State Time Delay Research Articles

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.

Robust Fault Estimation and Fault‐Tolerant Control for a Class of Fuzzy Singularly Perturbed Systems With State Time Delay Based on Learning Observer

ABSTRACTThis article studies the problem of fault estimation (FE) and dynamic output fault‐tolerant control (DOFTC) for a class of Takagi–Sugeno (T–S) fuzzy singularly perturbed systems (SPSs) which subject to time delay, external disturbance and actuator fault. A new fault estimation and fault‐tolerant control scheme was proposed and designed for the influence of the change of perturbation parameter on the singularly perturbed system. This scheme adopts the Takagi–Sugeno (T–S) fuzzy model, learning observer and dynamic output feedback fault‐tolerant mechanism, so that the system has multi‐time‐scale dynamic stability. The results show that this method has more accurate estimation effect, faster convergence speed, and very fast steady‐state response of fault‐tolerant control when faults occur. Furthermore, when constructing the Lyapunov function, the improved matrix was selected to ensure that the closed‐loop system is stable for all , and at the same time, the conservativeness of the results was reduced. Finally, the feasibility and correctness of the proposed design method were illustrated through two numerical examples.

Bumpless transfer control for switched time-delay systems with application to aero-engine control

For switched time-delay systems, the bumpless transfer control issue is investigated by utilizing the multiple piecewise Lyapunov–Krasovskii function approach. First, a time-delay-dependent bumpless transfer concept is put forward to depict the transient performance of switched time-delay systems, which restricts the bumps in the amplitude of the present state and the time-delay state, simultaneously. Second, a state-dependent switching signal with a prescribed time is designed to avoid switching frequently. A time-varying switching controller is developed to decrease control bumps. Third, under the premise of achieving asymptotic stability, a solvability condition ensuring a satisfactory bumpless transfer performance is derived through relaxing the traditional bumpless transfer condition. Finally, an instance of the aero-engine control system is used for exhibiting the validity of the presented method.

Adaptive Finite-Time-Based Neural Optimal Control of Time-Delayed Wheeled Mobile Robotics Systems.

For nonlinear systems with uncertain state time delays, an adaptive neural optimal tracking control method based on finite time is designed. With the help of the appropriate LKFs, the time-delay problem is handled. A novel nonquadratic Hamilton-Jacobi-Bellman (HJB) function is defined, where finite time is selected as the upper limit of integration. This function contains information on the state time delay, while also maintaining the basic information. To meet specific requirements, the integral reinforcement learning method is employed to solve the ideal HJB function. Then, a tracking controller is designed to ensure finite-time convergence and optimization of the controlled system. This involves the evaluation and execution of gradient descent updates of neural network weights based on a reinforcement learning architecture. The semi-global practical finite-time stability of the controlled system and the finite-time convergence of the tracking error are guaranteed.

Distributed State Observer for Systems with Multiple Sensors under Time-Delay Information Exchange.

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Wind and Wave-Induced Vibration Reduction Control for Floating Offshore Wind Turbine Using Delayed Signals

Active vibration control is a critical issue of the wind turbine in the field of marine energy. First, based on a three-degree-of-freedom wind turbine, a state space model subject to wind and wave loads is obtained. Then, a delayed state feedback control scheme is illustrated to reduce the vibration of platform pitch angle and tower top foreaft displacement, where the control channel includes time-delay state signals. The designed controller’s existence conditions are investigated. The simulation results show that the delayed feedback H∞ controller can significantly suppress wind- and wave-induced vibration of the wind turbine. Furthermore, it presents potential advantages over the delay-free feedback H∞ controller and the classic linear quadratic regulator in two aspects: vibration control performance and control cost.

Dynamic stability and control of vortex induced oscillations of tension leg platform tethers

Dynamic stability and control of sway oscillations of Tension Leg Platform (TLP) tether under regular vortex shedding are investigated. The TLP is modelled as a single degree of freedom simply supported uniform beam under pretension, assuming transverse oscillation to take place only in its fundamental natural mode. The tether is subjected to parametric excitation due to the heave motion of the TLP. The incremental harmonic balance (IHB) method is employed to investigate the period-1 and period-2 responses of the TLP as a function of the detuning parameter. The same system is then investigated under time-delayed state feedback control. Suitable control parameters are selected from the analysis of the local stability of the system equilibrium. The stability of solutions is analyzed by the semidiscretization method with the modified Floquet theory. The stable and periodic responses obtained by the IHB method are verified by directly integrating the equation of motion using the fifth-order Runge-Kutta algorithm at discrete points. Finally, the efficacy of the control scheme has been investigated in the plane of response amplitude versus excitation amplitude. The results show that appropriate selections of control parameters can effectively reduce the response amplitude to a great extent with the improved measure of stability.

Disturbance rejection design for repetitive control system with state delay based on equivalent input disturbance compensation

A modified equivalent-input-disturbance compensation method is investigated for repetitive control systems with state time delays, which achieve effective rejection of unknown disturbance and effective tracking control of periodic reference input. By incorporating the sliding mode observer into the equivalent-input-disturbance theory, the equivalent-input-disturbance estimator structure is determined. The structure presented in this work can effectively estimate the unknown disturbance without making use of the inverse model of the system. Moreover, an asymptotic stability condition is devised to ensure that the repetitive control systems are stable, as well as the corresponding controller gains are designed with the aim to guarantee the performance of the system to suppress unknown disturbances. Numerical example simulations demonstrate the effectiveness and advantages of the devise scheme.

Memristive Response and Capacitive Spiking in Aqueous Ion Transport through Two-Dimensional Nanopore Arrays.

In living organisms, information is processed in interconnected symphonies of ionic currents spiking through protein ion channels. As a result of dynamic switching of their conductive states, ion channels exhibit a variety of current-voltage nonlinearities and memory effects. Fueled by the promise of computing architectures entirely different from von Neumann, recent attempts to identify and harness similar phenomena in artificial nanofluidic environments focused on demonstrating analogue circuit elements with memory. Here we explore aqueous ionic transport through two-dimensional (2D) membranes featuring arrays of ion-trapping crown-ether-like pores. We demonstrate that for aqueous salts featuring ions with different ion-pore binding affinities, memristive effects emerge through coupling between the time-delayed state of the system and its transport properties. We also demonstrate a nanopore array that behaves as a capacitor with a strain-tunable built-in barrier, yielding behaviors ranging from current spiking to an ohmic response. By focusing on the illustrative underlying mechanisms, we demonstrate that realistically observable memory effects may be achieved in nanofluidic systems featuring crown-porous 2D membranes.

Robust [formula omitted] control for uncertain T–S fuzzy systems with state and input time delays: A time-varying matrix-dependent zero-equality method

This paper studies robust H∞ control problems for uncertain T–S fuzzy systems with state and input time delay. A modified Lyapunov–Krasovskii functional is constructed by considering membership-function-dependent matrices and delay-product-type matrices. To ensure that the derived results do not involve higher-order delay terms, a method of introducing augmented variables is used. In particular, a time-varying matrix-dependent method is used to link the zero-equalities generated during the mathematical derivation, which increases the freedom of selection of the constant connection matrix and may produce new time-delay cross-term information. Then, a less conservatism stability condition is established, and a robust H∞ controller is designed to ensure that the T–S fuzzy system achieves a predefined H∞ performance level. Finally, two examples are used to verify the feasibility and superiority of the obtained results.

Sampled-Data-Based Distributed Output Feedback Leader–Following Consensus for Time-Delay Multiagent Systems

This paper addresses the distributed output feedback leader-following consensus problem for high-order nonlinear multiagent systems (MASs) with time delays and disturbances under the directed network. Using sampled relative outputs to neighbors and the discrete control input, the continuous-discrete time compensator is constructed in each agent to compensate for the consensus errors, where the sampling time instants can be asynchronous and aperiodic without exceeding an explicit upper bound of sampling intervals. Based on the compensator, we propose a co-design algorithm for constructing the dynamic event-triggered protocol with a corresponding event-triggering mechanism which is a combination of discrete-time control input, continuous dynamic variables of each agent's own compensator, and a given threshold. The proposed methods can not only achieve consensus tracking under the effects of time delays in states and communications but also implement the discrete-time execution of measurement, communication, and control. Based on the novel lemmas, it is proved that the resulting closed-loop consensus error system is globally stable. Finally, a simulation is given to illustrate the effectiveness of proposed methods.

Leader–Follower Weighted Consensus of Nonlinear Fractional-Order Multiagent Systems Using Current and Time Delay State Information

Leader–Follower Weighted Consensus of Nonlinear Fractional-Order Multiagent Systems Using Current and Time Delay State Information

Neuroadaptive consensus tracking control of uncertain nonlinear multiagent systems with state time-delays

Neuroadaptive consensus tracking control of uncertain nonlinear multiagent systems with state time-delays

Stabilization analysis of incommensurate fractional-order memristor-based neural networks via delay-dependent distributed controller

This paper studies the stabilization analysis problem of a class of incommensurate fractional-order memristor-based neural networks with multiple time-varying delays (IFOMNNs-MTDs). In previously published studies of IFOMNNs-MTDs, the controller is usually designed as a general delay-independent feedback controller. Due to the simple form of the feedback controller, less system information is used and less adjustable parameters are considered, which limits the flexibility and control effect of controller. Specially, the use of delay information is insufficient in the existing results, which will make the controller insensitive to the influence of delay factors and affect the control performance. Thereby, the accurate analysis of the dynamic characteristics of IFOMNNs-MTDs by designing appropriate controller needs further study. This paper aims to propose a new delay-dependent controller to improve the stabilization analysis of IFOMNNs-MTDs. Firstly, a delay-dependent distributed controller with distributed control gain and time-delay state summation term is proposed, which accords with the transmission law of activation function weights and is helpful to consider the historical information (i.e., time delay factors) of system. Thereby, the flexibility and control effect of controller are improved by adding control parameters and improving the use of system information. Secondly, a new less-conservatism stabilization criterion of IFOMNNs-MTDs is established by using the designed controller. Moreover, the controller gain can be searched in a large range by using the established criterion. Finally, a numerical simulation is provided to verify the validity of the obtained results.

Improved sliding mode observer based repetitive control for linear systems with time‐varying input and state delays

SummaryControl systems are frequently subject to the negative effects of time delays and disturbances, which diminish the systems' tracking performance. In response to these challenges, this paper presents a novel approach, that is, the improved sliding mode observer based repetitive control (ISMO‐RC), to enhance the system's periodic signal tracking in the presence of the input and state time delays and the input disturbances. The design takes the advantages of RC and ISMO, in which RC effectively compensates periodic signals, while ISMO compensates both aperiodic disturbances and the time‐varying input and state delays. The stability of the whole system is guaranteed via the linear matrix inequality (LMI) and the Lyapunov–Krasovskii functional analysis. The proposed controller is evaluated through extensive simulations and experiments, which demonstrate its superiority over comparative control methods.

An underdamped and delayed tri-stable model-based stochastic resonance

Stochastic resonance (SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density (SPD) and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations (MCS) confirm the effectiveness of the theoretical results.

A supervisory control scheme for uncertain constrained time-delay discrete-time linear systems

In this paper, a two-layer supervisory control scheme is proposed for discrete-time linear systems with state/input constraints, including multiple state time-delays, parametric uncertainties, and exogenous disturbance. The inner control layer is designed to achieve robust H∞ tracking performance considering the delays as extra states but neglecting the input/state constraints. On the other hand, in the outer control layer, a command governor (CG) is designed to robustly guarantee the satisfaction of state and input constraints by computing a minimal Robust Positively Invariant (mRPI). To this end, the CG manipulates reference inputs by generating the nearest admissible value to be applied to the closed-loop system in both transient and steady-state response through the computation of the Maximal Output Admissible Set (MOAS). Finally, the validity of the proposed scheme is assessed in simulation using a numerical example and a continuous stirred tank reactor (CSTR) system.

Adaptive finite-time fault-tolerant control for the full-state-constrained robotic manipulator with novel given performance

Most robot manipulators usually operate under different nonlinearities, such as state constraints, time delays, and actuator input saturation faults. This paper proposes an adaptive finite-time fault-tolerant controller for the full-state-constrained robotic manipulator with novel prescribed performance and time-varying delays. Firstly, a novel prescribed performance function consisting of hyperbolic tangent and hyperbolic cotangent functions is constructed to the full-state performance constraints of the robotic manipulator. Such a design can circumvent the demands for accurate initial conditions of the state variables and guarantee the convergence of the state errors in a prescribed time. Then, based on the finite-time principle, a finite-time command filter and a compensation mechanism with fractional-power terms are used to bypass the “explosion of complexity” and further compensate for the filter errors within a finite time. Moreover, a proper Lyapunov–Krasovskii functional is devised within the controller design to compensate for the time-varying delays. And the radial basis function neural networks are used to estimate the other nonlinearities including actuator saturation faults, and external perturbations. Finally, simulation results exhibit that the controller designed in this paper has a faster convergence speed and minor state errors.

Controllability of Boolean control networks with multiple time delays in both states and controls

Controllability of Boolean control networks with multiple time delays in both states and controls

Event-Triggered Cooperative Adaptive Neural Control for Cyber–Physical Systems With Unknown State Time Delays and Deception Attacks

Event-Triggered Cooperative Adaptive Neural Control for Cyber–Physical Systems With Unknown State Time Delays and Deception Attacks