Uncertain Time Delay Research Articles

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Remote Fault-Tolerant Control for Industrial Smart Surveillance System

We design a remote fault-tolerant control for an industrial surveillance system. The designed controller simultaneously tolerates the effects of local faults of a node, the propagated undesired effects of neighboring connected nodes, and the effects of network-induced uncertainties from a remote location. The uncertain network-induced time delays of communication links from the sensor to the controller and from the controller to the actuator are modeled using two separate Markov chains and packet dropouts using the Bernoulli process. Based on linear matrix inequalities, we derive sufficient conditions for output feedback-based control law, such that the controller does not directly depend on output, for stochastic stability of the system. The simulation study shows the effectiveness of the proposed approach.

Adaptive Control of Multivariable Networked Systems With Uncertain Time Delays

A discrete-time adaptive control approach for uncertain linear multivariable networked systems is proposed. It is capable of dealing with unknown time delays introduced by a communication network between a plant and a controller. Based on the idea of model reference adaptive control, two adaptive laws are presented to reduce the conservativeness that is usually introduced when the time delays are unknown. The stability of the closed-loop system is proven. Simulation examples provide a comparison of the proposed techniques to a nonadaptive algorithm.

Adaptive Fractional-Order Sliding Mode Control for Admittance-Based Telerobotic System With Optimized Order and Force Estimation

This article proposes a variable structure control with neural network and optimized fractional-order selection policy for the sensorless telerobotic system with uncertain time delay, model uncertainty, fractional calculus numerical approximation bias, and external disturbance. Expanded from the integer-order calculus based on the definition of Caputo and the comparison principle, the Riemann–Liouville-based uniformly ultimately bounded stability is introduced to synthesize the sliding mode control with varying order, and the corresponding neural network based force estimation, which is optimized by the specified order based on the greed algorithm. Combined with the mixed-type error, the proposed hybrid integer-order and fractional-order analysis methodology is capable of guaranteeing the Riemann–Liouville-based uniformly ultimately bounded stability of tracking and synchronization errors under time delay. According to Euler difference, the proposed synthesis method can suppress the combined error in the boundedness of approximating double Euler difference errors. Numerical simulation and experiment of the telerobotic system under the control of the proposed method verify the stability analyses.

Exact computation of maximal allowable delay for general second‐order multi‐agents consensus

AbstractThe delay consensus margin (DCM) defines the largest delay range within which a distributed feedback control protocol can achieve and maintain the consensus robustly against uncertain time delays. This article investigates the exact computation of the DCM for general second‐order multi‐agent systems (MASs) under distributed proportional‐derivative (PD) feedback, or alternatively known as position and velocity feedback protocols over undirected graphs. We consider MASs with uncertain constant delays, and derive the DCM expression for second‐order agents and show that it can be determined by solving a non‐smooth quasi‐concave optimization problem. The DCM as such, can be computed via convex optimization methods.

A Robust Steered Response Power Localization Method for Wireless Acoustic Sensor Networks in an Outdoor Environment.

The localization of outdoor acoustic sources has attracted attention in wireless sensor networks. In this paper, the steered response power (SRP) localization of band-pass signal associated with steering time delay uncertainty and coarser spatial grids is considered. We propose a modified SRP-based source localization method for enhancing the localization robustness in outdoor scenarios. In particular, we derive a sufficient condition dependent on the generalized cross-correlation (GCC) waveform function for robust on-grid source localization and show that the SRP function with GCCs satisfying this condition can suppress the disturbances induced by the grid distance and the uncertain steering time delays. Then a GCC refinement procedure for band-pass GCCs is designed, which uses complex wavelet functions in multiple sub-bands to filter the GCCs and averages the envelopes of the filtered GCCs as the equivalent GCC to match the sufficient condition. Simulation results and field experiments demonstrate the excellent performance of the proposed method against the existing SRP-based methods.

A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems

This paper investigates the exponential stability of uncertain time delay systems using a novel descriptor redundancy approach based on delay partitioning. First, the original system is casted into an equivalent descriptor singular state–space representation by introducing redundant state variables so that the resulting delay is progressively reduced. From the equivalent model and applying Lyapunov Functional method, a sufficient condition based on Linear Matrix Inequalities (LMIs) for exponential stability with guaranteed decay rate performance is obtained. As a result, the inherent conservatism of Lyapunov–Krasovskii functional techniques can arbitrarily be reduced by increasing the number of delay partition intervals including decay rate performance and model uncertainties in polytopic form. Various benchmark examples are provided to validate the effectiveness of the proposed method, showing better trade-off between conservatism and performance in comparison to previous approaches.

Optimal V-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems

Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal robust stabilization approach for closed-loop fractional order proportional integral derivative (FOPID) control systems with interval parametric uncertainty and uncertain time delay. This stabilization approach, which is carried out in a v-plane, relies on the placement of the minimum angle system pole to a predefined target angle within the stability region of the first Riemann sheet. For this purpose, tuning of FOPID controller coefficients was performed to minimize a root angle error that is defined as the squared difference of minimum angle root of interval characteristic polynomials and the desired target angle within the stability region of the v-plane. To solve this optimization problem, a particle swarm optimization (PSO) algorithm was implemented. Findings of the study reveal that tuning of the target angle can also be used to improve the robust control performance of interval uncertain FOPID control systems. Illustrative examples demonstrated the effectiveness of the proposed v-domain, optimal, robust stabilization of FOPID control systems.

Real-Time Cache-Aided Route Planning Based on Mobile Edge Computing

Route planning is considered as one of the fundamental technologies in the navigation system, which finds an optimal route between a pair of source and target locations. Navigation services are required to provide real-time responses to route planning queries to promote user experiences on the road under different situations, such as sudden detour, unpredictable traffic congestion and loss of GPS signals. However, most commercial navigation products search the optimal path at the remote central server which suffer from several inherent limitations. First, the communication between the access network and the remote central server has a large uncertain Internet-induced time delay. Second, the computational cost of retrieving an optimal path is increasing exponentially with the distance from the source location to the destination in a large-scale road network. To address the above issues, we propose a real-time Cache-Aided Route Planning System based on Mobile Edge Computing (CARPS-MEC), aiming to greatly shorten the communication and computation time of route planning queries by caching those frequently requested paths. Different from traditional cache based route planning algorithms which require an exact path matching from point to point, CARPSMEC makes a rough path matching from region to region. Thus, it only needs to process unmatched road segments on a MEC server which is closer to the end users. This will significantly reduce the transmission latency due to the uncertainty of the Internet. Experiment results demonstrate that CARPS-MEC can increase the cache hit ratio and reduce the response time greatly.

Robust Mixed H2/H∞ Control for An Uncertain Wireless Sensor Network Systems with Time Delay and Packet Loss

In this paper, the problem of robust mixed H2/H∞ control is studied for an uncertain wireless sensor network (WSN) systems with random time delay, packet loss and sensor faults. A system model is established based on the characteristics of uncertain time delay and packet loss in WSN. In this model, system uncertainties are represented by random time delay and stochastic packet loss, which are described by a Markov chain. By using a Lyapunov-Krasovskii function, a mode-dependent mixed H2/H∞ controller is designed to guarantee both the stochastic stability of the closed-loop system and the prescribed H2, H∞ control performances. The sufficient conditions for the existence of the controller are proved by a series of Linear Matrix Inequalities (LMIs). If these LMIs are feasible, the mode-dependent mixed H2/H∞ controller can be obtained. Matlab LMI toolbox is used to calculate the control law. Finally, a numerical example and its simulation results demonstrated the effectiveness of the proposed method.

Backward Reachability Using Integral Quadratic Constraints for Uncertain Nonlinear Systems

A method is proposed to compute robust inner-approximations to the backward reachable set of nonlinear systems and to generate a robust control law that drives trajectories starting in these inner-approximations to a target set. The method merges dissipation inequalities and integral quadratic constraints (IQCs) with both hard and soft IQC factorizations, allowing for a variety of perturbations including parametric uncertainty, unmodeled dynamics, and uncertain time delays. Computational algorithms are developed using the generalized S-procedure and sum-of-squares techniques, and illustrated on a 6-state quadrotor with actuator uncertainties.

Modelling and Compensation of Uncertain Time-delays in Networked Control Systems with Plant Uncertainty Using an Improved Robust Model Predictive Control Method

Control systems with digital communication between sensors, controllers and actuators are called Networked Control Systems (NCSs). In general, NCSs encounter with some problems such as packet dropouts and network induced delays. When plant uncertainty is added to the aforementioned problems, the design of the robust controller that is able to guarantee the stability becomes more complex. In this paper, a method based on Robust Model Predictive Control (RMPC) is proposed to overcome model uncertainty together with unknown delay caused in NCSs. The previous RMPC methods, called Normal RMPC, was proposed to compensate delay or model uncertainty, individually. Hereby, we propose a method, named Improved RMPC, to compensate the effects of delay and model uncertainty on NCSs, simultaneously. The proposed method is based on uncertainty polytope and LMIs (Linear Matrix Inequlities). Also, an experimental evaluation of time-delays in MODBUS networked control systems is proposed. The simulation results show the ability of the proposed method. For comparison, the Normal RMPC is applied as well. The results show that the Normal RMPC has an acceptable performance for time delay compensation, but its performance gets destroyed or even get unstable when the model uncertainty is also considered.

Observer based control for strong practical stabilization of a class of uncertain time delay systems

In this paper, we address the strong practical stabilization problem for a class of uncertain time delay systems with a nominal part written in triangular form. We propose, firstly, a strong practical observer. Then, we show that strong practical stability of the closed loop system with a linear, parameter dependent, state feedback is achieved. Finally, a separation principle is established, that is, we implement the control law with estimate states given by the strong practical observer and we prove that the closed loop system is strong practical stable. With the help of a numerical example, effectiveness of the proposed approach is demonstrated.

A Robust Levitation Control of Maglev Vehicles Subject to Time Delay and Disturbances: Design and Hardware Experimentation

Maglev vehicles have become a new type of transportation system with higher speed, lower noise, and commercial appeal. Magnetic-suspension systems, which have high nonlinearity and open-loop instability, are the core components of maglev vehicles. The high-performance control of maglev vehicles has been the focus of numerous studies. Encountering challenges in the levitation control of maglev vehicles in the form of uncertain time delays and disturbances is unavoidable. To cope with these problems, this study presents the design of an adaptive robust controller based on the Riccati method and sliding-mode technology, simultaneously taking into account the influence of time delays and disturbances. The asymptotic stability of the closed-loop system with the proposed control law is proved by the Lyapunov method. Control performances of the proposed controller are shown in the simulation results. Together with the consistently stabilizing outputs, the presented control approach can handle time delays and disturbances well. Finally, experiments were also implemented to examine its practical control performance of the robust levitation-control law.

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

SummaryThis article studied the global output feedback regulation problem for a class of uncertain nonlinear time delay systems subject to unknown measurement faults on sensors. Different from the existing works, we consider the unknown time‐varying delays on the system states and relax their conservative condition on nonlinear functions. By introducing two novel time‐varying gains, a new global output feedback regulation algorithm is proposed, which ensures control parameters can be chosen flexibly. The proposed linear‐like controller is independent of the unknown time‐varying delays. Moreover, it has a simple structure, which is convenient for the implementation in practice. Based on the Lyapunov stability theory, it is strictly proved that all signals of the resulting closed‐loop system are globally bounded with the designed controller. Finally, a simulation example is presented to illustrate the effectiveness of the proposed output feedback regulation algorithm.

Comprehensive analysis and synthesis of time delay compensated deadbeat control strategy

This research comprehensively investigates the effect of uncertain time delay on performance of the deadbeat control. A solution based on a non-integer order Smith predictor has been proposed and analyzed to compensate uncertain time delays occurring in a stable closed loop system. Deadbeat control has been widely and conveniently used in the control of linear and non-linear systems. However, this control technique is severely sensitive to unmodeled dynamics and parameter uncertainties. Thus the performance of system may deviate significantly and hence lead to instability in practical cases. Time delay in a closed loop control system is a common source of unmodeled dynamics, which severely deteriorates control accuracy and results in reduced stability margin of the deadbeat control system. Physical system considered in this research work is a single-phase inverter. The simulation results indicate that the Smith predictor based deadbeat control scheme offers accurate time delay compensations and thus enhances the robustness and stability margin. Application example comprehensively illustrates effectiveness of the proposed control technique.

Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertainties: LMI approach

Without separating complex-valued neural networks into two real-valued systems, the state estimation of fractional-order complex-valued neural networks (FCNNs) with uncertain parameters and time delay is investigated in this paper. Based on Lyapunov-Krasovskii functional approach, a new linear matrix inequality (LMI) criterion is derived for asymptotic stability of the estimation error system. A numerical example with simulations is given to confirm the feasibility and availability of the raised result.

Wireless sensor network model with uncertain delay and packet loss based on intelligent fuzzy system

The utilization of fuzzy logic in WSNs is demonstrated to be a promising procedure since it permits joining and assessing various parameters in an effective way. Fuzzy logic is a decent methodology because of the execution prerequisites can be effectively supported by sensor hubs, while it can improve the general system execution. This paper studies the robust H∞ control considering time delay and packet loss related uncertainty in wireless sensor network system based on the basic theory of intelligent fuzzy systems. The model of a wireless sensor network with questionable time lag and packet loss is given first. The stability of the system is proved by the augmented Lyapunov functional and the linear matrix inequality (LMIs) method, with its demonstrated H∞ property. In order to solve the uncertain time delay and packet loss, the memory robust H∞ controller is proposed based on LMIs. Numerical examples and simulation results examines the potency of the presented method in solving the delay and packet loss of wireless sensor networks as well as the accuracy and precision of the system.

L2 Disturbance Suppression Controller Design for Multiple Time Delays Offshore Wind Turbines

With the large-scale development of offshore wind power and the rapid development of smart grid, more and more attention has been paid to the stable operation of wind turbines under various conditions. In the actual operation process of wind turbines, there are inevitably many kinds of uncertain time delays, and also external or parameter disturbances, which affect the stable operation of wind turbines and make the system deviate from the original stable state. Based on Hamiltonian energy theory, the disturbance rejection of doubly fed wind turbines with multiple time delays is studied in this paper. Firstly, the doubly fed wind turbine is Hamiltonian realized to obtain its port controlled Hamiltonian with dissipation(PCH-D) model. Then, aiming at the PCH-D model, a multiple time delays controller is designed based on Casimir function, which can make wind turbines run stably under multiple time delays. Furthermore, based on the passive control theory, L2 gain disturbance rejection control technology is introduced to eliminate the steady-state error caused by external disturbance and improve the stability of wind turbines. Finally, the simulation results show that the proposed controller can effectively solve the multiple time delays and disturbance problems in the system, and improve the stability and anti-interference of wind turbines.

Introduction of a Complex Reaction Time Tester Instrument

The reaction time, which is also referred as reflex delay in the literature, is an important factor in human balancing, since reaction time highly affects the ability of self stabilization. Increased reaction time delay may cause dangerous fall-over accidents related to elderly people. Reaction time depends on age, health, everyday activities, the general and actual physical and mental state of the individual and the environmental conditions.The reaction time is considered as a parameter in many of the mathematical models of the neural processes in human balancing. It is beneficial in many cases to estimate the reaction time based on experimental data.The present paper introduces the prototype of a complex reaction time tester instrument. The novelty of the instrument is that the reaction time can be measured in various combinations of sensory organs and reaction movements. The reaction time is defined as the time duration in between the initial time instant of the stimulus of the sensory organs (input signal) and the onset of the response that is typically indicated by a button or a pedal. Another novelty is that the instrument is free of any uncertain time delay, which is not the case for several instruments available.Usually, human simple reaction time is considered to be roughly about 200 ms. The shortest (aural) reaction time for skilled athletes is 85ms. In our measurements the shortest reaction time was 97 ms, and the mean about 190 ms in simple reaction cases. So our collected experimental data are in agreement with the literature.