Class Of Uncertain Time-delay Systems Research Articles

Super Twisting Based Lyapunov Redesign for Uncertain Linear Delay Systems

We present a new continuous Lyapunov redesign (LR) methodology for the robust stabilization of a class of uncertain time-delay systems that is based on the so-called super twisting algorithm. The main feature of the proposed approach is that allows one to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> adjust the chattering effect and achieve asymptotic stabilization of the uncertain system, which is lost when continuous approximation of the unit control is considered. At the basis of the super twisting based LR methodology is a well-known class of Lyapunov–Krasovskii functionals. The particular form of the time derivative of this class of functionals allows one to define a delay-free sliding manifold on which some class of smooth uncertainties are compensated.

State-estimation-based adaptive sliding mode control for a class of uncertain time-delay systems: a new design

In this article, state estimation-based adaptive control problem for a class of uncertain systems subject to time-delay and external disturbance is investigated within sliding mode framework. A simplified state observer without any inputs is designed to reconstruct the unmeasured state variables, from which a novel linear switching surface is provided. By applying a novel adaptive reaching motion controller, the existence and arrival of the defined switching surface are established. It is shown that in the framework of Lyapunov stability theory and linear matrix inequality technique, the proposed control scheme achieves the desirable performance for the closed-loop system. Two illustrative examples are given to substantiate the effectiveness of the proposed method.

Adaptive robust state stabilisation of uncertain non linear time-varying systems with delayed perturbation

The problem of robust stabilisation for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown and an improved adaptation law with modification is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds, we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes in the presence of multiple delayed state perturbations is globally uniformly practically exponentially stable. Finally, a numerical example is given to demonstrate the validity of the results.

Prediction-based Adaptive Robust Control for a Class of Uncertain Time-delay Systems

Abstract This paper presents an integrated control design approach for a class of dynamical systems that satisfy a certain matching condition subject to known input time-delay, unknown parameters, and time-varying disturbances, simultaneously. A novel nonlinear predictor adaptive robust control (PARC) is proposed to track a desired state trajectory. The controller uses predictor-based model compensation to attenuate the effect of input time-delay, gradient type projection with prediction-based learning mechanisms to reduce the parameter uncertainties, and prediction-based nonlinear robust feedback to attenuate the effect of model approximation errors and disturbances, simultaneously. The controller guarantees a prescribed transient performance (with global exponential convergence) and final steady-state tracking error with an ultimate bound proportional to the time-delay, the disturbances, and the switching gain. The effectiveness of the proposed control design is illustrated with a simple tumor growth example.

Robust Actuator and Sensor Faults Reconstruction Based on New Sliding Mode Observer for a Class of Output Time-Delay Systems

ABSTRACTIn this paper, we present a new robust sliding mode observer (SMO) design method for a class of uncertain time-delay systems. The uncertainty is unknown and bounded, and the time-delay is also bounded and affects the output of the system. To ensure the stability of the estimation error, sufficient conditions are derived using linear matrix inequality optimization and a Lyapunov–Krasovskii functional. Using the designed SMO and the concept, a robust actuator and sensor faults reconstruction are obtained. To illustrate the validity and the applicability of the proposed approaches, a numerical example is given.

H∞ Tracking Control for a Class of Uncertain Time-delay Systems

This paper considers the  H tracking control for a class of uncertain systems with time-delay and disturbance. The solvable sufficient conditions for the tracking control with state time delay are presented. The tracking controller is designed by using convex combination technique and Lyapunov functional method. The controller enables the system to meet the model reference  H tracking performance index. The delay-independent  H tracking control criteria is derived and formulated in the form of linear matrix inequality (LMI). A numerical simulation example is presented to verify the validity of the proposed method.

Sliding Mode Control for A Class of Uncertain Time-Delay Systems

This paper investigates the stability and stabilization pr oblems for a class of uncertain time-delay systems. For exploring the stability problem, the Lyapunov-Krasovskii function (LKF) method and Leibniz-Newton formula are adopted to analyze the stability problems of a class of uncertain time-delay systems. In addition, the proposed delay-dependent stability conditions f or a class of time-delay unforced systems can be formulated by linear matrix inequalities (LMIs). By examining the stabilization pr oblem, based on the sliding mode control scheme, some assumptions, and some transformations, the delay-dependent stabilization condition for uncertain time-delay system is propounded to guarantee the asymptotic stabilization of uncertain time-delay system i n this paper. Moreover, based on the Schur complement formula and some variable transformations, the delay-dependent stabilizatio n conditions of the uncertain time-delay system can be presented in terms of linear matrix inequality (LMI) form. Finally, a numerical example is illustrated to demonstrate the effectiveness and validity of the proposed control scheme.

Dynamic output feedback RBF neural network sliding mode control for robust tracking and model following

A dynamic output feedback radial basis function (RBF) neural network sliding mode control (SMC) scheme is proposed to realize the problem of robust tracking and model following for a class of uncertain time-delay systems. The algorithm is based on dynamic output feedback SMC, RBF neural network and adaptive control. The design of sliding surface and the existence of sliding mode have been addressed. The proposed robust tracking controller guarantees the stability of overall closed-loop system and achieves zero-tracking error in the presence of state delays, input delays, time-varying parameter uncertainties and external disturbances. Moreover, the knowledge of upper bound of uncertainties is not required, and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme.

Robust tracking and model following based on discrete-time neuro-sliding mode control for uncertain time-delay systems

This paper proposes a discrete-time neuro-sliding mode control (NSMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time-delay systems. It is shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of state delays, input delays, parameter uncertainties, and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme not only assures robustness against time-delays, system uncertainties and disturbances, but also avoids chattering phenomenon and reaching phase. Moreover, the knowledge of upper bound of uncertainties is not required. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme.

RobustH∞Filtering for a Class of Uncertain Markovian Jump Systems with Time Delays

This paper studies the problem of robustH∞filtering for a class of uncertain time-delay systems with Markovian jumping parameters. The system under consideration is subject to norm-bounded time-varying parameter uncertainties. The problem to be addressed is the design of a Markovian jump filter such that the filter error dynamics are stochastically stable and a prescribed bound on theℒ2-induced gain from the noise signals to the filter error is guaranteed for all admissible uncertainties. A sufficient condition for the existence of the desired robustH∞filter is given in terms of two sets of coupled algebraic Riccati inequalities. When these algebraic Riccati inequalities are feasible, the expression of a desiredH∞filter is also presented. Finally, an illustrative numerical example is provided.

Robust Sliding Mode Control for a Class of Uncertain Time-Delayed Systems

Robust Sliding Mode Control for a Class of Uncertain Time-Delayed Systems

Observer-based robust control of time-delay uncertain systems with application to engine idle speed control

A combined controller-observer design procedure for a class of timedelay uncertain systems is proposed. First, a sufficient condition for robust asymptotical stability of the closed-loop systems is presented based on Lyapunov function theory. Next, by using matrix’s Singular Value Decomposition (SVD) and Linear Matrix Inequality (LMI) techniques, the existence condition and method of designing an observer-based feedback controller is derived. The result is obtained in terms of LMI, which make all the gain matrices can be easily obtained by Matlab’s LMI toolbox. Finally, the developed design techniques are applied to an engine idle speed control problem. The simulation results demonstrate the validity of this approach.

Notice of Violation of IEEE Publication Principles: Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters

Notice of Violation of IEEE Publication Principles <br><br> After careful consideration by a duly constituted committee, an author of this article, Hamid Reza Karimi, was found to have acted in violation of the IEEE Principles of Ethical Publishing by artificially inflating the number of citations to this article. <br/> The problem of robust mode-dependent delayed state feedback <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control is investigated for a class of uncertain time-delay systems with Markovian switching parameters and mixed discrete, neutral, and distributed delays. Based on the Lyapunov-Krasovskii functional theory, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired control is derived based on a convex optimization method such that the resulting closed-loop system is stochastically stable and satisfies a prescribed level of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance, simultaneously. Finally, two numerical examples are given to illustrate the effectiveness of our approach.

Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems

In this paper, we study exponential stability and tracking control problems for uncertain time-delayed systems. First, sufficient conditions of exponential stability for a class of uncertain time-delayed systems are established by employing Lyapunov functional methods and algebraic matrix inequality techniques. Furthermore, tracking control problems are investigated in which an uncertain linear time-delayed system is used to track the reference system. Sufficient conditions for solvability of tracking control problems are obtained for the cases that the system state is measurable and non-measurable, respectively. When the state is measurable, we design an impulsive control law to achieve the tracking performance. When the state information is not directly available from measurement, an impulsive control law based on the measured output will be used. Finally, numerical examples are presented to illustrate the effectiveness and usefulness of our results.

Robust Stabilization of Uncertain Fuzzy-Time-Delay Systems Using Sliding-Mode-Control Approach

Based on sliding-mode-control theory, we develop a fuzzy controller design method for a class of uncertain time-delay systems that can be represented by Takagi-Sugeno (T-S) fuzzy models. In terms of linear-matrix inequalities (LMIs), we derive a sufficient condition for the existence of stabilizing sliding-mode controllers. We show that the sliding-surface parameter matrix can be characterized in terms of the solution of the LMI-existence condition. Our LMI condition does not require stabilization of the pair of the state and input matrices. Thus, our method can be applied to a broad class of uncertain systems. We also give an LMI-based algorithm to design a switching feedback-control strategy so that a stable sliding motion is induced in finite time. Finally, we give a numerical-design example to show that our method can be better than the previous results.

Adaptive robust control of uncertain dynamical systems with multiple time-varying delays

The problem of adaptive robust stabilisation is considered for a class of dynamical systems with multiple time-varying delayed state perturbations, time-varying uncertain parameters, and external disturbances. It is assumed that the upper bounds of the delayed state perturbations, uncertainties and external disturbances are unknown, and that the time-varying delays are any non-negative continuous and bounded functions. In particular, it is not required that the derivatives of time-varying delays have to be less than one. For such a class of uncertain time-delay systems, a new method is presented whereby a class of memoryless continuous adaptive robust state feedback controllers is proposed. By employing a quasi-Lyapunov function, it is shown that the solutions of uncertain time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed adaptive robust state feedback controllers are completely independent of time delays, the results obtained in the study may be also applicable to a class of dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.

Repetitive control by output error for a class of uncertain time-delay systems

The problem of designing output error controllers to track periodic reference signals for a class of uncertain linear time-delay systems subject to periodic disturbances is addressed. A repetitive controller, which is a type of output error controller, is developed for these systems and a sufficient condition for stability of the closed-loop system is derived by applying the Lyapunov–Krasovskii functional and linear matrix inequalities (LMIs). In order to relax the stability condition, the theory of the modified repetitive control (RC) system is extended to the systems represented by irrational transfer functions. Based on the extended theory of the modified RC system, a modified repetitive controller, another type of output error controller, is developed for these systems and sufficient conditions for stability of the closed-loop system are derived in terms of a frequency-domain criterion and LMI. Numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.

Memoryless State Feedback Controller Design for Time Delay Systems With Matched Uncertain Nonlinearities

The robust control problem for a class of uncertain time-delay systems is investigated. The systems include multiple time delays and uncertain nonlinear functions. To our best knowledge, no controller design method for the systems is reported in the literature except for sliding mode control (SMC). However, the sliding mode controller must use the delayed state of the system, so that the precise time delays have to be known, and also a large memory is needed for controller implementation. To overcome the shortcomings, we employ the backstepping method to design a memoryless state feedback controller. By constructing a novel Lyapunov-Krasovskii functional, we show that the resulting closed-loop system is asymptotically stable. Simulations are done to verify the effectiveness of the proposed method.

전차수 슬라이딩 모드 관측기를 대체하는 축소차수 관측기의 LMI 기반 설계

This paper presents an LMI-based method to design reduced order observers by which we can substitute full order sliding mode observers for a class of uncertain time-delay systems. We show that a reduced order observer can be constructed as long as the uncertain system satisfies the previous LMI existence conditions of a full order sliding mode observer. And we give explicit formulas of the reduced order observer gain matrices. Finally, we give a simple LMI-based design algorithm, together with a numerical design example.

Improved robust absolute stability criteria for uncertain time-delay systems

Improved delay-dependent robust absolute stability conditions for a class of uncertain time-delay systems with nonlinearities subject to sector-bounded constraints are proposed. These conditions are in terms of linear matrix inequalities, which are obtained by choosing new Lyapunov–Krasovskii functionals. Both the cases with time-varying and time-invariant nonlinearities are considered. Numerical examples are provided to show that the robust absolute stability conditions are less conservative than some existing ones in the literature.