Asymptotic stabilization of a class of uncertain nonlinear time-delay fractional-order systems via a robust delay-independent controller

2017 ◽  
Vol 24 (19) ◽  
pp. 4541-4550 ◽  
Author(s):  
T. Binazadeh ◽  
M. Yousefi
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Delay Systems ◽  
Time Varying ◽  
State Variables ◽  
Parameter Uncertainties ◽  
External Disturbances ◽  
Sliding Manifold

This paper studies the robust stabilization for a class of nonlinear time-delay fractional order (FO) systems in the presence of some practical aspects. The considered aspects in the FO system include: nonlinear Lipschitz functions; time-varying norm-bounded uncertain terms; and time-delays in the state variables. A major challenge in the control of time-delay systems is that the value of delay is usually not perfectly known or it may be even time-varying. In this paper, a novel asymptotic stabilizing control law is proposed which is delay independent and also has a robust manner in the presence of uncertain terms in the model which may be due to model uncertainties (parameter uncertainties or model simplification) and/or external disturbances. The proposed controller is a FO sliding mode controller that is designed such that the closed-loop system is asymptotically delay-independent stable. For this purpose, a FO sliding manifold is introduced and the occurrence of the reaching phase in a finite time is proved. Finally, in order to validate the theoretical results, an example is given and simulation results confirm the appropriate performance of the proposed controller.

scholarly journals T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yilin Hao ◽  
Xiulan Zhang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Control Method ◽  
Fuzzy Model ◽  
Linear Structure ◽  
Adaptive Method ◽  
Delay Systems ◽  
Robust Controller ◽  
External Disturbances ◽  
Fuzzy Adaptive

In this article, the adaptive control of uncertain fractional-order time-delay systems (FOTDSs) with external disturbances is discussed. A Takagi-Sugenu (T-S) fuzzy model with if-then rules is adopted to characterize the dynamic equation of the FOTDS. Besides, a fuzzy adaptive method is proposed to stabilize the model. By utilizing the Lyapunov functions, a robust controller is constructed to stabilize the FOTDS. Due to the uncertainty of system parameters, some fractional-order adaptation laws are designed to update these parameters. At the same time, some if-then rules with linear structure based on the fuzzy T-S adaption concept are established. The designed method not only guarantees that the state of closed-loop system asymptotically converges to origin but also keeps the signal in the FOTDS bounded. Finally, the applicability of the control method is proved by simulation examples.

Memoryless Adaptive Decentralized Sliding Mode Control for Uncertain Large-Scale Systems With Time-Varying Delays

2003 ◽  
Vol 125 (2) ◽  
pp. 172-176 ◽  
Author(s):  
Jun-Juh Yan
Keyword(s):  
Sliding Mode Control ◽  
Large Scale ◽  
Composite System ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Time Varying ◽  
Large Scale Systems ◽  
Mode Control ◽  
Sliding Manifold ◽  
Local Controller

The problem of robust stabilization for uncertain large-scale systems with time-varying delays is investigated through sliding mode control. A memoryless adaptive decentralized sliding mode controller (ADSMC) is developed. The proposed controller ensures the occurrence of the sliding manifold of the composite system. It is worthy of note that the proposed ADSMC does not involve any information of coupling states and is a local controller. Furthermore, it also does not include any delayed state or the upperbounds of uncertainties. Thus, such ADSMC is memoryless, and the limitation of knowing the upperbounds of uncertainties in advance is certainly released. A numerical example is given to verify the validity of the developed memoryless ADSMC.

Delay-independent sliding mode control of time-delay linear fractional order systems

2016 ◽  
Vol 40 (4) ◽  
pp. 1212-1222 ◽  
Author(s):  
M Yousefi ◽  
T Binazadeh
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Control Law ◽  
State Delay ◽  
New Approach ◽  
Mode Control ◽  
Sliding Manifold ◽  
Theoretical Results

This paper considers the problem of delay-independent stabilization of linear fractional order (FO) systems with state delay. As in most practical systems in which the value of delay is not exactly known (or is time varying), a new approach is proposed in this paper, which results in asymptotic delay-independent stability of the closed-loop time-delay FO system. For this purpose, a novel FO sliding mode control law is proposed in which its main advantage is its independence to delay. Furthermore, a novel appropriate delay-independent sliding manifold is suggested. Additionally, two theorems are given and proved, which guarantee the occurrence of the reaching phase in finite time and the asymptotic delay-independent stability conditions of the dynamic equations in the sliding phase. Finally, in order to verify the theoretical results, two examples are given and simulation results confirm the performance of the proposed controller.

Finite-Time Tracker Design for Uncertain Nonlinear Fractional-Order Systems

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Tahereh Binazadeh
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Reference Signal ◽  
Convergence Time ◽  
Time Varying ◽  
Terminal Sliding Mode ◽  
Output Tracking ◽  
Time Control ◽  
Sliding Manifold

This paper considers the problem of finite-time output tracking for a class of nonautonomous nonlinear fractional-order (FO) systems in the presence of model uncertainties and external disturbances. The finite-time control methods indicate better properties in terms of robustness, disturbance rejection, and settling time. Thus, design of a robust nonsingular controller for finite-time output tracking of a time-varying reference signal is considered in this paper, and a novel FO nonsingular terminal sliding mode controller (TSMC) is designed, which can conquer the uncertainties and guarantees the finite-time convergence of the system output toward the desired time-varying reference signal. For this purpose, an appropriate nonsingular terminal sliding manifold is designed, where maintaining the system's states on this manifold leads to finite-time vanishing of error signal (i.e., ensures the finite-time occurrence of both reaching and sliding phases). Moreover, by tacking the fractional derivative of the sliding manifold, the convergence of system's trajectories into the terminal sliding manifold in a finite time is proven, and the convergence time is estimated. Finally, in order to verify the theoretical results, the proposed method is applied to an FO model of a horizontal platform system (FO-HPS), and the computer simulations show the efficiency of the proposed method in finite-time output tracking.

Applied Technology in Simple Robust Stabilization Design for Time-Delay Systems with Parametric Uncertainties

2014 ◽  
Vol 540 ◽  
pp. 368-371 ◽  
Author(s):  
Chien Hua Lee ◽  
Ping Sung Liao
Keyword(s):  
Time Delay ◽  
Riccati Equation ◽  
Robust Stabilization ◽  
Control Design ◽  
Delay Systems ◽  
Parametric Uncertainties ◽  
Time Varying ◽  
Time Delay Systems ◽  
Applied Technology ◽  
Continuous Time Delay

The robust stabilization design problem for the continuous time-delay systems subjected to parametric uncertainties is addressed in this paper. The uncertainties are time-varying. By using the Riccati equation approach associated with some linear algebraic techniques and an upper bound of the solution of the Riccati equation, a new stabilizability criterion and the corresponding control design are proposed. This criterion is independent of the Riccati equation and hence is easy to be tested and the corresponding controller is also easy to be implemented. It is shown that the criterion is sharper than a previous one. A numerical algorithm is also proposed to construct the controller.

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