Unknown Time-varying Delays Research Articles

Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics

Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics

Decentralized learning control for high-speed trains with unknown time-varying speed delays

Treating the multi-point-mass dynamic model of high-speed trains as an interconnected system, this study proposes a decentralized iterative learning control scheme for high-speed trains to achieve the trajectory tracking goal. By making reasonable estimates of the interaction term and compensating for it, the proposed control scheme utilizes only local information from each carriage and does not need any inter-carriage information exchange. The zero-error tracking of the desired trajectory is guaranteed even in a restricted communication environment. Considering unknown time-varying speed delays in the actual high-speed train operations, a modified decentralized iterative learning control scheme is also provided to address the negative impact of speed delays. The convergence of tracking errors is strictly proven by constructing appropriate composite energy functions. Numerical simulations further verify the theoretical results.

Fixed-time prescribed performance tracking for nonlinear systems with unknown time-varying input delay

Fixed-time prescribed performance tracking for nonlinear systems with unknown time-varying input delay

Output Feedback Consensus for High-order Stochastic Multi-agent Systems With Unknown Time-varying Delays

Output Feedback Consensus for High-order Stochastic Multi-agent Systems With Unknown Time-varying Delays

Performance Guaranteed Robust Tracking Control of MIMO Nonlinear Systems With Input Delays: A Global and Low-Complexity Solution.

This article presents a global performance guaranteed tracking control method for a class of general strict-feedback multi-input and multi-output (MIMO) nonlinear systems with unknown nonlinearities and unknown time-varying input delays. By introducing a novel error transformation embedded with the Lyapunov-Krasovskii functional (LKF), the developed control scheme exhibits several appealing features: 1) it is able to achieve global prescribed performance tracking for uncertain MIMO systems with delayed inputs, while at the same time eliminating the constraint conditions imposing on initial values between the tracking/virtual error and the performance function; 2) there is no need for any a priori knowledge regarding the nonlinearities of the system nor a prior knowledge of time derivatives of the desired trajectory, making the resultant controller simpler in structure and less expensive in computation; 3) the control scheme includes a new differentiable time-varying feedback term, which gracefully compensates the unknown input delays and unknown control gain coefficient matrices; and 4) the controllability condition is relaxed, which enlarges the applicability of the proposed strategy. Finally, a two-link robotic manipulator example is provided to demonstrate the reliability of the theoretical results.

Observer-Based Finite-Time Adaptive Fault-Tolerant Control for Nonlinear System with Unknown Time-Varying Delay

Observer-Based Finite-Time Adaptive Fault-Tolerant Control for Nonlinear System with Unknown Time-Varying Delay

Adaptive path tracking control for autonomous vehicles with sideslip effects and unknown input delays

This paper presents an adaptive path-tracking control of autonomous ground vehicles with sideslip effects and time-varying input delays. To handle the problem of unknown time-varying input delays, the vehicle kinematic model is transformed into a novel chain model, and a delay-based auxiliary integral term is introduced for the estimation of the unknown terms caused by time-varying delays. To avoid modeling errors caused by existing linear approximation methods, a new adaptive path-tracking control strategy is proposed, such that the optimal tracking performance is achieved by appropriately adjusting certain design parameters. In addition, the inherent complexity explosion issue is avoided with the aid of a boundary estimation strategy. All signals of the closed-loop systems are guaranteed to be bounded. Simulation results illustrate the effectiveness of the method proposed.

Observer-based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay.

This article introduces an observer-based control strategy tailored for regulating plasma glucose in type 1 diabetes mellitus patients, addressing challenges like unknown time-varying delays and meal disturbances. This control strategy is based on an extended Bergman minimal model, a nonlinear glucose-insulin model to encompass unknown inputs, such as unplanned meals, exercise disturbances, or delays. The primary contribution lies in the design of an observer-based state feedback control in the presence of unknown long delays, which seeks to support and enhance the performance of the traditional artificial pancreas by considering realistic scenarios. The observer and control gains for the observer-based control are computed through linear matrix inequalities formulated from Lyapunov conditions that guarantee closed-loop stability. This design deploys a soft and gentle dynamic response, similar to a natural pancreas, despite meal disturbances and input delays. Numerical tests demonstrate the scheme's effectiveness in glycemic level regulation and hypoglycemic episode avoidance.

Non-predictor event-triggered controller for high-order feedforward nonlinear systems with unknown time-varying delays in the states and input

This paper studies the global regulation problem by a non-predictor event-triggered controller for high-order feedforward nonlinear systems with unknown time-varying delays in the states and input. We propose a non-predictor-based event-triggered controller with a dynamic gain-scaling factor, in which any information on the delays is not required in controller design. The dynamic gain-scaling factor is utilised to deal with high-order terms so that the considered class of systems are generalised over the previous results. The simulation results effectively demonstrate the validity of our proposed control method.

Event-Triggered State and Disturbance Estimation for Lipschitz Nonlinear Systems With Unknown Time-Varying Delays.

We consider the event-triggered state and disturbance simultaneous estimation problem for Lipschitz nonlinear systems with an unknown time-varying delay in the state vector. For the first time, state and disturbance can be robustly estimated by using an event-triggered state observer. Our method uses only information of the output vector when an event-triggered condition is satisfied. This contrasts with previous methods of simultaneous state and disturbance estimation based on augmented state observers where the information of the output vector was assumed to be always continuously available. This salient feature, thus, lessens the stress on communication resources while can still maintain an acceptable estimation performance. First, to solve the new problem of event-triggered state and disturbance estimation, and to tackle unknown time-varying delays, we propose a novel event-triggered state observer and establish a sufficient condition for its existence. Then to overcome some technical difficulties in synthesizing observer parameters, we introduce some algebraic transformations and use inequalities, such as the Cauchy matrix inequality and the Schur complement lemma to establish a convex optimization problem in which observer parameters and optimal disturbance attenuation levels can be systematically derived. Finally, we demonstrate the applicability of the method by using two numerical examples.

Asymptotic Tracking Control for Uncertain Nonlinear Strict-Feedback Systems With Unknown Time-Varying Delays.

It is nontrivial to achieve asymptotic tracking control for uncertain nonlinear strict-feedback systems with unknown time-varying delays. This problem becomes even more challenging if the control direction is unknown. To address such problem, the Lyapunov-Krasovskii functional (LKF) is used to deal with the time delays, and the neural network (NN) is applied to compensate for the time-delay-free yet unknown terms arising from the derivative of LKF, and then an NN-based adaptive control scheme is constructed on the basis of backstepping technique, which enables the output tracking error to converge to zero asymptotically. Besides, with a milder condition on time delay functions, the notorious singularity issue commonly encountered in coping with time delay problems is subtly settled, which makes the proposed scheme simple in structure and inexpensive in computation. Moreover, all the signals in the closed-loop system are ensured to be semiglobally uniformly ultimately bounded, and the transient performance can be improved with proper choice of design parameters. Both the theoretical analysis and numerical simulation are carried out to validate the relevance of the proposed method.

Dynamic Gain Reduced-Order Observer-Based Global Adaptive Neural-Network Tracking Control for Nonlinear Time-Delay Systems.

In this article, a globally adaptive neural-network tracking control strategy based on the dynamic gain observer is proposed for a class of uncertain output-feedback systems with unknown time-varying delays. A reduced-order observer with novel dynamic gain is proposed. An n th-order continuously differentiable switching function is constructed to achieve the continuous switching control of the system, thus further ensuring that all the closed-loop signals are globally uniformly ultimately bounded (GUUB). It is proved that by adjusting the designed parameters, the tracking error converges to a region which can be adjusted to be small enough. The effectiveness of the control scheme is demonstrated by two simulation examples.

Event-triggered guaranteed cost control for uncertain polytopic fractional-order systems subject to unknown time-varying delays

Event-triggered guaranteed cost control for uncertain polytopic fractional-order systems subject to unknown time-varying delays

Adaptive Variable Structure Controller Design for Uncertain Switched Systems With Unknown Time-varying Delay

Adaptive Variable Structure Controller Design for Uncertain Switched Systems With Unknown Time-varying Delay

Event-triggered tracking control for nonlinear time-varying delay systems with full state constraints and unknown control coefficients

This paper addresses the problem of event-triggered control for a class of nonlinear systems with unknown control coefficients, time-varying delays, full state constraints and external disturbances, simultaneously. Firstly, based on integral Barrier-Lyapunov Functionals, an adaptive event-triggered controller is designed to account for the impacts of complete state constraints, unknown time-varying delays and external disturbances. Using fuzzy logic systems, the unknown functions of systems are then roughly estimated. The system redundancy can be significantly reduced by implementing the event-triggered control technique in the meanwhile. By introducing the separation technique and Lyapunov–Krasovskii functionals, it is shown that the strategy can ensure tracking performance greatly and all the closed-loop signals of the system are bounded. Compared with the existing results, the proposed design scheme is less conservative and has a wilder application range. Finally, the simulation results show the effectiveness of the proposed approach.

Fixed-time tracking control for high-order nonlinear systems with unknown time-varying input delay

Fixed time tracking control for nonstrict feedback high-order nonlinear systems with unknown time-varying external disturbance and unknown time-varying input delay has been studied in this research. Firstly, the obstacle caused by unknown time-varying input delay has been tackled by introducing a compensation signal. The unknown nonlinear functions are identified by neural networks and the algebraic loop problem for nonstrict feedback systems has been overcome by using the properties of neural networks. Further, a bound estimation mechanism is employed to estimate the identify error and unknown time-varying external disturbance without using the priori knowledge of the boundary. Regarding the obstacle caused by high-order terms and the singularity problem have been tackled by using adding a power integrator mechanism and the inequality transformation technique, respectively. The boundedness of all the signals in the closed-loop systems has been proved by using the Lyapunov stability theorem, and the convergence time is independent of the initial value of the system state. Finally, the simulation results show the effectiveness of the proposed method.

Analysis and design of control systems via parameter‐based approach

Analysis and design of control systems via parameter‐based approach

Event-triggered stabilization of linear input-delay systems with state quantization and unknown time-varying delay: A Razumikhin stability theorem-based approach

Benefiting from the input-to-state stability (ISS) version of the Razumikhin stability theorem, this paper deals with the stabilization of continuous linear input-delay systems with state quantization and without any knowledge about the delay. An event-triggered delay independent truncated predictor feedback (ET-DITPF) controller with a switched feedback control law is proposed to guarantee the globally uniformly asymptotic stability (GUAS)/globally uniformly exponential stability (GUES) of the closed-loop system. As a prominent feature, this controller uses no information about the time delay (neither its value nor its upper bound). In the proposed event-triggered framework, a lower bound for each two consecutive events is derived to show the non-occurrence of the Zeno behavior. Numerical simulations confirm the effectiveness of the obtained theoretical results.

Neural network adaptive compensation control based on the backstepping method for nonlinear systems with time-varying delays

ABSTRACT Control of nonlinear systems with time-varying delays is a common problem, particularly when the time-varying delays are unknown. This paper presents an adaptive compensation control method based on multiple neural networks. Firstly, considering the nonlinear systems with time-varying delays, a neural network method is adopted to approximate the unknown nonlinear structure with time-varying delays. On this basis, a backstepping controller is designed. Considering the unknown time-varying delays, the control effect of the neural network controller based on the backstepping method is not optimal. To deal with the problem, a double-layer adaptive compensator for the neural network is proposed. Furthermore, for the neural network adaptive compensation controller based on the backstepping method, the stability is also proved by a Lyapunov method. Finally, simulation results demonstrate the effectiveness of the scheme, especially when the nonlinear systems have an unknown time-varying delay.

Robust Cadence and Power Tracking on a Switched FES Cycle With an Unknown Electromechanical Delay

Functional electrical stimulation (FES) is commonly used to facilitate cycling tasks for people with lower-limb movement disorders. In this work, FES and motor controllers are designed to track a desired power and cadence, respectively, and a Lyapunov-based switched systems analysis is performed to guarantee uniformly ultimately bounded power tracking and global exponential cadence tracking for a switched, delayed, nonlinear, and uncertain FES-cycling system. A unique challenge in this problem is that there is an unknown time-varying input delay to produce force, and a different unknown time-varying residual input delay where force is still produced after stimulation is removed. These delays impact the dwell-time conditions that dictate stimulation timing, and if not properly accounted for can lead to undesired effects such as antagonistic muscles exerting force at the same time or potential instabilities. The proposed controllers were validated by experimental analysis of four participants with neurological conditions (NCs) and five able-bodied participants, and yielded average power and cadence tracking errors of 0.01 ± 0.09 W and −0.05 ± 0.65 revolutions per minute (RPM), respectively, for the able-bodied participants and 0.01 ± 1.11 W and −0.07 ± 1.17 RPM, respectively, for the participants with NCs.