Unknown Delay Research Articles

Synchronization for Linear Networked Systems Subject to Input and Communication Delays

This paper investigates the synchronization problem for generic linear multi-agent systems with known or unknown heterogeneous input and communication delays. We propose two protocols that consist of consensus-based internal controller states and decentralized controllers. This kind of distributed dynamic control methodology is able to circumvent the interactive nature of two delays by translating the synchronization problem of agents into the stability of a set of delay differential equations. We examine the synchronization problem for two distinct cases, namely, known delays and unknown delays. When the delays are known, the stability criteria are satisfied by the feasibility of an input-delay-dependent linear matrix inequality and a communication-delay-dependent coupling strength bound. The margin on the communication delay is dependent not only on the network topology but also on the system matrix, which does not have any eigenvalues with positive real parts. We also develop a distributed dynamic control protocol that can handle unknown input and communication delays, and the stability criteria are realized by using the feasibility of a linear matrix inequality and a positive coupling strength. Synchronization is guaranteed even if the unknown communication delays are arbitrarily large but bounded and the upper bound on the heterogeneous input delays is known. The proposed control methodology guarantees that inaccurate measurements of the actual states of a particular agent will not lead to an irretrievable failure of the mission.

Prediction-based stabilization of single-input nonlinear systems with unknown delay

We introduce an inexact prediction-based controller for nonlinear systems with single-input unknown delay. The controller is established by an inexact predictor that compensates for the delay robustly, guaranteeing exponential stability for the closed-loop system. As a precondition, we are requested to select a suitable constant in a narrow enough range as the prediction horizon, which can offset the partial effect of the delay. In the end, a simulation example is presented to illustrate the validity of the theoretical results.

HAVOK Model Predictive Control for Time-Delay Systems with Applications to District Heating

A computationally efficient Model-Predictive Control (MPC) approach is proposed for systems with unknown delay using only input/output data. We use the Koopman operator framework and the related Hankel Alternative View of Koopman (HAVOK) algorithm to identify a model in a basis of projected time-delay coordinates and demonstrate a novel MPC structure that reduces and bounds the computational complexity. The proposed HAVOK-MPC approach is validated experimentally on a laboratory-scale District Heating System (DHS), demonstrating excellent prediction and tracking performance while only requiring knowledge of a conservative upper bound on the system delay.

Adaptive delay dependent sliding mode fault-tolerant controller design for nonlinear systems with unknown time-varying input and state delays

This paper presents a novel adaptive delay-dependent fault-tolerant sliding mode control (SMC) strategy for the class of nonlinear Lipschitz systems with time-varying unknown delays in system states and inputs. A modified integral sliding surface (ISS) based on which the SMC approach is developed using a linear matrix inequality. Lyapunov-Krasovskii stability theory is employed to guarantee asymptotic stability of the closed-loop system such that system states starting from any arbitrary initial conditions with time-varying delays reach the predefined sliding surface in a finite time. It is also proved that states stay on the surface for all subsequent time, and the effects of the actuator’s faults are simultaneously attenuated. Adaptive tuning laws are used to adjust controller parameters and estimate actuators’ faults. The controllers’ structures are more straightforward than the most existing recent fault-tolerant control methods. Simulation results of practical nonlinear inverted pendulum system verified the outstanding merits and capabilities of the proposed scheme in the presence of actuators’ faults and multiple delays in the system states and inputs.

An adaptive control framework for a class of nonlinear time-delay systems

This paper aims to formulate an adaptive control framework capable of producing desirable tracking performance for uncertain nonlinear systems with an unknown delay in the control input and a nonlinear control coefficient matrix. Since the control framework inherits common components of the classical model-reference adaptive controller (MRAC), it is easy to implement with a low barrier to entry. In addition, the work shows that the deviation of the state of the proposed control scheme from an ideal dynamics system is bounded given that the delays are within a certain margin. Simulation results are presented to illustrate the theoretical contribution and demonstrate the efficacy of the proposed controller in comparison with an existing competing controller. The limitation of this control framework is also discussed with a suggestion for overcoming the limitation toward the end of the paper.

Delay-Adaptive Control of a 7-DOF Robot Manipulator: Design and Experiments

We present an analytical design and experimental verification of trajectory-tracking control of a 7-DOF robot manipulator with an unknown long actuator delay. To compensate for this unknown delay, we formulate a delay-adaptive prediction-based control strategy to simultaneously estimate the unknown delay while driving the robot manipulator toward the desired trajectory. To the best of the authors’ knowledge, this article is the first to present a delay-adaptive approach for a nonlinear system with multiple inputs. Through Lyapunov analysis, we first establish local input-to-state stability with respect to temporal derivatives of the reference trajectory, along with regulation of the tracking errors when the reference trajectory approaches a stationary configuration. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of tracking the desired trajectory with desirable performance despite a large initial delay mismatch, which would cause nonadaptive prediction-based controllers to become unstable.

Iterative Learning Tracking Control of High-Speed Trains With Nonlinearly Parameterized Uncertainties and Multiple Time-Varying Delays

The precise operation control of high-speed trains is pivotal to maintain the safety and efficiency of trains, while the inevitable state delays will seriously attenuate the performance of control system. In this paper, an adaptive iterative learning control (ILC) approach for high-speed trains is presented in the presence of the nonlinearly parameterized uncertainties and multiple unknown state delays, aiming to drive that the displacements and velocities of trains can track the desired reference trajectories. To describe the operational dynamics of trains more realistically, the multi-particle model of trains involving multiple time-varying delays is established by analyzing the aerodynamic resistance, mechanical resistance, and coupler force acting on different cars. The proposed adaptive ILC scheme fully leverages various techniques, e.g., the hyperbolic tangent function, the parameter separation, to cope with the inherent nonlinearities, uncertainties and couplings of system. Specially, to eliminate the negative influence of unknown delays, an appropriate Krasovskii function is integrated into the Lyapunov criterion to devise the learning controller and check the stability of control systems. The novelties of our work lie in that the refinement model and periodical characteristic are simultaneously utilized to improve the practicability and performance of control scheme for the high-speed trains with multiple state delays.

Control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delays

This paper presents a control strategy for plasma glucose regulation in the presence of input with unknown time delay (constant or variable) and meal disturbances in the system. The control scheme proposed is an observer-based state feedback controller. The observer achieves to estimate the state vector even if the control input in the system presents an unknown time delay in the input. The main advantage of the controller is that the gains are selected so the control law will provide positive values that ensure an implementable case. The observer-based control scheme is validated considering different disturbance and unknown delays scenarios, in both cases, glucose regulation is achieved, rejecting meal disturbances in 4 hours and avoiding hypoglycemic episodes.

Simultaneous actuator and sensor fault reconstruction of singular delayed linear parameter varying systems in the presence of unknown time varying delays and inexact parameters

SummaryIn this article, robust fault diagnosis of a class of singular delayed linear parameter varying systems is considered. The considered system has delayed dynamics with unknown time varying delays and also it is affected by noise, disturbance and faults in both actuators and sensors. Moreover, in addition to the aforementioned unknown inputs and uncertainty, another source of uncertainty related to inexact measures of the scheduling parameters is present in the system. Making use of the descriptor system approach, sensor faults in the system are added as additional states into the original state vector to obtain an augmented system. Then, by designing a suitable proportional double integral unknown input observer (PDIUIO), the states, actuator, and sensor faults are estimated. The uncertainty due to the mismatch between the inexact parameters that schedule the observer and the real parameters that schedule the original system is formulated with an uncertain system approach. In the PDIUIO, the uncertainty induced by unknown inputs (disturbance, noise and actuator, and sensor faults), unknown delays, and inexact parameter measures are attenuated in H∞ sense with different weights. The constraints regarding the existence and the robust stability of the designed PDIUIO are formulated using linear matrix inequalities. The efficiency of the proposed method is verified using an application example based on an electrical circuit.

Global Regulation of a Chain of Integrators with an Unknown Delay in the Input via Reduced-order Observer Based Output Feedback with a Gain-scaling Factor

Global Regulation of a Chain of Integrators with an Unknown Delay in the Input via Reduced-order Observer Based Output Feedback with a Gain-scaling Factor

Neural network state observer-based robust adaptive iterative learning output feedback control for the rigid-flexible coupled robotic systems with unknown delays and backlash-like hysteresis

Neural network state observer-based robust adaptive iterative learning output feedback control for the rigid-flexible coupled robotic systems with unknown delays and backlash-like hysteresis

Event-Triggered Global Regulation of an Uncertain Chain of Integrators under Unknown Time-Varying Input Delay

Event-Triggered Global Regulation of an Uncertain Chain of Integrators under Unknown Time-Varying Input Delay

Single Phase Second Order Sliding Mode Controller for Mismatched Uncertain Systems with Extended Disturbances and Unknown Time-Varying Delays

In this paper, a novel single phase second order sliding mode controller (SPSOSMC) is proposed for the mismatched uncertain systems with extended disturbances and unknown time-varying delays. The main achievements of this study consist of three tasks: 1) a reaching phase in conventional sliding mode control (CSMC) technique is removed to ensure the global stability of the system; 2) an influence of the undesired high-frequency oscillation phenomenon in control input is vanished; 3) an exogenous perturbation is generally extended to the k-order disturbance of state variable. Firstly, a single phase switching manifold function is defined to eliminate the reaching phase in CSMC. Secondly, an unmeasurable state variable is estimated by using the proposed reduced-order sliding mode observer (ROSMO) tool. Next, a SPSOSMC is built based on the help of ROSMO tool and output information only. Then, a sufficient condition is established by employing the linear matrix inequality (LMI) technique and Lyapunov function theory such that the resulting sliding mode dynamics is asymptotically stable. Finally, a numerical example is simulated via the well-known MATLAB software to validate the effectiveness of the proposed technique.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Procrastinated Tree Search: Black-Box Optimization with Delayed, Noisy, and Multi-Fidelity Feedback

In black-box optimization problems, we aim to maximize an unknown objective function, where the function is only accessible through feedbacks of an evaluation or simulation oracle. In real-life, the feedbacks of such oracles are often noisy and available after some unknown delay that may depend on the computation time of the oracle. Additionally, if the exact evaluations are expensive but coarse approximations are available at a lower cost, the feedbacks can have multi-fidelity. In order to address this problem, we propose a generic extension of hierarchical optimistic tree search (HOO), called ProCrastinated Tree Search (PCTS), that flexibly accommodates a delay and noise-tolerant bandit algorithm. We provide a generic proof technique to quantify regret of PCTS under delayed, noisy, and multi-fidelity feedbacks. Specifically, we derive regret bounds of PCTS enabled with delayed-UCB1 (DUCB1) and delayed-UCB-V (DUCBV) algorithms. Given a horizon T, PCTS retains the regret bound of non-delayed HOO for expected delay of O(log T), and worsens by T^((1-α)/(d+2)) for expected delays of O(T^(1-α)) for α ∈ (0,1]. We experimentally validate on multiple synthetic functions and hyperparameter tuning problems that PCTS outperforms the state-of-the-art black-box optimization methods for feedbacks with different noise levels, delays, and fidelity.

Finite‐time estimation for a class of systems with unknown time‐delay using modulating functions‐based method

AbstractTime‐delay systems are widely used to model real problems. Most of the works on such systems assume prior knowledge of the delay, which is mostly unknown in real applications. This paper aims to fast and robustly estimate unknown delay, parameters, and output derivatives for a class of linear time‐delay systems in noisy environment. First, the classical modulating functions method is combined with the recursive least square algorithm and the Gauss–Newton method to estimate the coefficients and the time‐delay, respectively. Second, the generalized modulating functions method is adopted to provide algebraic integral formulas to estimate the output derivatives using the estimated parameters. Finally, numerical simulations are given to demonstrate the efficiency and robustness of the proposed methods.

Robust adaptive fault detection and diagnosis observer design for a class of nonlinear systems with uncertainty and unknown time-varying internal delay

This paper introduces a novel robust adaptive fault detection and diagnosis (FDD) observer design approach for a class of nonlinear systems with parametric uncertainty, unknown system fault and time-varying internal delays. The conditions for the existence of the proposed FDD are obtained based on the well-known Linear Matrix Inequalities (LMI) technique. Using Lyapunov stability theory, the adaptation laws for updating the observer weights and unknown faults estimation are derived based on which the convergence of the state estimation error to zero and asymptotic stability of the error dynamics are proven. Toward this, a new structural algorithm for FDD observer design is also derived based on LMIs. The performance of the proposed method is also investigated while applying to some industrial systems. Simulation results illustrate superior performance of the proposed method for the systems subject to time-varying unknown delays on states, uncertainty in nonlinear system modeling and unknown system faults.

Global stabilisation of nonlinear systems with unknown time-varying delay and measurement uncertainty

ABSTRACT Based on a new constructive solution of a couple of matrix inequalities containing an unknown time-varying parameter, this paper proposes a novel dual-gain scaling approach including a dynamic-gain observer and an output feedback controller with static and dynamic gains. In particular, our control approach is applicable to a class of nonlinear time-delay systems with nonlinear growth constraint and large unknown measurement sensitivity that may be non-differentiable. With the help of the Razuminkhin theorem, it is shown that the global adaptive stability of the resulting closed-loop system is achieved and our controller is robust to arbitrary bounded time-varying delay. In addition, the control approach proposed is non-backstepping and has low computing complexity.

Observer-Based Control Design for Nonlinear Systems With Unknown Delays

In this brief, we study the problem of designing observer-based controller for nonlinear system subject to unknown time-varying state delay. The unknown delay is assumed to be upper bounded, but nevertheless the bound is not required to be known. In order to tackle this interesting problem, we utilize a Halanay-inequality-based criterion which can guarantee exponential stability of the closed-loop system as well as the estimation error system. This exponential stability criterion allows us to design observer-based controller for the nonlinear time-delay system without invoking differentiability assumption on the unknown delay. A robotic system is considered to illustrate the efficiency of the new results.

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.

Adaptive Neural Tracking Control for a Two-Joint Robotic Manipulator with Unknown Time-Varying Delays

This paper presents an adaptive neural tracking control approach for a two-joint robotic manipulator with unknown time-varying delays. In order to work out the effect of unknown time-varying delays on the two-joint robotic manipulator, the appropriate Lyapunov–Krasovskii functionals (LKFs) and separation technology are chosen to settle this matter. The neural networks work as an approximator that has the advantage of estimating the unknown function in the system. In this paper, Lyapunov stability analysis can prove that all signals of the closed-loop system are semiglobal uniformly ultimately bounded and the tracking error can converge to a compact neighborhood with respect to zero. The simulation consequences demonstrate the availability of the feedforward control approach.