Control For Uncertain Time-delay Systems Research Articles

Robust composite nonlinear feedback control based on integral sliding-mode control of uncertain time-delay systems under input saturation

In this research, based on the integral sliding-mode scheme, a robust composite nonlinear feedback (CNF) control is addressed for time-delayed uncertain systems. Such an uncertain system may contain some complexities like time-varying delays, actuators saturation, and exterior disturbances. Hence, the tracking problem would be solved under the mentioned constraints. Thus, for achieving these goals, the tracking problem is firstly formulated by considering system’s limitations. The controller parameters may be determined via a solution for linear matrix inequality. As a result, the CNF tracker law is numerically simulated in some control cases. The simulation outcomes are compared with a similar technique in terms of the transient response, boundedness of the error, and the disturbance rejections. Thus, the findings illustrate the efficiency of the advised CNF control method comparing to the recent technique.

Anti-Saturation Control of Uncertain Time-Delay Systems with Actuator Saturation Constraints

The problem of anti-saturation control for a class of time-delay systems with actuator saturation is considered in this paper. By introducing appropriate variable substitution, a new delay time-delay systems model with actuator saturation systems is established. Based on the Lyapunov stability theory, the stability condition and the anti-saturation controller design method are obtained by using the linear matrix inequality approach. By introducing the matrix into the Lyapunov function, the proposed conditions are less conservative than the previous results. Finally, a simulation example shows the validity and rationality of the method.

Robust output feedback control of uncertain time-delay systems with actuator saturation and disturbances

This paper investigates the problem of robust output feedback control of uncertain continuous-time time-delay systems with both external disturbances and saturating actuators. Both the system uncertainties and the external disturbances are assumed to be time-varying and bounded, and the states of the system under consideration are not available but detectable. First, in the absence of external disturbances, some delay-dependent conditions for designing observer-based output feedback controller are derived which ensure that the system without perturbations on its input matrices can be stabilized together with the domain of attraction. To obtain a maximal estimate of the domain of attraction, an iterative optimization algorithm is proposed. When the system input matrices are subject to perturbations, new stabilization conditions are obtained to adjust the gain of the observer on the basis of the above-mentioned controller design rules. Second, in the presence of external disturbances, the robust observer-based output feedback controller is designed to guarantee that the corresponding closed-loop system converges uniformly exponentially to a ball with an initial admissible domain. Finally, numerical results are given to demonstrate the effectiveness of the proposed method.

Fault Tolerant Control for Uncertain Time-Delay Systems with a Trajectory Tracking Approach

This paper studies the problem of fault tolerant control by trajectory tracking for a class of linear constant time-delay systems. The aim is to design a control law by considering the fault detected by the observer to make the faulty system track the reference model even if faults occur. By considering two kinds of actuator faults, one constant and another time-varying, the corresponding proportional integral observers and active FTC control laws are designed, respectively. State tracking error, state estimation error, output estimation error, and fault estimation error are combined into a descriptor system. Based on Lyapunov-Krasovskii functional approach stability problems of the descriptor system are easily solved in terms of the Linear Matrix Inequalities (LMI). Finally, a numerical example is considered to prove the effectiveness in both cases.

Robust finite-time fuzzy [formula omitted] control for uncertain time-delay systems with stochastic jumps

This paper investigates the problem of robust finite-time H∞ control for a class of uncertain discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi–Sugeno (T–S) model. Initially, the concepts of stochastic finite-time boundedness and stochastic finite-time H∞ stabilization are presented. Then, by using stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastically finite-time bounded and satisfies a prescribed H∞ disturbance attenuation level in a given finite-time interval. Furthermore, sufficient criteria on stochastic finite-time H∞ stabilization using a fuzzy state-feedback controller are provided, and the controller is designed by solving an optimization problem in terms of linear matrix inequalities. Finally, two numerical examples are exploited to show the validity of the proposed design techniques.

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.

H∞Observer-Based Sliding Mode Control for Uncertain Stochastic Systems with Time-Varying Delays

The paper is concerned with sliding mode control for uncertain time-delay systems subjected to input nonlinearity and stochastic perturbations. Using the sliding mode control, a robust law is derived to guarantee the reachability of the sliding surface in a finite time interval. The sufficient conditions on asymptotic stability of the error system and sliding mode dynamics with disturbance attenuation level are presented in terms of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the efficiency and effectiveness of the proposed method.

Non-fragile observer-based sliding mode control for uncertain time-delay systems

Abstract The problem of H ∞ sliding mode control for uncertain time-delay systems subjected to input nonlinearity is investigated. Using the sliding mode control, a robust law is established such that the reachability of the sliding surface in the state-estimation space is guaranteed, and the sufficient condition for asymptotic stability of the error system and sliding mode dynamics with disturbance attenuation level is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to verify the validity of the proposed method.

Robust Reliable Control for Uncertain Time-Delay Systems with IQC Performance

A robust reliable control with integral quadratic constraint (IQC) performance for a class of uncertain systems with state and input delays is considered in this paper. Two classes of failure situations for sensor or actuator are studied. In the first class, a delay-dependent criterion for time-delay systems without perturbations is proposed to design the reliable control with IQC performance. Next, a criterion for uncertain time-delay systems with parameter uncertainties is obtained via simple derivations. The linear matrix inequality (LMI) approach is used to design a robust reliable state feedback control with IQC performance. In the second class, a reliable control with IQC performance is also provided from he previous method. A numerical example is given to illustrate the effectiveness of the procedure.

Further results on adaptive robust control of uncertain time-delay systems

The problem of adaptive robust control for uncertain systems with multiple time delays is considered. The parameter uncertainties are assumed to be time-varying norm-bounded, whose bounds are unknown. The objective is to design adaptive robust state-feedback controllers such that the resulting closed-loop system is globally uniformly exponentially convergent to a ball with a certain convergence rate. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the expression of a desired adaptive robust state-feedback controller is given. It is shown that the result obtained improves certain existing ones in the literature.

A full-block S-procedure application to delay-dependent H∞ state-feedback control of uncertain time-delay systems

This paper deals about the robust stabilization of uncertain systems with time-varying state delays in the delay dependent framework. The system is represented using LFR and stability is deduced from Lyapunov-Krasovskii theorem and full-block S-procedure. We derive sufficient conditions to the existence of a robust Hinfin;state-feedback control law. As this sufficient condition is expressed in terms of NMI we propose a relaxation based on the cone-complementary algorithm which is known to lead to good results for such problems. We show the efficiency of our method trough an example.

Delay-dependent robust passivity control for uncertain time-delay systems

The robust passivity control problem is addressed for a class of uncertain delayed systems with time-varying delay. The parameter uncertainties are norm-bounded. First, the delay-dependent stability sufficient condition is obtained for the nominal system, and then, based-on the former, the delay-dependent robust passivity criteria is provided and the corresponding controller is designed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the proposed approach.

Comments and Remarks on "On Improved Delay-Dependent Robust Control for Uncertain Time-Delay Systems

The purpose of this note is to correct some statements and numerical examples' results in the above paper. A few remarks are also given to clarify the facts that for systems with small delay, the results in Han (2003) are much less conservative than those in Kwon and Park (2004); for systems with nonsmall delay, the criterion in Kwon and Park (2004) fails to make any conclusion, while the criterion in Han (2003) can be applicable to these kinds of systems

LMI Optimization Approach to Observer-Based Controller Design of Uncertain Time-Delay Systems via Delayed Feedback

In this paper, we propose a design method of an observer-based controller for uncertain time-delay systems by delayed feedback. Based on the Lyapunov method, an LMI (linear matrix inequality) criterion is derived to design an observer-based controller which makes the system stable. A numerical example is included to illustrate the design procedure.

Robust H∞ output dynamic observer-based control of uncertain time-delay systems

In this paper, the robustness and H∞ control problems of output dynamic observer-based control for a class of uncertain linear systems with time delay are considered. Under no disturbance input, the asymptotic stabilization for uncertain time-delay systems will be guaranteed. Linear matrix inequality (LMI) optimization approach is used to design three classes of the H∞ output dynamic controls. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls.

Robust adaptive control for uncertain time‐delay systems

AbstractThe problem of robust stabilization for uncertain dynamic time‐delay systems is considered. Firstly a class of time‐delay systems with uncertainties bounded by high‐order polynomials and unknown coefficients are considered. The corresponding controller is designed by employing adaptive method. It is shown that the controller designed can render the closed‐loop system uniformly ultimately bounded stable based on Lyapunov–Krasovskii method and Lyapunov stability theory. Then the proposed adaptive idea is applied to stabilizing a class of large‐scale time‐delay systems with strong interconnections. A decentralized feedback adaptive controller is designed which guarantees the closed‐loop large‐scale systems uniformly ultimately bounded stable. Finally, numerical examples are given to show the potential of the proposed techniques. Copyright © 2005 John Wiley & Sons, Ltd.

Observer-based adaptive control for uncertain time-delay systems

In this paper, we will focus on investigating the observer-based controlling problem of time-delay systems. First, we investigate a class of simple time-delay systems. The corresponding adaptive observer and controller are designed, which are both independent of the time-delays. Based on Lyapunov stability theory, we prove that the closed-loop system is asymptotically stable. Next we further consider the interconnected time-delay system case. The corresponding adaptive observer and controller are designed, we prove that the resulting closed-loop system is also asymptotically stable. Simulations on controlling time-delay systems and interconnected systems are investigated, and the results show that the designed controllers are feasible and efficient.

Delay-dependent robust H∞ control for uncertain time-delay systems

Robust stabilisability and H∞ control criteria are provided for a class of uncertain time-delay systems with multiple state delays. Simpler and less conservative delay-dependent results given in terms of linear matrix inequalities (LMIs) are derived based on Lyapunov-Krasovskii functional method and Riccati equation transformation technique.

Observer-based robust H∞, control for uncertain time-delay systems

AbstractIn this paper, we present a method for the construction of a robust observer-based H∞ controller for an uncertain time-delay system. Cases of both single and multiple delays are considered. The parameter uncertainties are time-varying and norm-bounded. Observer and controller are designed to be such that the uncertain system is stable and a disturbance attenuation is guaranteed, regardless of the uncertainties. It has been shown that the above problem can be solved in terms of two linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the effectiveness of the proposed techniques.

Sliding mode control design for uncertain time‐delay systems subjected to a class of nonlinear inputs

AbstractA sliding mode controller is developed for uncertain time‐delay systems with a class of nonlinear inputs. Two main results are derived in this paper. The first result is the presentation of a new delay‐dependent stability condition of uncertain time‐delay systems. In a comparison example, this stability condition is shown to be less conservative than the ones reported recently. The second result is to present a new sliding mode control for uncertain time‐delay systems subjected to a class of nonlinear inputs. The stability of time‐delay systems with unmatching condition in the sliding mode is also discussed. Two illustrative examples are included to demonstrate the superiority of the obtained results. Copyright © 2003 John Wiley & Sons, Ltd.