Heterogeneous Time-varying Delays Research Articles

New global exponential stability conditions for nonlinear delayed differential systems with three kinds of time-varying delays

For a class of nonlinear differential systems with heterogeneous time-varying delays, including distributed, leakage and transmission time-varying delays, a novel global exponential stability (GES) analysis method was developed. Based on the GES definition, some sufficient conditions and rigorous convergence analysis of nonlinear delayed differential systems are presented directly, which ensure all states to be globally exponentially convergent. The proposed analysis method not only avoids the construction of the Lyapunov–Krasovskii functional, but also uses some simple integral reduction techniques to determine the global exponential convergence rate. Furthermore, the main advantages and low calculation complexity are demonstrated through a theoretical comparison. Finally, three numerical examples are provided to verify the effectiveness of the theoretical results.

Submission to Special Issue to Explainable Representation Learning-Based Intelligent Inspection and Maintenance of Complex Systems: Synchronization of Inertial Neural Networks With Unbounded Delays via Sampled-Data Control.

This article addresses the synchronization issue for inertial neural networks (INNs) with heterogeneous time-varying delays and unbounded distributed delays, in which the state quantization is considered. First, by fully considering the delay and sampling time point information, a modified looped-functional is proposed for the synchronization error system. Compared with the existing Lyapunov-Krasovskii functional (LKF), the proposed functional contains the sawtooth structure term V8(t) and the time-varying terms ex(t-βħ (t)) and ey(t-βħ (t)) . Then, the obtained constraints may be further relaxed. Based on the functional and integral inequality, less conservative synchronization criteria are derived as the basis of controller design. In addition, the required quantized sampled-data controller is proposed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness and superiority of the proposed scheme in this article.

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization.

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Distributed Low-Effort Load Balancing in the Presence of Time-Delays

In this paper, we investigate the problem of distributed load balancing under network capacity constraints, where the participating agents cooperate with the aim of jointly minimizing both the workload disparity among them as well as the overall workload transfer. Classical approaches for asymptotic convergence to the global optimum in a distributed fashion typically assume timely exchange of information between neighboring agents of a given multi-agent system. This assumption is not necessarily valid in practical settings due to non-commensurate (heterogeneous) communication and processing delays that might affect transmissions at different times. More specifically, we consider what effect multiple heterogeneous time-varying delays, among the agents can have on the distributed load balancing problem. We show that the distributed load balancing problem under bounded heterogeneous time-varying delays is globally asymptotically stable, but the rate of convergence is affected. Bounds on the convergence rate are provided with respect to an upper bound on the delays. Simulation examples are provided to show the validity and performance of our theoretical results.

Distributed Adaptive Consensus Protocol for Connected Vehicle Platoon With Heterogeneous Time-Varying Delays and Switching Topologies

This paper studies the distributed consensus protocol for the connected vehicle platoon with heterogeneous time-varying delays and switching topologies. A third-order dynamics model with powertrain inertial lag is proposed to characterize the node longitudinal dynamics of vehicles in platoon. A novel distributed adaptive consensus protocol considering the time-varying delays and the random switched inter-vehicular communication topologies is designed to stabilize the heterogeneous vehicle platoon in the presence of external disturbance. The delay-range-dependent approach is used to deal with the system heterogeneous time-varying delays by considering the characteristics of the heterogeneous platoon. Directed graphs are adopted to describe the accessible information flow among vehicles. The necessary and sufficient conditions for the unified closed-loop vehicle platoon system are derived by using matrix analysis and Lyapunov-Krasovskii approach. Numerical simulations demonstrate the proposed method is effective.

Distributed Anytime-Feasible Resource Allocation Subject to Heterogeneous Time-Varying Delays

This paper considers distributed allocation strategies, formulated as a distributed sum-preserving (fixed-sum) allocation of resources over a multi-agent network in the presence of heterogeneous arbitrary time-varying delays. We propose a double time-scale scenario for unknown delays and a faster single time-scale scenario for known delays. Further, the links among the nodes are considered subject to certain nonlinearities (e.g, quantization and saturation/clipping). We discuss different models for nonlinearities and how they may affect the convergence, sum-preserving feasibility constraint, and solution optimality over general weight-balanced uniformly strongly connected networks and, further, time-delayed undirected networks. Our proposed scheme works in a variety of applications with general non-quadratic strongly-convex smooth objective functions. The non-quadratic part, for example, can be due to additive convex penalty or barrier functions to address the local box constraints. The network can change over time, is not necessarily connected at all times, but is only assumed to be uniformly-connected. The novelty of this work is to address all-time feasible Laplacian gradient solutions in presence of nonlinearities, switching digraph topology (not necessarily all-time connected), and heterogeneous time-varying delays.

Cooperative Finite-time Control for autonomous vehicles platoons with nonuniform V2V communication delays

In this paper we introduce a novel fully distributed finite-time cooperative control law able to solve the platoon formation control problem for a network of autonomous vehicles, whose dynamics is represented via the third-order drivetrain linear model. Internet of Vehicle (IoV) communication latencies have been considered and modeled via heterogeneous time-varying delays. The resulting control protocol is computed via outdated information and embeds vehicles acceleration error, which allows improving control reactivity during sudden acceleration/deceleration maneuvers. The finite-time stability of the vehicular network has been analyzed and proved by leveraging Multi-Agent Systems (MASs) paradigm along with Lyapunov-Krasovskii method. This latter leads to stability conditions in the forms of Linear Matrix Inequalities, whose solution allows finding control gains and state trajectories threshold. Simulation results confirm the effectiveness of the theoretical derivation in guaranteeing the cooperative driving despite the presence of IoV communication latencies.

Distributed State Estimation under Heterogeneous Time-Varying Communication Delays

In this paper we study the distributed leader state estimation problem in leader-follower multi-agent systems over a deterministic network and under time-varying communication delays. In this work we propose a distributed estimation technique that allows the follower agents to collectively reconstruct the leader agent states by communicating their estimates with neighboring agents. Additionally, we assume that the communications between the leader and followers are subject to heterogeneous time-varying delays. By using the low gain methodology, sufficient stability conditions of the estimation error dynamics in the presence of network latency are derived, including an upper bound for the delay magnitude. Lastly, the proposed distributed state estimation method is applied to develop a solution to the leader tracking problem in leader-follower multi-agent systems. An illustrative example is also presented to verify the effectiveness of our theoretical results.

On the exponential leader-tracking control for high-order multi-agent systems via distributed PI strategy in the presence of heterogeneous time-varying delays

On the exponential leader-tracking control for high-order multi-agent systems via distributed PI strategy in the presence of heterogeneous time-varying delays

Synchronization of Inertial Neural Networks With Time-Varying Delays via Quantized Sampled-Data Control.

This article addresses the quantized sampled-data (QSD) synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays, in which the sampled-data control and state quantization effect have been considered. By utilizing a proper variable substitution to transform the original system into a first-order differential system, choosing a new Lyapunov-Krasovskii functional (LKF) containing both the continuous terms and the discontinuous terms, and applying Jensen inequality and an improved reciprocally convex inequality to estimate the derivative of the LKF, the sufficient conditions for QSD synchronization for INNs are newly obtained in terms of linear matrix inequalities (LMIs), and the desired QSD controllers are designed by solving a set of LMIs. Finally, three numerical examples are provided to validate the effectiveness and benefit of the proposed results.

EXPONENTIAL STABILITY OF A CLASS OF POSITIVE NONLINEAR SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

This paper is concerned with the problem of exponential stability of a class of positive nonlinear systems with heterogeneous time-varying delays which describe a model of Hopfield neural networks with nonlinear self-inhibition rates. Based on a novel comparison technique via a differential and integral inequalities, testable conditions are derived to ensure system state trajectories converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.

Quantized Sampled-Data Control for Synchronization of Inertial Neural Networks With Heterogeneous Time-Varying Delays.

This paper is concerned with the problem of synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) through quantized sampled-data control. The control scheme, which takes the communication limitations of quantization and variable sampling into account, is first employed for tackling the synchronization of INNs. A novel Lyapunov-Krasovskii functional (LKF) is constructed for synchronizing an error system. Compared with existing LKFs by the largest upper bound of all HTVDs, the proposed LKF is superior, since it can make full use of the information on the lower and upper bounds of each HTVD. Based on the LKF and a new integral inequality technique, less conservative synchronization criteria are derived. The desired quantized sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and conservatism reduction of the proposed results.

Novel discontinuous control for exponential synchronization of memristive recurrent neural networks with heterogeneous time-varying delays

This paper investigates the exponential synchronization problem of memristive recurrent neural networks (MRNNs) with heterogeneous time-varying delays (HTVDs). First, a novel discontinuous feedback control is designed, in which a tunable scalar is introduced. The tunable scalar makes the controller more flexible in reducing the upper bound of the control gain. Based on this control scheme, the double integral term can be successfully used to construct the LKF. Second, New method for tackling memristive synaptic weights and new estimation technique are presented. Third, based on the LKF and estimation technique, synchronization criterion is derived. In comparison with existing results, the established criterion is less conservatism thanks to the double integral term of the LKF. Finally, numerical simulations are presented to validate the effectiveness and advantages of the proposed results.

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.

Consensus in time-delayed multi-agent systems with quantized dwell times

This paper investigates the effects of quantized dwell times in solving consensus problems in time-delayed multi-agent systems with the asynchronous property of unpredictable quantization jumps in inter-agent communications. The quantized dwell times can be introduced on purpose or be inherent from quantizing devices. They beneficially avoid undesirable fast chattering of quantizers’ outputs and mathematical difficulties in convergence analysis. The main result shows that the largest eigenvalue of the interaction graph Laplacian well characterizes the dependence of maximum allowable time delay on quantized dwell times and quantizer parameters under the assumption of heterogeneous time-varying transmission delays. Simulations are presented to show the effectiveness of the main result.

Exponential Stability of Non-Autonomous Neural Networks with Heterogeneous Time-Varying Delays and Destabilizing Impulses

In this paper, the problem of global exponential stability analysis of a class of non-autonomous neural networks with heterogeneous delays and time-varying impulses is considered. Based on the comparison principle, explicit conditions are derived in terms of testable matrix inequalities ensuring that the system is globally exponentially stable under destabilizing impulsive effects. Numerical examples are given to demonstrate the effectiveness of the obtained results.

An LMI-based functional estimation scheme of large-scale time-delay systems with strong interconnections

In this paper, the problem of distributed functional state observer design for a class of large-scale interconnected systems in the presence of heterogeneous time-varying delays in the interconnections and the local state vectors is considered. The resulting observer scheme is suitable for strongly coupled subsystems with multiple time-varying delays, and is shown to give better results for systems with very strong interconnections while only some mild existence conditions are imposed. A set of existence conditions are derived along with a computationally simple observer constructive procedure. Based on the Lyapunov–Krasovskii functional method (LKF) in the framework of linear matrix inequalities (LMIs), delay-dependent conditions are derived to obtain the observer parameters ensuring the exponential convergence of the observer error dynamics. The effectiveness of the obtained results is illustrated and tested through a numerical example of a three-area interconnected system.

Exponential Synchronization of Memristive Neural Networks With Delays: Interval Matrix Method.

This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Third-order consensus in vehicles platoon with heterogeneous time-varying delays

We theoretically address the problem of achieving third-order consensus for a platoon of vehicles in the presence of heterogenous time-varying communication delays. A Lyapunov-Krasovkii function is constructed for the stability analysis. Necessary and sufficient conditions are derived to guarantee that all vehicles asymptotically reach the relative acceleration, speed and position according to the spacing policy. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results in different driving conditions and in the presence of external disturbances.

Stability and Performance of Continuous-Time Power Control in Wireless Networks

This paper develops a comprehensive stability analysis framework for general classes of continuous-time power control algorithms under heterogeneous time-varying delays. Our first set of results establish global asymptotic stability of power control laws involving two-sided scalable interference functions, and include earlier work on standard interference functions as a special case. We then consider contractive interference functions and demonstrate that the associated continuous-time power control laws always have unique fixed points which are exponentially stable, even under bounded heterogeneous time-varying delays. For this class of interference functions, we present explicit bounds on the decay rate that allow us to quantify the impact of delays on the convergence time of the algorithm. When interference functions are linear, we also prove that contractivity is necessary and sufficient for exponential stability of continuous-time power control algorithms with time-varying delays. Finally, numerical simulations illustrate the validity of our theoretical results.