Presence Of Time-varying Delays Research Articles

Distributed Observer for Linear Systems with Multirate Sampled Outputs Involving Multiple Delays

This paper focuses on the design of a continuous distributed observer for linear systems under multirate sampled output measurements involving multiple delays. It is mathematically proved that the continuous distributed observer can achieve estimation in a sensor network environment, where output measurements from each sensor are available at different sampling instants, whether these times are periodic or aperiodic, and despite the presence of multiple time-varying delays. Each sampled and delayed measurement represents a node of the network, necessitating a dedicated observer for each node, which has access to only part of the system’s output and communicates with its neighbors according to a given network graph. The exponential convergence of the error dynamics is ensured by Lyapunov stability analysis, which accounts for the influence of the sampled and delayed measurements at each node. To demonstrate the effectiveness of the proposed observer, simulation tests were conducted on the tracking control of chasing satellites in low Earth orbit (LEO), encompassing both small and large sampling rates and delays. The continuous distributed observer with sampled output measurements exhibited convergence in scenarios with different sampling intervals, even in the presence of time-varying delays, achieving asymptotic omniscience, as demonstrated in the convergence analysis.

Fixed-time synchronization of delayed inertial Cohen–Grossberg neural networks with desynchronizing impulses

This article focuses on achieving fixed-time (FXT) synchronization of inertial Cohen–Grossberg neural networks (ICGNNs) in the presence of time-varying delays and desynchronizing impulsive effects. Firstly, a new lemma is presented to achieve FXT stability of the impulsive systems with destabilizing impulses. The settling-time function is shown to depend on both the parameters of impulsive sequence and continuous-time subsystems. Furthermore, based on the proposed lemma, sufficient conditions are established to achieve FXT synchronization of ICGNNS with desynchronizing impulses by designing a unified controller. Two numerical examples are taken into consideration to verify the efficacy of the proposed theoretical results.

Dynamic event-triggered-based global output feedback control for stochastic nonlinear systems with time-varying delay

The current study addresses the issue of global dynamic event-triggered control based on reduced-order observer for a class of nonstrict-feedback stochastic systems in the presence of time-varying delay. Firstly, a lemma about the variable separation technique is proposed and proved for dealing with nonlinear functions in stochastic time-delay systems, which avoids the restrictive growth assumption that nonlinear functions need to satisfy. Secondly, a reduced-order observer is devised to reconstruct partial unmeasured state variables in systems, which equilibrates the control behavior between output feedback and state feedback. Then, without imposing any constraints on the derivative of time-varying delay, a dynamic event-triggered controller based on the symbol function technique is constructed to reduce the waste of resources in data transmissions and improve the communication efficiency. Furthermore, in the light of the stability theory of stochastic systems and Lyapunov-Razumikhin lemma, it is proved that the designed control algorithm can ensure that the controlled system is globally asymptotically stable in probability. Finally, two simulation examples are provided to verify the effectiveness of the developed approach.

Intention-reflected predictive display for operability improvement of time-delayed teleoperation system

Robotic teleoperation is highly valued for its ability to remotely execute tasks that demand sophisticated human decision-making or that are intended to be carried out by human operators from a distance. However, when using the internet as a communication framework for teleoperation, high latency, and fluctuations make accurate positioning and time-dependent tasks difficult. To mitigate the negative effects of time delay, this paper proposes a teleoperation system that uses cross reality (XR) as a predictive display of the outcome of operators’ intended actions and develops a time-delay aware shared control to fulfill the intention. The system targets a liquid pouring task, wherein a white ring that indicates the intended height of the liquid surface is overlayed onto the beaker in a delayed camera image to close the visual feedback loop on the leader side. Simultaneously, the shared control automatically completes the pouring action to track the intended liquid height. The performance of the proposed system is validated based on liquid pouring experiments performed by human subjects. When compared with direct control, the absolute error rate decreased significantly for a constant round-trip time delay of 0.8 s and 1.2 s, similarly for a time-varying delay of 0.4 s and 0.8 s. Moreover, when the time-varying delay was 0.8 s, operators achieved significantly higher accuracy while maintaining comparable operation time. These results indicate that our proposed system improves operability even in the presence of time-varying delays in communication networks.

Consensus-Based Robust Filtering Over Sensor Networks With Weighted and Unweighted Topologies and Communication Delays

In this article, a consensus-based robust filter is proposed for sensor networks with weighted and unweighted topologies, and communication delays. The system is considered to be linear time-varying (LTV) with bounded uncertainties. In order to achieve the desired filter, first, a robust optimization problem is defined based on the consensus protocol for unweighted topologies. The consensus protocol ensures an agreement between the estimates of all sensors. By solving this problem, the proposed consensus-based robust filter is obtained and its algorithm is presented. Then, to increase the applicability of the filter, another optimization problem for weighted topologies is introduced. Next, due to the impact and high importance of communication delays in sensor networks, by considering the time-varying delays in consensus protocols, new optimization problems are solved again to achieve a suitable filter. One of the most significant features of the proposed consensus-based robust filters is that the loss of a large part of the network links does not pull down the filtering performance. Finally, in the simulation section, the robust performance and efficiency of the proposed consensus-based robust filters have been investigated for weighted and unweighted networks in the presence of time-varying delays and loss of communication links.

Prescribed Performance Tracking of Uncertain MIMO Nonlinear Systems in the Presence of Delays

In this article, we design a low-complexity state-feedback controller for uncertain multi-input and multi-output (MIMO) nonlinear systems, capable of imposing prespecified performance attributes (in terms of maximum steady-state error and minimum convergence rate) on the output tracking errors, in the presence of time-varying delays both in the state measurement and control input signals. The state measurement delay is considered known and the control input delay unknown though bounded by some known constant. The control design does not incorporate any knowledge regarding the controlled system nonlinearities and does not require derivatives of the desired trajectories. We verify the theoretical results by simulation studies performed on a two-link robotic manipulator.

Dynamic output feedback robust [formula omitted] control of networked control systems with time-Varying delays via T-S fuzzy models

This paper addresses the problem of robust stabilization for networked control systems (NCS) where the stochastic behavior of the network does not allow correct and complete transmission of data to both the actuators and the controller. The objective is to model the NCS using Takagi-Sugeno (T-S) fuzzy systems with uncertainties and external disturbances and to design a time-varying delay fuzzy controller such that the closed-loop system is robustly exponentially stable with a prescribed decay rate. Sufficient conditions are derived using the delay-dependent Lyapunov-Krasovskii functional with a robust H∞ controller in terms of linear matrix inequalities (LMIs). Accordingly, desired fuzzy controllers are designed by using feasible solutions to the obtained LMIs. The proposed fuzzy controller can keep the T-S fuzzy system stable in the presence of time-varying delay, uncertainties, and external disturbance. Two numerical examples with different conditions on parameters are provided to illustrate the performance and robustness of the proposed approach.

AUV Formation Coordination Control Based on Transformed Topology under Time-Varying Delay and Communication Interruption

Aiming at the control problem of autonomous underwater vehicle (AUV) pilot-following formation with communication delay and communication interruption, a controller based on feedback linearization and the PD control method is designed in this paper. Firstly, the nonlinear, strongly coupled vehicle model is transformed into a second-order model via the feedback linearization method, and then the formation coordination controller is designed based on consistency theory and the PD control method. The Markov random jump process is used to simulate the formation topology in the event of communication interruption. The condition of stable convergence of the AUV pilot-following formation is analyzed in the presence of time-varying delay and Markov transformation topology. A Lyapunov–Krasovskii equation is established, and linear matrix inequality (LMI) is used to solve the problem of communication interruption and communication delay. The boundary conditions of error convergence of the control system are obtained. Finally, the effectiveness of the formation coordination controller based on the second-order integral model under the unstable conditions of underwater acoustic communication is verified by simulation.

Active Disturbance Rejection Control for Delayed Electromagnetic Docking of Spacecraft in Elliptical Orbits

In this article, an active disturbance rejection control (ADRC) scheme is proposed for the electromagnetic docking of spacecraft in the presence of time-varying delay, fault signals, external disturbances, and elliptical eccentricity. By introducing an auxiliary variable, an intermediate observer (IO) is presented to estimate the relative motion information and the total disturbance resulting from fault signals, unknown mass, external disturbances, and elliptical eccentricity. Then, an ADRC scheme is developed to guarantee that the relative position, relative velocity, and the estimation errors of relative motion information and the total disturbance can all converge into the neighborhood of the equilibrium. With the proposed control scheme, the time-delay factor is fully considered in the controller design to avoid adverse effect, and the uniform ultimate boundedness stability of the entire closed-loop system is analyzed with a rigorous theoretical proof. In comparison to conventional ADRC and other state-of-the-art schemes, the proposed ADRC scheme has several advantages, e.g., high accuracy, strong robustness, and requires no prior knowledge of the fault, time-varying delay and states information due to IO-based relative motion information and total disturbance estimations. Finally, numerical simulations are performed to show the effectiveness of the proposed control scheme.

Type-2 fuzzy consensus control of nonlinear multi-agent systems: An LMI approach

This paper considers a class of nonlinear fractional-order multi-agent systems (FOMASs) with time-varying delay and unknown dynamics, and a new robust adaptive control technique is proposed for cooperative control. The unknown nonlinearities of the systems are online approximated by the introduced recurrent general type-2 fuzzy neural network (RGT2FNN). The unknown nonlinear functions are estimated, simultaneously with the control process. In other words, at each sample time the parameters of the proposed RGT2FNNs are updated and then the control signals are generated. In addition to the unknown dynamics, the orders of the fractional systems are also supposed to be unknown. The biogeography-based optimization algorithm (BBO) is extended to estimate the unknown parameters of RGT2FNN and fractional-orders. A LMI based compensator is introduced to guarantee the robustness of the proposed control system. The excellent performance and effectiveness of the suggested method is verified by several simulation examples and it is compared with the other methods. It is confirmed that the introduced cooperative controller results in a desirable performance in the presence of time-varying delay, unknown dynamics, and unknown fractional-orders.

Observer-Based Adaptive Hybrid Fuzzy Resilient Control for Fractional-Order Nonlinear Systems With Time-Varying Delays and Actuator Failures

This article investigates the adaptive output feedback resilient control problem for a class of incommensurate fractional-order (FO) nonlinear systems in the presence of time-varying delays and actuator faults by combining with an adaptive backstepping technique and a modified FO dynamic surface control (FODSC) method. Considering that the information of system states is not fully available, a hybrid fuzzy observer is designed to estimate the unmeasurable system states, where the neuro-fuzzy network system is introduced to handle the unknown nonlinear functions existing in the system. Furthermore, in order to overcome the problem of the explosion of complexity caused by traditional backstepping design procedure, an FO filter is constructed to pass the virtual control signal based on the FODSC scheme. Moreover, according to an indirect Lyapunov stability method, an adaptive hybrid fuzzy output feedback controller is designed to guarantee that all the signals of the closed-loop systems are bounded. Finally, three examples are given to verify the validity and superiority of the presented control scheme.

An Improved Result on Stabilization of Switched Linear Systems with Time-varying Delay

Abstract This paper revisits the stabilization problem of switched linear systems with time-varying delay via state dependent switching strategies. In contrast to the existing works, the commonly adopted stable convex combination assumption is relaxed in this paper. For switched systems satisfying the relaxed assumption, we design a state dependent switching strategy, under which the considered system is asymptotically stable at the origin in the presence of time-varying delay. An optimization problem is formulated to estimate the upper bound of tolerable time delay. Numerical examples are presented to show that our method is applicable to a larger class of switched systems and leads to greater delay bound.

Advanced Finite-Time Control for Bilateral Teleoperators With Delays and Uncertainties

In this paper, a finite-time control method is presented for bilateral teleoperators to ensure coordination of the master and slave manipulators in the presence of time-varying delays, external disturbances, and dynamic uncertainties. Without the requirement of acceleration measurement, the master and slave manipulators are assured to coordinate with each other within finite time in free motion. Additionally, the coordination errors are ensured to converge to a neighborhood of the origin in finite time. In the constrained motion, where both the master and slave manipulators are affected by unknown external force from the human operator and the removed environment, the bilateral teleoperation system is proved to be stably provided a certain degree of transparency performance during operation. Stability and finite-time tracking are investigated via Lyapunov-Krasovskii theory for the bilateral teleoperation system under time-varying delays and external forces. Subsequently, numerical examples and experiments are presented to demonstrate the efficiency and efficacy of the proposed control approach for teleoperators.

Hierarchical Two-Layer Distributed Control Architecture for Voltage Regulation in Multiple Microgrids in the Presence of Time-Varying Delays

The Multiple Microgrids (MMGs) concept has been identified as a promising solution for the management of large-scale power grids in order to maximize the use of widespread renewable energies sources. However, its deployment in realistic operation scenarios is still an open issue due to the presence of non-ideal and unreliable communication systems that allow each component within the power network to share information about its state. Indeed, due to technological constraints, multiple time-varying communication delays consistently appear during data acquisition and the transmission process and their effects must be considered in the control design phase. To this aim, this paper addresses the voltage regulation control problem for MMGs systems in the presence of time-varying communication delays. To solve this problem, we propose a novel hierarchical two-layer distributed control architecture that accounts for the presence of communication latencies in the information exchange. More specifically, the upper control layer aims at guaranteeing a proper and economical reactive power dispatch among MMGs, while the lower control layer aims at ensuring voltage regulation of all electrical buses within each MG to the desired voltage set-point. By leveraging a proper Driver Generator Nodes Selection Algorithm, we first provide the best choice of generator nodes which, considering the upper layer control goal, speeds up the voltage synchronization process of all the buses within each MG to the voltage set-point computed by the upper-control layer. Then, the lower control layer, on the basis of this desired voltage value, drives the reactive power capability of each smart device within each MG and compensates for possible voltage deviations. Simulation analysis is carried out on the realistic case study of an MMGs system consisting of two identical IEEE 14-bus test systems and the numerical results disclose the effectiveness of the proposed control strategy, as well as its robustness with respect to load fluctuations.

Salp swarm algorithm‐based fractional‐order PID controller for LFC systems in the presence of delayed EV aggregators

Electric vehicles (EVs) battery has the ability to enhance the balance between the load demand and power generation units. Random behaviour of owners and EVs low capacity are some factors that develop the EV aggregator notion to increase the EV participation in the ancillary services market. In the presence of EVs aggregator, the frequency control service is capable of causing time-varying delay in load frequency control (LFC) systems. Owing to the dependency of controller effectiveness on its parameters, these parameters should be designed optimally in order to have a better result in an LFC system in the presence of time-varying delay. Therefore, a salp swarm algorithm (SSA) is utilised to adjust the fractional-order proportional integral derivative (PID) (FOPID) controller coefficients. Also, some evaluations are performed about the proposed LFC performance by an integral absolute error, integral time absolute error and mean absolute error indicators. In this study, both single and two-area LFC systems containing EVs aggregator with time-varying delay are simulated and analysed. The results indicate that the proposed controller has fewer frequency variations in contrast to other controllers presented in the case studies. Moreover, it is concluded that the FOPID controller could significantly decrease the overshoot and settling time of the frequency variation signal.

Event-triggered control of vehicular platoon system with time-varying delay and sensor faults

This paper addresses the problem of control of a vehicular platoon system with limited on-board resources in the presence of time-varying delay and sensor faults. A platoon system with predecessor-leader following topology in which each vehicle suffers from probabilistic sensor faults and time-varying delay is considered. To reduce the utilization of communication and energy resources in the system, a novel event-triggering communication strategy at the sensor-controller channel is proposed. Based on the proposed triggering strategy, a criteria for co-designing of the triggering parameter and the control law ensuring internal stability of the platoon system is developed. Furthermore, additional conditions are established for the obtained controller to guarantee string stability of the platoon system. The efficacy of the proposed methodology is demonstrated through numerical simulations.

Stability analysis for a class of fractional-order nonlinear systems with time-varying delays

This paper presents the stability analysis problem of fractional-order nonlinear systems with time-varying delay. After formulating the problem and selecting the nonlinear model as the system under study, stability analysis and expression of the sufficient conditions for fractional-order nonlinear systems with time-varying delay are obtained using two different methods. In these methods, sufficient conditions for stability of fractional-order nonlinear systems are found in the form of satisfying some inequalities based on norms of nonlinear functions in the system and in terms of linear matrix inequality according fractional-order and nonlinear functions. In each case, despite the presence of time-varying delay, the system stability is ensured by meeting the stability sufficient conditions in terms of an inequality of functions and system parameters. Finally, numerical examples are given to determine the effectiveness of the proposed theorem.

An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters

The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings.

Robust filtered Smith predictor for processes with time-varying delay: A simplified stability approach

This paper presents a family of simplified stability conditions for the filtered Smith predictor control of uncertain systems with time-varying delay. The delay can vary arbitrarily, but its maximum value is assumed to be bounded. Simple design rules are proposed to ensure robust stability in the presence of time-varying delay and model uncertainty. Frequency analysis and design methods can be directly used. Moreover, if (i) the process is open-loop stable and (ii) the closed-loop system without time-varying delay is stable for a given filtered Smith predictor controller, then the robustness filter can always be re-designed to recover robust stability in the presence of any bounded time-varying delay. It is shown that the main results can be extended to multivariable systems. Simulation examples and an experimental case study are presented to illustrate the benefits of the proposed stability conditions and design rules.

Gradient Extremum Seeking With Nonconstant Delays

This paper proposes a gradient extremum seeking method to address locally quadratic static maps in the presence of time-varying delays. Accommodating nonconstant delays has a strong impact in the predictor construction in terms of the associated transport partial differential equation (PDE) with variable convection speeds beyond the restrictions imposed on the delay regarding its arbitrary duration but bounded variation. A novel predictor design using perturbation-based estimates of the unknown Gradient and Hessian of the map must be introduced to handle this variable nature of the delays, which can arise both in the input and output channels of the nonlinear map to be optimized. Local exponential stability and convergence to a small neighborhood of the unknown extremum point are guaranteed. This technical result is assured by using backstepping transformation and averaging theory in infinite dimensions. Implementation aspects of the presented predictor for variable delays as well as the extension to state-dependent delays are also discussed. At last, we introduce the first results in the topic of extremum seeking control for cascades of transport PDEs that are interconnected through boundary conditions. Such a PDE-PDE cascade is useful to represent simultaneous time- and state-dependent delays. A simulation example illustrates the effectiveness of the proposed predictor-based extremum seeking approach for time-delay compensation.