Nonlinear Time-delay Systems Research Articles

Asymptotic Tracking Control of Nonlinear Time-Delay Systems With Mismatched Disturbances

This brief considers the asymptotic tracking control problem of nonlinear time-delay system in the presence of mismatched disturbances. By using dynamic gain based design method, a delay-independent dynamic tracking controller is constructed. Besides, a smooth function is introduced into the virtual controller to compensate the mismatched disturbances. By choosing appropriate Lyapunov-Krasovskii functionals, it is shown that the closed-loop system signals are bounded, and the system output can asymptotically track the desired signal. Finally, a simulation example is conducted to show the effectiveness of the proposed control scheme.

Event-triggered-based adaptive asymptotic tracking control for stochastic nonlinear time-delay systems with actuator and sensor faults

The issue of dynamic event-triggered adaptive asymptotic tracking control for stochastic nonlinear time-delay systems with actuator and sensor faults is investigated in this article. Utilizing fuzzy logic systems and projection operator, unknown time delays are calculated. Compared with the existing methods to overcome the effect of time delay, the estimation of the time delay information is considered to avoid the controller singularity problem. Moreover, to reckon the upper bound of fuzzy logic system approximation errors and other residuals, an error adaptive law is developed in the controller construction. With the assistance of stochastic Barbalat’s lemma and adaptive fuzzy control strategy, a novel asymptotic tracking fuzzy controller is proposed under multiple faults, which guarantees that the whole signals are bounded in probability. Besides, a dynamic event triggering control (DETC) is employed to save the communication resources. A practical example is supplied to demonstrate the effectiveness of the proposed control approach.

Output feedback neural adaptive control design for nonlinear time-delay systems

This paper addresses the adaptive output feedback control design problem for a class of nonlinear systems with unknown state time delays by combining the dynamic gain and neural network. A novel reduced-order dynamic gain observer is introduced to estimate the unmeasured system states. Radial basis function neural networks (RBF NNs) are used to approximate unknown functions. An adaptive NN output feedback controller is designed based on the backstepping technique. By arranging the proper Lyapunov–Krasovskii functional, we prove that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a physical example and a numerical example are given to prove the effectiveness of the proposed control scheme.

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

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.

Quantized Feedback Stabilization for Nonlinear Hybrid Stochastic Time-Delay Systems With Discrete-Time Observation.

The quantized feedback stabilization problem is investigated for nonlinear hybrid stochastic time-delay systems with discrete-time observation in this article. A quantized discrete-time observation feedback controller is designed. The designed controller can make the H∞ stability and mean-square sense of the controlled system. Particularly, this note is the first to develop the stability criteria, which is not only related to the duration between two successive observations but also links to time lag of the system. By utilizing the Lyapunov method and inequality scaling techniques, the estimates for the duration and the time delay of the system are gained, respectively. Some case simulations are also provided to testify the proposed method and demonstrate its power.

Global Stabilization for a Class of Stochastic Nonlinear Time-Delay Systems With Unknown Measurement Drifts and Its Application.

This article studies the control problem for a class of stochastic nonlinear time-delay systems with uncertain output functions. Under the appropriate assumptions, a stabilization controller is explicitly constructed by applying the adding a power integrator method. Then, using the Lyapunov-Krasovskii functionals to address time-delay, it is proven that the designed controller can guarantee the closed-loop system to be globally asymptotically stable (GAS) in probability. Finally, two simulations show that the control strategy is effective and can be applied to the actual system.

Stabilization Control for Strict-Feedback Nonlinear Systems With Time Delays

In this article, the output-feedback control problem for a class of nonlinear time-delay systems has been considered. Unmeasured system states and the time-varying delays which appear in all state variables bring great challenges to the controller design. Novel Lyapunov–Krasovkii functionals with control gains are proposed for a delay-independent controller. The system is proved to be asymptotically stable driven by the controller with suitable design parameters. Finally, we apply the new control scheme to a two-stage chemical reactor system and the time-delay tension leg platform system, the effectiveness of the control scheme is illustrated in the simulation results.

Switched-observer-based adaptive neural networks tracking control for switched nonlinear time-delay systems with actuator saturation

This paper deals with adaptive neural networks (NNs) output-feedback tracking control problem for a general class of switched nonlinear time-delay systems with actuator saturation. To estimate unmeasurable states, a constructive delay-independent switched-observer-based adaptive NNs control approach for solving the problem is provided by using the average dwell time (ADT) method and the backstepping technique. Design obstacles stemmed from unknown time delays and actuator saturation and unknown nonlinear functions are overcome by using appropriate multiple Lyapunov–Krasovskii functionals method, the Nussbaum gain technique, and neural network approximations, respectively. The proposed control strategy guarantees that i) all the closed-loop signals for the switched system are bounded in the semi-global sense under a class of switching signals with ADT, attaining semi-global uniformly ultimately boundedness (SGUUB); and, ii) the output tracking error is driven towards, and kept within, a small neighbourhood around the origin. Simulation results verify the effectiveness of the proposed control strategy on two numerical examples, including a practical switched continuous stirred tank reactor (CSTR) system.

Stability analysis of nonlinear time-delay singular systems via improved barbălat’s lemma

This paper revisits asymptotic stability problem of nonlinear time-delay singular systems (NTDSs). Many existing stability results for this problem are derived based on the classical Barbălat’s lemma. This lemma puts two requirements on the considered functions or functionals. One is uniform continuity, the other is boundedness of the infinite integral. However, in some cases, the first requirement is difficult to be satisfied. To mitigate this limitation, a novel improved Barbălat’s lemma is proposed in some literature. In this improved lemma, the requirement of uniform continuity is relaxed by quasi-uniform continuity. By virtue of this improved Barbălat’s lemma, this paper establishes a less conservative stability theorem for NTDSs. Then, the derived results related to NTDSs are applied to investigate stability problem of linear time-delay singular systems. To demonstrate the effectiveness of the proposed results, a numerical example about circuit systems is provided.

Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to "deeper" stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

New criteria for asymptotic stability of a class of nonlinear real-order time-delay systems

New criteria for asymptotic stability of a class of nonlinear real-order time-delay systems

A Semiglobal Approach for Stabilizing Nonlinear Systems With State Delays by Memoryless Linear Feedback

This article investigates the problem of how to control nonlinear systems with delays in the state by memoryless linear feedback. The notions of semiglobal asymptotic stabilization and sublevel sets are introduced in the context of time-delay systems. With the aid of Razumikhin theorem, we develop a semiglobal design method for the construction of Lyapunov functions, associated sublevel sets, and delay-free linear state feedback laws, step-by-step, achieving semiglobal asymptotic stabilization for time-delay nonlinear systems in a lower triangular form. In contrast to the global stabilization of nonlinear systems with delays in the state, which is usually achieved by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dynamic state</i> feedback (Lin and Zhang, 2020), the significance of this work is to point out that a tradeoff of the control objectives, e.g., semiglobal versus global stabilization, makes it possible to control a class of time-delay nonlinear systems by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">static linear</i> feedback. Extensions to nonlinear systems with globally asymptotically locally expoentially stable (GALES)-like inverse dynamics are also included in this article.

Homogeneity, Forward Completeness, and Global Stabilization of a Family of Time-Delay Nonlinear Systems by Memoryless Non-Lipschitz Continuous Feedback

For a family of genuinely nonlinear systems with delays in the input and state, global strong stabilization (GSS) in the sense of Kurzweil is shown to be possible by memoryless state and/or output feedback under two conditions: 1) The input delay is within an appropriate range although the state delays can be sufficiently large; 2) the time-delay bounding system is homogeneous of degree zero and has a lower triangular structure. The proof is based on the Lyapunov–Krasovskii functional theorem combined with the homogeneous domination philosophy. Using the emulation approach, we design memoryless homogeneous state and output feedback controllers, respectively, achieving GSS of the time-delay closed-loop systems with severe nonlinearity. Extensions to a wider class of time-delay nonlinear systems in the Hessenberg form are also given. Examples and counter-examples presented in this article illustrate not only the necessity of the homogeneous growth conditions but also the significance of the memoryless non-Lipschitz continuous feedback control strategies.

Adaptive Neural Control of a Class of Uncertain State and Input-Delayed Systems With Input Magnitude and Rate Constraints

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

A Switched Integral-Based Event-Triggered Control of Uncertain Nonlinear Time-Delay System With Actuator Saturation.

This article explores the asymptotic stabilization criteria of the uncertain nonlinear time-delay system subject to actuator saturation. A switched integral-based event-triggered scheme (IETS) is established to reduce the redundant data transmission over the networks. The switched IETS condition uses the integration of system states over a time period in the past. A fixed waiting time is included to avoid the Zeno behavior. In order to estimate a larger domain of attraction, a delay-dependent polytopic representation method is presented to deal with the effects of actuator saturation in the proposed model. A new series of less conservative linear matrix inequalities (LMIs) is proposed on the basis of delay-dependent Lyapunov-Krasovskii functional (LKF) to ensure the stability of nonlinear time-delay system subject to actuator saturation using the proposed IETS. Numerical examples are used to confirm the effectiveness and advantages of the proposed IETS approach.

Stabilization of nonlinear time-delay systems: Flexible delayed impulsive control

This paper studies the stabilization of nonlinear time-delay systems under flexible delayed impulsive control. Some sufficient conditions are provided for establishing stability property in terms of exponential Lyapunov-Razumikhin functions. It is shown that the size of delay in continuous dynamics can be flexible. Specially, it can be smaller or larger than the impulsive intervals, and there is no magnitude relationship between the delay in continuous flow and impulsive delay. In most existing results, from the impulsive control point of view, the Lyapunov functions were based on the assumption that there was a common threshold at every impulse point. In this study, utilizing the proposed method of average impulsive estimation (AIE), the rate coefficients are flexible, and the impulsive delay can be integrated to guarantee the effect of stabilization of impulses. As an application, the theoretical results are applied to the synchronization of a chaotic neural network, and the impulsive control input is formalized in terms of linear matrix inequalities (LMIs). The efficiency of the derived results is illustrated by two numerical examples.

Bipartite consensus for nonlinear time-delay multiagent systems via time-varying gain control method

Bipartite consensus for nonlinear time-delay multiagent systems via time-varying gain control method

Study on Setpoint Tracking Performance of the PID SISO and MIMO Under Noise and Disturbance for Nonlinear Time-Delay Dynamic Systems

This paper presents a case study of the setpoint tracking performance of the proportional integral derivative (PID) controller on the Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) nonlinear digital plants under Gaussian white noise and constant load disturbance for the nonlinear time-delay dynamic system. With the objective of getting a better understanding of the nonlinear discrete-time PID controller, we proposed a case study using two SISO and two MIMO digital plants, and then do the numerical simulations along with the addition of Gaussian white noise and load disturbance to simulate the real environment. In this paper, we compare the results of the system working with and without noise and load disturbance. The study result of this paper shows that on the discrete-time digital nonlinear plant, the PID controller is working well to follow the nonlinear setpoint even under heavy noise and load disturbance. The study compared the performance indexes of the controllers in terms of the maximum error, the Root mean square error (RMSE), the Integral square error (ISE), the Integral absolute error (IAE), and the Integral of time-weighted absolute error (ITAE).

Adaptive NN Finite-Time Resilient Control for Nonlinear Time-Delay Systems With Unknown False Data Injection and Actuator Faults.

This article considers neural network (NN)-based adaptive finite-time resilient control problem for a class of nonlinear time-delay systems with unknown fault data injection attacks and actuator faults. In the procedure of recursive design, a coordinate transformation and a modified fractional-order command-filtered (FOCF) backstepping technique are incorporated to handle the unknown false data injection attacks and overcome the issue of "explosion of complexity" caused by repeatedly taking derivatives for virtual control laws. The theoretical analysis proves that the developed resilient controller can guarantee the finite-time stability of the closed-loop system (CLS) and the stabilization errors converge to an adjustable neighborhood of zero. The foremost contributions of this work include: 1) by means of a modified FOCF technique, the adaptive resilient control problem of more general nonlinear time-delay systems with unknown cyberattacks and actuator faults is first considered; 2) different from most of the existing results, the commonly used assumptions on the sign of attack weight and prior knowledge of actuator faults are fully removed in this article. Finally, two simulation examples are given to demonstrate the effectiveness of the developed control scheme.