Class Of Nonlinear Time-delay Systems Research Articles

Global output feedback stabilisation of nonlinear time-delay systems with unknown output function

ABSTRACTThis paper studies the problem of global output feedback stabilisation for a class of nonlinear time-delay systems with the unknown output function. By constructing the appropriate Lyapunov–Krasovskii functional and observer, skillfully combining generalised adding a power integrator technique, sign function and homogeneous domination approach, an output feedback controller is designed to guarantee globally uniformly asymptotical stability of nonlinear time-delay systems with the unknown output function.

Nonsmooth Feedback Control of Time-Delay Nonlinear Systems: A Dynamic Gain Based Approach

This technical note addresses the problem of global control for a class of time-delay nonlinear systems. Under a smoothness condition on the system nonlinearities, a delay-independent, non-smooth dynamic state compensator is constructed by developing a dynamic gain based design method. With the help of appropriate Lyapunov-Krasovskii functionals, it is shown that all the states of the time-delay nonlinear system can be regulated to the origin while maintaining boundedness of the closed-loop system. A benchmark example is given to illustrate the effectiveness of the proposed non-smooth feedback controller.

Semi-global stabilization via homogeneous output feedback for a class of nonlinear time-delay systems

The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. By using Lyapunov-Krasovskii functional method and homogeneous domination approach, a homogeneous observer and an output feedback controller with a scaling gain are designed. Then the scaling gain is adjusted such that the closed-loop system is semi-global asymptotically stable. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper.

Adaptive control for a class of nonlinear time-delay systems with dead-zone input

In this paper, we consider the same class of systems as in a previous paper, i.e. a class of uncertain nonlinear systems with state time-varying delays and nonsymmetric dead-zone input. The dead-zone parameters are unknown, and the delay-related nonlinearity is bounded by the partially known nonlinear functions. No knowledge is assumed on the slope sign of the dead-zone nonlinearity and the upper bounds of the time delays and their derivatives. By employing the Nussbaum gain approach and choosing a proper Lyapunov–Krasovskii functional, an adaptive compensation control algorithm is developed. The explicit expression of the control gain function is constructed. The boundedness of all the closed-loop signals is established, and the desired tracking performance is guaranteed by choosing the appropriate design parameters. The effectiveness of the proposed control algorithm is demonstrated by two simulation examples.

Adaptive fuzzy memory fault‐tolerant control of non‐linear systems with partially known time‐varying delays

This studies the fuzzy-approximation-based adaptive memory fault-tolerant control problem for a class of non-linear time-delay systems with non-affine non-linear delayed faults. The main advantages of the developed scheme are as follows: first, based on the partial information of time-varying delays, the unknown delay terms are approximated by combing fuzzy logic systems and adaptive mechanisms, and then, based on the obtained delay estimates, a memory controller is constructed, which removes the restriction on delays and time-delay functions due to the Krasovskii function in the existing results; second, non-affine non-linear delayed faults are initially considered, and this new technique combing the property of hyperbolic tangent function, implicit function theorem and mean value theorem is adopted to circumvent the algebraic loop problems in controller design. It is proved that the proposed controller can ensure that the closed-loop system is semi-globally bounded, and all entire state tracking errors converge to a priori known accuracy. Finally, a simulation example is included for validating the advantages of the proposed approach.

Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances

This paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time-varying delays and bounded disturbances. The disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero. We first derive a sufficient condition for the existence of componentwise ultimate bounds. This condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound. Then, by using the comparison method, we extend the obtained result to a class of nonlinear time-delay systems which has linear positive bounds. Two numerical examples are given to illustrate the effectiveness of the obtained results.

Simultaneous observation and identification for nonlinear systems under unknown time-varying delays

In this paper, a class of time-delayed nonlinear systems with unknown parameters and unknown time-varying delays is considered. A high gain observer approach is proposed for simultaneous state observation and parameter identification. Sufficient conditions are obtained to ensure the boundedness of both observation and identification errors. Consequently a practical stability of the proposed observer is achieved. Moreover, an exponential stability of the observer is derived from the knowledge of time-delay. Simulation results are given to illustrate the performances of the proposed observer design under time-varying delay function and a piecewise unknown parameter.

Global exponential stabilisation of a class of nonlinear time-delay systems

ABSTRACTThis paper deals with the state and output feedback stabilisation problems for a family of nonlinear time-delay systems satisfying some relaxed triangular-type condition. The delay is supposed to be constant. Parameter-dependent control laws are used to compensate for the nonlinearities. Based on the Lyapunov–Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. Finally, an extension to nonlinear time-varying delay systems is given.

Nonlinear time-delay anti-windup compensator synthesis for nonlinear time-delay systems: A delay-range-dependent approach

This paper addresses the novel architectures׳ formulation and linear matrix inequality (LMI)-based design of dynamic nonlinear anti-windup compensator (AWC) for nonlinear time-delay systems with continuous interval time-varying delays under input saturation. An internal model control (IMC)-based AWC architecture is suggested for stable nonlinear time-delay systems and, in addition, a decoupling AWC architecture, applicable to a broader class of nonlinear time-delay systems, is proposed for compensation of the undesirable saturation effects. Further, a correspondent decoupled architecture is derived and recommended for characterizing the delayed nonlinear AWC synthesis goals. By employing Lyapunov–Krasovskii functional, local sector condition, Lipschitz condition, L2 gain minimization, and the delay-interval information, several sufficient conditions are derived for the design of nonlinear time-delay AWC. Numerical examples for FitzHugh–Nagumo neuron and Hopfield neural network under input saturation and time-delay are presented to reveal effectiveness of the proposed anti-windup approach.

Observer-Based Adaptive Fuzzy Control for a Class of Nonlinear Delayed Systems

This paper considers the problem of observer-based adaptive fuzzy control for a class of nonlinear time-delay systems in nonstrict-feedback form, which includes the nonlinear strict-feedback systems as a special case. An adaptive fuzzy output feedback backstepping approach is first proposed for nonlinear systems in nonstrict-feedback form. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Adaptive technique and backstepping are utilized to construct a controller. The proposed adaptive fuzzy output feedback controller guarantees that all the signals in the adaptive closed-loop system are semi-globally uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness of the presented approach.

Output feedback tracking control for nonlinear time-delay systems with tracking errors and input constraints

The adaptive tracking control problem is considered for a class of nonlinear time-delay systems in the presence of input and tracking error constraint. A reduced-order observer is designed to estimate the unmeasured state variables at first. Then, a constraint variable is utilized to ensure that the tracking error is within the prescribed boundaries. An auxiliary state is introduced to deal with the input saturation constraint. With the time-delay functions unavailable, we employ adaptive RBF neural network systems to approximate unknown functions. It is proved that the resulting closed-loop system is stable in the sense of semiglobal uniformly ultimately boundedness. The simulations are performed and the results demonstrate the effectiveness of the proposed approach.

Optimal control of a class of non-linear time-delay systems via hybrid functions

Optimal control problems for a class of time-delay non-linear systems with quadratic performance index are studied. The properties of the hybrid functions which consist of block-pulse functions and orthonormal Taylor series are presented. By expanding various time functions in the systems as their truncated hybrid functions, we attain to algebraic equations and by means of operational matrices of integration, delay and product we reduce the solution of optimal control problem to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Global practical tracking by output feedback for a class of non-linear time-delay systems

Global practical tracking by output feedback for a class of non-linear time-delay systems

Single-approximation-based adaptive control of a class of nonlinear time-delay systems

This paper presents a simple adaptive control approach for uncertain strict-feedback nonlinear systems with unknown time-varying delays. All nonlinear functions and time delays in the systems are assumed to be unknown. Compared with the existing works, the contribution of this study is the design of a simple adaptive control law using single function approximator, without the implementation of virtual controllers derived from the backstepping design procedure. Unlike the existing backstepping methods, virtual controllers are only used as intermediate signals for designing the actual control. Therefore, the proposed control scheme is simpler than the existing methods for strict-feedback time-delay systems because the problems of using multiple approximators and calculating virtual controllers are eliminated. In addition, it is shown that all signals in the closed-loop system are uniformly ultimately bounded.

Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays

The problem of designing observer-based controller for a class of nonlinear time-delay systems subjected to input and output time-varying delays is addressed in this paper. More incisively, a delay-range-dependent criterion, incorporating variation of delays between known lower and upper bounds, is established for control of nonlinear time-delay systems. The proposed methodology ensures asymptotic stability of the closed-loop system's state and the estimation error between states of the system and observer. By application of a Lyapunov–Krasovskii functional, Jensen's inequality, standard matrix inequality procedures, Luenberger-type observer, delay-interval bounds and delay-derivative limits, observer-based controller synthesis approach using nonlinear matrix inequalities for the nonlinear time-delay systems is provided. Further, a decoupling approach is employed to render a simpler condition for the observer and the controller synthesis. A novel observer-based control scheme for the linear time-delay systems with interval time-varying input as well as output lags is derived from the proposed control strategy. The traditional delay-dependent controller design, incorporating zero lower bound of the delay, for the time-delay systems is a particular scenario of the projected delay-range-dependent approach. The proposed decoupled observer-based controller synthesis condition is cast into linear matrix inequalities by means of the cone complementary linearization approach. Finally, a numerical simulation example of control of one-link flexible joint robotic arm is provided to verify the proposed design methodology.

A separation principle for the stabilization of a class of time delay nonlinear systems

In this paper, we establish a separation principle for a class of time-delay nonlinear systems satisfying some relaxed triangular-type condition. Under delay independent conditions, we propose a nonlinear time-delay observer to estimate the system states, a state feedback controller and we prove that the observer-based controller stabilizes the system.

Adaptive Neural Network Dynamic Surface Control for a Class of Time-Delay Nonlinear Systems With Hysteresis Inputs and Dynamic Uncertainties.

In this paper, an adaptive neural network (NN) dynamic surface control is proposed for a class of time-delay nonlinear systems with dynamic uncertainties and unknown hysteresis. The main advantages of the developed scheme are: 1) NNs are utilized to approximately describe nonlinearities and unknown dynamics of the nonlinear time-delay systems, making it possible to deal with unknown nonlinear uncertain systems and pursue the L∞ performance of the tracking error; 2) using the finite covering lemma together with the NNs approximators, the Krasovskii function is abandoned, which paves the way for obtaining the L∞ performance of the tracking error; 3) by introducing an initializing technique, the L∞ performance of the tracking error can be achieved; 4) using a generalized Prandtl-Ishlinskii (PI) model, the limitation of the traditional PI hysteresis model is overcome; and 5) by applying the Young's inequalities to deal with the weight vector of the NNs, the updated laws are needed only at the last controller design step with only two parameters being estimated, which reduces the computational burden. It is proved that the proposed scheme can guarantee semiglobal stability of the closed-loop system and achieves the L∞ performance of the tracking error. Simulation results for general second-order time-delay nonlinear systems and the tuning metal cutting system are presented to demonstrate the efficiency of the proposed method.

Adaptive-gain observer-based control of a class of time-delay systems subject to output-slope non-linearities

A non-linear adaptive observer is proposed to estimate the unmeasured states of a class of time-delay non-linear systems. Irrespective of the size of the constant delay, it is shown that the observer is globally convergent if the growth rate of the system non-linearities is output dependent. The presented results generalize previous results on observation of Lipschitz time-delay systems. Subsequently, the observerbased control problem of time-delay systems, having triangular structure, is discussed for arbitrary large constant delay.

Semi-Global Stabilization for a Class of Nonlinear Time-Delay Systems by Linear Output Feedback

The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. Sufficient conditions are derived by using Lyapunov-Krasovskii functional method and adjusting the scaling gain to guarantee the systems as well as the resulted closed-loop systems under a linear output feedback controller to be semi-globally stable. Numerical example is presented to illustrate the effectiveness of the obtained results in this paper.

Reachable set bounding for nonlinear perturbed time-delay systems: The smallest bound

In this letter, we propose a new approach to obtain the smallest box which bounds all reachable sets of a class of nonlinear time-delay systems with bounded disturbances. A numerical example is studied to illustrate the obtained result.