy of the proposed theoretical approach.

Rendezvous of Heterogeneous Multiagent Systems With Nonuniform Time-Varying Information Delays: An Adaptive Approach

This article considers the rendezvous problem of a group of heterogeneous second-order agents subject to information transmission delays. A major challenge to construct a fully distributed rendezvous protocol is to deal with these delays, which are assumed to be nonuniform and time-varying. Inspired by the fact that a large enough damping coefficient can improve the robustness of a second-order agent against external disturbance, we overcome the above challenge by studying the impact of the damping coefficient on the rendezvous problem. To theoretically analyze the impact, one type of static rendezvous protocol is first proposed and employed. It is interesting to find that agents can reach rendezvous under the static protocol if the damping coefficient is large enough, even though the duration of the time-delay is uncertain. This fact indicates that a large damping coefficient can make the static protocol be robust to the uncertainty of time-delay, which is consistent with the common sense. Then, we apply this impact to deal with the uncertainty introduced by the nonuniform time-varying information delays. To fully apply this impact, we adopt an adaptive approach to making the damping coefficient automatically adapt with the changes of the time-delay. Hence, two classes of fully distributed and adaptive rendezvous protocols are designed, which do not need the global information of the entire communication graph or the value of these time-delays at all. The difference between two classes of protocols is whether it can realize low-frequency learning or not. Finally, some numerical simulations are performed on multiple robots to illustrate the analytical results.

Consensus in multi-agent systems subject to input saturation and time-varying delays

This paper deals with the problem of consensus in multi-agent systems. The consensus is investigated considering directed networks composed by identical agents described by linear models of arbitrary order, subject to input saturation and non-uniform time-varying delays. The main results are sufficient conditions for consensus analysis and design of distributed consensus protocols for multi-agent systems. In addition, because the saturation might prevent the multi-agent system to attain consensus on some set of initial conditions, it is also proposed a strategy to calculate a region in which the consensus is guaranteed. The results follow from the Lyapunov–Krasovskii theory and are formulated in the linear matrix inequalities (LMIs) framework. Finally, we present examples to illustrate the effectiveness of the proposed method in contrast with similar approaches existing in the literature.

Consensus of Heterogeneous Second-Order Nonlinear Uncertain Multiagent Systems Under Switching Networks

The consensus problem of heterogeneous second-order nonlinear uncertain multiagent systems under switching networks is addressed by a distributed control approach. The network communication of all systems is subject to arbitrarily bounded and nonuniform time-varying delays. Based on the internal model principle, a nonlinear distributed dynamic controller is developed to solve the problem. By means of Lyapunov analysis, consensus of heterogeneous second-order nonlinear multiagent systems is achieved in the presence of system uncertainties, disturbances, and uniformly connected topologies as well as arbitrarily bounded and nonuniform time-varying communication delays.

Reduced-order observer-based consensus control of linear multi-agent systems over directed networks with nonuniform communication delays

This paper considers a consensus control of a general linear multi-agent system with time-varying communication delays. Since each agent can only use the relative output information from its neighbors, a reduced-order observer-based control protocol is proposed to guarantee consensus on the directed communication network. The stability of the closed-loop system is analyzed for the cases with uniform delays and nonuniform time-varying delays, respectively. Moreover, the upper bounds of the communication delays are obtained respectively for the two cases. Finally, two numerical examples are provided to illustrate the proposed theoretical results.

Finite-Time Observer-Based Leader-Following Consensus for Nonlinear Multiagent Systems With Input Delays.

This article studies the finite-time observer-based leader-following consensus problem for a class of nonlinear multiagent systems with nonuniform time-varying input delays. Existing works usually assume that input delays are the same constants and the input of the leader is available for each follower. In this article, we propose a new distributed consensus algorithm to relax the conservative condition. A novel finite-time distributed observer is designed for each follower, which can accurately estimate the state information of the leader in a setting time. By means of the observer, the distributed controller is proposed for each follower, and it depends only on the state information of the follower and the estimated-state information of its neighbor agents. Based on the Lyapunov stability theory, it is strictly proved that all agents can achieve a consensus. Finally, the effectiveness of the theoretical results is verified by numerical simulation on a group of single-link manipulators.

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.

Stability and Formation Error of Homogeneous Vehicular Platoons With Communication Time Delays

The problem of decentralized control of vehicular platoon is addressed, subject to non-uniform time-varying delays in the communication links among the vehicles. Our control goal is to drive the vehicles to reach a specified line formation, while moving forward according to the platoon leader speed. The control law in each vehicle is computed only by local relative information regarding its neighboring vehicles. The first result shows that communication delays cause steady-state formation error, whose value can be analytically calculated from the system data, and may lead to instability, if the delays values surpass a threshold. Hence, in the light of this finding, we present a decentralized control law to compensate for the delay effect, providing zero steady-state formation error. The paper is concluded by showing simulated experiments over six different communication topologies illustrating the applicability of our proposal.

Distributed Optimal Energy Management for Microgrids in the Presence of Time-Varying Communication Delays

This paper investigates the issues of the distributed energy management problem (EMP) of Microgrids in the presence of communication delays. To address this issue, a consensus-based distributed algorithm is proposed to integrate the economic dispatch and demand response, which can optimally assign the energy among generation units and load units with the objective of maximizing the total social welfare of the power system. Different from existing energy management algorithms, a nonuniform time-varying delays model is considered and embedded into the design of our algorithm, such that each unit can achieve collaborative optimization without the requirement of fixed delays information, which has both theoretical merits and practical engineering value for the efficient and stable operation of Microgrids. Moreover, it is proved that the proposed algorithm can converge to the optimal solution under some sufficient conditions. Finally, the correctness and effectiveness of the proposed method are validated by several simulation results.

Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

We study synchronization of coupled linear systems over networks with weak connectivity and nonuniform time-varying delays. We focus on the case where the internal dynamics are time-varying but nonexpansive (stable dynamics with a quadratic Lyapunov function). Both uniformly jointly connected and infinitely jointly connected communication topologies are considered. A new concept of quadratic synchronization is introduced. We first show that global asymptotic quadratic synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns out that the existence of a uniform time interval for the jointly connected communication topology is not necessary and quadratic synchronization can be achieved when the time-varying nonuniform delays are arbitrarily bounded. Simulation results are provided to validate the theoretical results.

Event-triggered Consensus Seeking under Non-uniform Time-Varying Delays

In this paper, we study consensus seeking for a class of linear multi-agent systems (MAS) subject to the inevitable imperfections of packet-based networked communication. These imperfections include unknown non-uniform time-varying transmission delays and limited communication resources. To reduce the utilization of communication resources, we propose a dynamic event-triggered control scheme resulting in aperiodic transmission of information between agents. The proposed framework leads to event-triggered controllers that guarantee the MAS to asymptotically reach consensus, strictly positive lower bounds on the inter-event times and robustness for unknown non-uniform time-varying delays in terms of maximum allowable delays.

Droop-Based Distributed Cooperative Control for Microgrids With Time-Varying Delays

This paper develops a droop-based distributed cooperative control scheme for microgrids under a switching communication network with non-uniform time-varying delays. We first design a pinning-based frequency/voltage controller containing a distributed voltage observer and then design a consensus-based active/reactive power controller, which are employed into the secondary control stage to generate the nominal set points used in the primary control stage for different distributed generators (DGs). By this approach, the frequencies and the weighted average value of all DGs’ voltages can be pinned to the desired values while maintaining the precise active and reactive power sharing. With the proposed scheme, each DG only needs to communicate with its neighbors intermittently, even if their communication networks are local and time-varying, and their variant delays may be non-uniform. Sufficient conditions on the requirements for the network connectivity and the delay upper bound that guarantee the stability and reliability of the microgrid are presented. The effectiveness of the proposed control scheme is verified by the simulation of a microgrid test system.

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.

Consensus Analysis in Multi-Agent Systems Subject to Delays and Switching Topology

This paper presents a consensus analysis method for multi-agent systems subject to nonuniform and non-differentiable time-varying delays and switching topology. It is considered that the topology changes according to a continuous time Markov chain and the existence of nonuniform time-varying delays in the agents control laws. The main result formulated as linear matrix inequalities is obtained by showing that the consensus analysis in the multi-agent system can be performed by analyzing the stability of an associated Markov jump linear system. The results are illustrated by numerical examples.

L 2 – L ∞ containment control of multi‐agent systems with Markovian switching topologies and non‐uniform time‐varying delays

In this study, the authors investigate L 2 − L ∞ containment control problem of multi-agent systems with multiple stationary leaders and external disturbances. Furthermore, the interaction topology is Markovian switching and non-uniform time-varying delays are considered. By using a model transformation, the containment control problem of the multi-agent systems is turned into a normal L 2 − L ∞ control problem. Based on the theory in stochastic stability for time-delays systems, sufficient conditions in terms of a set of linear matrix inequalities are given to ensure that all the followers will move into the convex hull formed by the leaders in mean square sense with a prescribed L 2 − L ∞ performance. Two numerical simulations are provided to show the effectiveness of theoretical results.

Practical consensus for high-order linear time-invariant swarm systems with interaction uncertainties, time-varying delays and external disturbances

Practical consensus problems for general high-order linear time-invariant swarm systems with interaction uncertainties and time-varying external disturbances on directed graphs are investigated in this article. A dynamic consensus protocol with non-uniform time-varying delays is adopted to deal with the practical consensus problem. Using state space decomposition, practical consensus problems of a swarm system are converted into stability problems of a disagreement subsystem. Based on the Lyapunov–Krasovskii functional approach and the linear matrix inequality technique, sufficient conditions for swarm systems to achieve practical consensus are proposed where the time-varying external disturbance can be in L 2 or L ∞. Numerical simulations are presented to demonstrate theoretical results.

Average Consensus in Multi-Agent Systems with Non-uniform Time-Varying Delays and Random Packet Losses

Average consensus with delays and data losses is investigated for multi-agent systems with undirected topology. The communication constraints are considered in two aspects: (1) the time-varying delays are non-uniform and bounded; (2) data losses are governed by Bernoulli processes with non-uniform probabilities. We discretize the single-integrator dynamics and convert the consensus problem into its corresponding error dynamics. By assuming symmetry in communication topology, conditions of ensuring the mean square stability are developed, by explicitly incorporating the probabilities of data losses. Simulation is offered to verify the validity of the proposed approach.

Decentralised adaptive output feedback synchronisation tracking control of spacecraft formation flying with time-varying delay

This study deals with the problem of decentralised cooperative position tracking with time-varying delays of interconnect communication in the leader-follower spacecraft formation flight. More specifically, a class of low-pass linear filters is developed to derive a control law without absolute and relative velocity measurement, which is significant for practical applications with low-cost configurations of spacecrafts. Using a well-chosen Lyapunov function, it proves that the proposed control law can make the spacecrafts in formation flying achieve global convergence to the desired position and velocity relevant to the leader, in the face of modelling uncertainties, external disturbances, as well as non-uniform time-varying delays in communication links. Moreover, to release the heavy communication pressures of the leader, a modified control law is designed by introducing a finite-time sliding-mode estimator for a tree-type transformation topology of the formation, in which delays only affect the state (position and velocity) information received from neighbours of each spacecraft. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control schemes.