Stabilization of Unknown Nonlinear Discrete-Time Delay Systems Based on Neural Network

Deolia, Vinay Kumar; Purwar, Shubhi; Sharma, T.N.

doi:10.4236/ica.2012.34039

Cited by 7 publications

(7 citation statements)

References 32 publications

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“…Consider the following discrete-time state delay system as in [26] (Figure 1) ( ) ( ) g x k is a unknown nonlinear function of a given system in Equation (4), and h is a positive number representing delay.…”

Section: Problem Formulationmentioning

confidence: 99%

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Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

Goyal¹,

Deolia²,

Sharma³

2015

ICA

Self Cite

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This paper presents a robust sliding mode controller for a class of unknown nonlinear discretetime systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.

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Section: Problem Formulationmentioning

confidence: 99%

“…The following assumptions are needed for the stability analysis of the given unknown nonlinear system [26].…”

Section: Stability Analysismentioning

confidence: 99%

Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

Goyal¹,

Deolia²,

Sharma³

2015

ICA

Self Cite

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“…[1][2][3][4] Among the works for nonlinear systems with time-delay, the ones that use neural networks take advantage of their learning capabilities for task s like stabilization and tracking control but they still need at least partial knowledge of the model or bound or uncertainties and delay, and report only simulation results. [5][6][7][8] On the other hand, another issue to consider is that most control techniques need a model of the system and measurement of all its state variables, which for inaccessible state variables, sensors can be the first solution; however, they are a source of delay and noise, and they are not always available or can be expensive. Another solution is the use of state observers; observers estimate state variables based on available measures and knowledge about the system into consideration.…”

Section: Introductionmentioning

confidence: 99%

Real‐time neural observer‐based controller for unknown nonlinear discrete delayed systems

Rios

Alanis

Arana‐Daniel

et al. 2020

Intl J Robust & Nonlinear

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This work presents a neural observer-based controller for uncertain nonlinear discrete-time systems with unknown time-delays. The proposed neural observer does not need previous knowledge of the model about the system under consideration, neither the value of its parameters, delays, nor their explicit estimations. The proposed neural observer is based on a neural network composed of two recurrent high order neural networks (RHONNs) for nonmeasurable state variables, one in a parallel configuration, and for measurable state variables one in a series-parallel configuration. The neural network is trained on-line with an extended Kalman filter algorithm. The proposed RHONN observer provides a mathematical model for the system. Based on such a resulting mathematical model, a control law is designed using discrete-time sliding mode block control. Applicability is presented using real-time results that show the performance of the proposal using a linear induction motor prototype as the selected system; this prototype is under the presence of varying time-delays. A Lyapunov analysis is included to prove the semi-globally uniformly ultimately boundedness (SGUUB) of the proposed RHONN observer-controller scheme for uncertain nonlinear discrete-time systems with unknown delays. K E Y W O R D S discrete-time sliding modes, Lyapunov stability, neural block control, neural state estimation, real-time, time-delay systems 8402

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“…To control the yarn vibration, a reasonable controller is needed. At present, there are many control methods for nonlinear systems, such as neural network control [3][4][5], sliding mode control [6][7][8][9], adaptive control [10,11], and so on. Among them, sliding mode control has many advantages, such as quick response, online monitoring, simple realization, and strong anti-interference ability.…”

Section: Introductionmentioning

confidence: 99%

Vibration Reduction of the Nonlinearly Tufted Carpet Yarn by a Modified Sliding Mode Control Method

Huang

2019

Shock and Vibration

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The yarn vibration causes the yarn tension value to fluctuate, causing a change in the amount of yarn feed, thus causing a deviation of the carpet pile height from the predetermined value. To solve this problem, the sliding mode control algorithm is used to design the sliding mode function and the sliding mode control law. And four variables in the yarn vibration system are controlled by the MATLAB software. For solving the chattering problem of the control law, the sliding mode control law is improved. The fuzzy sliding mode control algorithm based on the quasisliding mode is adopted. The results show that the sliding mode control algorithm is effective, but the sliding mode control force needs to be switched at high frequency and there is severe chattering. The fuzzy sliding mode control algorithm based on quasisliding mode is adopted to achieve better control effect with a smaller force. In addition, the control force does not have high-frequency switching, and the change is relatively stable, which reduces the chattering phenomenon of sliding mode control.

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Stabilization of Unknown Nonlinear Discrete-Time Delay Systems Based on Neural Network

Cited by 7 publications

References 32 publications

Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

Real‐time neural observer‐based controller for unknown nonlinear discrete delayed systems

Vibration Reduction of the Nonlinearly Tufted Carpet Yarn by a Modified Sliding Mode Control Method

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