Nonlinear Time-delay Systems Research Articles

Adaptive Neural Indirect Inverse Control for a Class of Fractional-Order Hysteretic Nonlinear Time-Delay Systems and Its Application

Adaptive Neural Indirect Inverse Control for a Class of Fractional-Order Hysteretic Nonlinear Time-Delay Systems and Its Application

Tube-based integral sliding mode predictive control scheme for constrained uncertain nonlinear time-delay system

Tube-based integral sliding mode predictive control scheme for constrained uncertain nonlinear time-delay system

Sampled-data control of a class of stochastic feedforward nonlinear systems with large delays and sparse sampling

This paper investigates the problem of sampled-data control for a class of stochastic nonlinear systems with delays in the input and state. It is shown that under an upper-triangular linear growth condition, a linear memoryless sampled-data feedback controller is able to globally stabilise the stochastic nonlinear time-delay systems, no matter how large the time delay and sampling period are. The memoryless sampled-data feedback controller is designed by using the emulation method together with the feedback domination technique. With the aid of Lyapunov-Krasovskii functional method, the constructed memoryless sampled-data feedback controller achieves global exponential stability (GES) in mean square of the hybrid closed-loop systems. Application of the sampled-data control scheme is demonstrated through a practical example with simulation.

Predictor-based sampled-data output-feedback control for feedforward nonlinear time-delay systems

Predictor-based sampled-data output-feedback control for feedforward nonlinear time-delay systems

Adaptive Fuzzy Tracking Control for Nonlinear Time-Delay Systems With Performance Constrained by Deferred Monotone Tube Boundaries

Adaptive Fuzzy Tracking Control for Nonlinear Time-Delay Systems With Performance Constrained by Deferred Monotone Tube Boundaries

Observer-based control for time-delayed quasi-one-sided Lipschitz nonlinear systems under input saturation

This paper addresses the observer-based controller design problem for nonlinear time-delayed systems under input saturation. The nonlinearities are supposed to satisfy the quasi-one-sided Lipschitz condition, which is less conservative than the one-sided Lipschitz condition. Based on the nonlinear matrix inequalities, control law for nonlinear systems subject to input saturation, time delays, and unavailable states, some sufficient conditions have been developed for an augmented system containing the system state vector and the error vector to ensure the convergence of all states to zero. The paper used a decoupling approach to reduce the complexity of the corresponding observer and controller gain computations. Finally, the effectiveness of the developed results is validated using suitable examples.

Adaptive output feedback command filter control based on extreme learning machine for nonaffine time delay systems with input saturation

This paper is concerned with the tracking control problem of nonlinear time delay systems. For time delay systems, we consider nonaffine pure-feedback structure. Additionally, the case where the time delay systems are subject to input saturation and unknown states is also taken into account. To begin with, a mean value theorem and an implicit function theorem are exploited to transform the systems into an affine form. Afterwards, a state observer is developed to estimate the unknown state variables and an extreme learning machine (ELM) is used to approximate the unknown functions. The output of the command filter replaces the virtual control signal'derivative, thereby circumventing the problem of ‘explosion of complexity’. Meanwhile, compensation signals are introduced to eliminate the filtering errors in a dynamic surface control (DSC). A Lyapunov–Krasovskii functional is designed to mitigate the unknown constant state time delay. During the controller design process, combining a prescribed performance control (PPC) with a command filter control, the tracking error can converge to a predetermined bound. Additionally, the effect of input saturation is eliminated with the aid of an auxiliary system. Finally, the effectiveness of such controller is further proved by taking an electromechanical system as an application object.

Digital-Twin Predictive Control of Nonlinear Systems With Time Delays, Unknown Dynamics, and Communication Delays.

With the advancement of computing technology and big data technology, digital twins have gradually been applied in various fields, such as manufacturing, energy, and healthcare. This article studies the predictive control of nonlinear dynamic systems using digital twins. Based on a digital-twin control system framework, predictive control is discussed for three different nonlinear systems with time delays: 1) known nonlinear systems; 2) unknown nonlinear systems; and 3) unknown nonlinear cyber-physical systems. Both a digital-twin predictive control strategy and a digital-twin control predictor are proposed to compensate for time delays and communication delays actively. With the strategy and predictor, the digital-twin controller of a time-delay nonlinear system can be designed to achieve the desired performance based on the nonlinear system without time delays, which vastly simplifies the controller design procedure. A digital model is constructed using data to deal with unknown nonlinear dynamics. The three different closed-loop digital-twin predictive control systems are analyzed to derive a unified stability criterion. The simulation results show how the proposed digital-twin predictive control method performs well for nonlinear systems with time delays, unknown dynamics, and/or communication delays.

Energy-harvesting recursive filtering for delayed systems with amplify-and-forward relays: Cooperative communication manner

The recursive filtering problem is explored for a class of nonlinear time-delayed systems with amplify-and-forward (AF) relay and energy-harvesting (EH) technology. In order to enhance the signal quality of the remote transmission in wireless communication, the relay under the AF protocol is introduced that posing the merits of low complexity, less energy consumption and fast transmission rate. Meanwhile, to further alleviate the fading and improve the robustness of the signals, the cooperative communication manner is employed, which is different from the commonly encountered two-hop one. In the cooperative communication, the maximal ratio combining (MRC) method is utilized to make sure that the signal-to-noise ratio of the combined output can reach theoretical maximum. In addition, in order to achieve sustainable power supply in harsh environments, the EH sensors and relays are deployed, which can collect energy from external environments with certain probabilities. The aim of this paper is to develop a proper filter so as to reduce the impacts caused by the channel fading and insufficient energy. Furthermore, a minimized upper bound of the filtering error covariance is gained through appropriately designing the filter parameters. Then, the exponential boundedness is analyzed with regard to filtering error. Finally, a numerical example is exhibited to test the validity of the proposed filtering scheme.

Finite-time adaptive fuzzy event-triggered control for nonlinear time-delay system with input quantization via command filter

This paper investigates the problem of finite-time adaptive fuzzy event-triggered control for a class of uncertain nonlinear systems with input quantization. The nonlinear systems under consideration contain unmodeled dynamics and time-varying delays. Fuzzy logic systems are used to handle unknown nonlinear terms. Additionally, finite-time filters are introduced to solve the problem of “explosion of complexity” as well as to ensure that the derivative of the virtual controller can be approximated in finite time. The Lyapunov–Krasovskii function is used to handle time-varying delays. The hysteresis quantizer is used to ensure adequate precision when there is a low transmission rate requirement. The control strategy combines event-triggered mechanisms and quantization technology to ensure that all signals of the closed-loop system remain bounded in finite time. Finally, two examples are included to demonstrate the effectiveness of the proposed controller.

Adaptive distributed fault estimation observer design for nonlinear time-delay multi-agent systems with directed graphs

This paper focuses the development of an adaptive observer-based distributed fault estimation observer (DFEO) for multi-agent nonlinear time-delay systems under a directed communication topology. The process involves constructing a fault estimation observer for each agent based on their relative output estimation errors. An adaptive DFEO design is proposed for multi-agent systems with a directed communication topology. Furthermore, investigating the effect of faulty agents on the criteria of fault detection on healthy agents. The proposed design is represented with Linear Matrix Inequalities (LMIs) to establish a systematic design procedure. The study also includes simulation results to demonstrate the effectiveness of the proposed design techniques.

Stability, bifurcation, and chaos in a class of scalar quartic polynomial delay systems.

In this paper, a class of scalar quartic polynomial delay systems is investigated. We found rich dynamics in this system through numerical simulation, including chaotic attractors, chaotic saddles, and intermittent chaos. Moreover, this chaotic quartic system may serve as an approximation, through Taylor expansion, for a wide class of scalar delay differential equations. Thus, these nonlinear systems may exhibit chaotic behaviors, and the studies in our paper may provide an insight into the emergence of chaos in other time-delay nonlinear systems. We also conduct a detailed theoretical analysis of the system, including the stability of equilibria and Hopf bifurcation analysis based on the theory of normal form and center manifold. Additionally, a numerical analysis is provided to give numerical evidence for the existence of chaos.

Improved Full-Error Constrained Control for Unknown Interconnected Time-Delay Nonlinear Systems With Input Saturation

Improved Full-Error Constrained Control for Unknown Interconnected Time-Delay Nonlinear Systems With Input Saturation

H ∞ consensus control via intermittent communication for nonlinear multi-agent systems with unknown parameters and external disturbances

The consensus control problem is investigated for time-delayed nonlinear leader-following multi-agent systems, in which the unknown parameters and external disturbances are considered. Instead of using only one control method, a control scheme combining periodically intermittent control with H ∞ performance is employed. By manipulating the algebraic graph theory and constructing appropriate Lyapunov–Krasovskii functionals, sufficient solutions assuring the exponential H ∞ consensus of the considered systems are established in the form of linear matrix inequalities. The communication graph among the followers is directed, which removes the restrictions on undirected graph or balanced graph in the literature. Simulation analyses are finally presented to verify the theoretical results.

Finite-time prescribed performance tracking control for nonlinear time-delay systems with state constraints and actuator hysteresis

In this paper, the problem of adaptive neural network prescribed performance tracking control for a class of non-strict feedback time-delay systems constrained by full-state is studied. Radial basis function (RBF) neural networks (NNs) are integrated into the backstepping medium to deal with the uncertain functions and the barrier Lyapunov function (BLF) technique ensures that the state of the system does not exceed its limits. Subsequently, integrated with the Lyapunov–Krasovskii functional, the proposed control scheme makes the tracking errors converge to the preset region while the state constraint is not violated. Finally, the effectiveness of the scheme is supported by two simulation experiments.

Adaptive control for a class of stochastic nonlinear time-delay systems with unknown control coefficients

This paper mainly investigates the adaptive state feedback control problem for a class of stochastic nonlinear systems with time-delay and unknown control coefficients. The proposed control scheme leverages the dynamic gain technology and Nussbaum function to develop a state feedback controller, aiming to simplify its implementation and eliminate the influence of unidentified time-varying control coefficients. Through the utilization of suitable Lyapunov–Krasovskii (L–K) functionals and stochastic stability theories, it is demonstrated that the designed control mechanism guarantees the boundedness in probability for all closed-loop signals, ultimately regulating the state of the plant to zero. The availability and superiority of the developed adaptive management strategy are further certified through simulation results.

Off-Equilibrium Linearization-Based Control of Nonlinear Time-Delay System and Application to a Turbofan Engine

Off-Equilibrium Linearization-Based Control of Nonlinear Time-Delay System and Application to a Turbofan Engine

Adaptive fuzzy event-triggered control for a class of nonlinear time-delay multi-agent systems with dead zone and partial state constraints

This paper presents an adaptive fuzzy event-triggered control (ETC) method for a class of time-delay nonlinear multi-agent systems (MASs) with dead zone (DZ) and partial state constraints (PSCs). It should be pointed out that the states considered in this paper are unmeasurable and part of the system states are constrained by time-varying boundary. By utilizing fuzzy logic systems (FLSs) and backstepping design framework, a fuzzy state observer is constructed to estimate the unmeasured states, while the introduction of a time-varying barrier Lyapunov function (BLF) addresses the partial state constrained problem. Furthermore, during the design process of the state observer, compensation for the influence of the unknown DZ input on the system is achieved through utilization of known designed event-triggered input signal and adaptive parameter. Building upon this foundation, employing the Lyapunov stability theory and adaptive backstepping technique with ETC strategy, the developed distributed control mechanism demonstrates that all variables of the closed-loop system are bounded, the consensus error of the system can converge to a small region of origin and Zeno behavior can be ruled out. Finally, two simulation examples further illustrate the proposed control strategy and theorem.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

Event-Triggered Control of Switched Nonlinear Time-Delay Systems With Asynchronous Switching.

This article investigates the event-triggered switching control (ETSC) of switched nonlinear time-delay systems (SNTDSs) with asynchronous switching. First, we study the input-to-state stability (ISS) and integral ISS (iISS) for SNTDSs with asynchronous switching, where switching instants are generated based on the designed event-triggered mechanism. Among existing works on the ETSC, systems behavior at event-triggered instants is neglected. In fact, whenever an event is triggered, the systems mode will jump suddenly such that a switch is imposed to the systems, leading to the change of subsystems. Moreover, asynchronous switching behavior may occur between the actual subsystem and its corresponding controller. These facts bring great challenges for the event-triggered mechanism design and ISS analysis. To tackle these problems, a new Lyapunov-based event-triggered mechanism with adjustable parameters is designed to establish the relationship between systems switches and event triggers, and exclude the Zeno phenomenon. The analysis of the asynchronous switching behavior can be implemented and some ISS and iISS criteria of SNTDSs are derived utilizing the merging switching technique. Finally, two numerical examples, including a practical stirred tank reactor system, are presented to show the validity of the proposed methods.