A Novel Input–Output Linearization Minimum Sliding Mode Error Feedback Control for Synchronization of FitzHugh–Nagumo Neurons

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Lu Cao ◽  
Xiaoqian Chen
Keyword(s):  
Feedback Control ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Error Feedback ◽  
Input Output ◽  
External Disturbances ◽  
Control Error ◽  
Equivalent Control ◽  
System Uncertainties ◽  
Input Output Linearization

A novel input–output linearization minimum sliding mode error feedback control (I/OMSMEFC) is proposed for the synchronization between two uncoupled FitzHugh–Nagumo (FHN) neurons with different ionic currents and external electrical stimulations. To estimate and offset the system uncertainties and external disturbances, the concept of equivalent control error is introduced, which is the key to utilization of I/OMSMEFC. A cost function is formulated on the basis of the principle of minimum sliding mode covariance constraint; then the equivalent control error is estimated and fed back. It is shown that the proposed I/OMSMEFC can compensate various kinds of system uncertainties and external disturbances. Meanwhile, it can reduce the steady-state error more than the conventional sliding mode control (SMC). In addition, the sliding mode after the I/OMSMEFC will tend to be the ideal SMC, resulting in improved control performance and quantity. Sufficient conditions are given based on the Lyapunov stability theorem and numerical simulations are performed to verify the effectiveness of presented I/OMSMEFC for the chaotic synchronization accurately.

scholarly journals A Robust Noise-Free Linear Control Design for Robot Manipulator with Uncertain System Parameters

Actuators ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 121
Author(s):  
Yi-Liang Yeh
Keyword(s):  
Feedback Control ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Uncertain System ◽  
Linear Control ◽  
Linear Feedback ◽  
External Disturbances ◽  
Mode Control ◽  
System Uncertainties

In robot control, the sliding mode control is known for its robustness against external disturbances and system uncertainties. However, it has the disadvantage of control chattering, which can damage the actuator and degrade system performance. With a new stability proof, this paper presents an alternative simple linear feedback control that can cope with large system uncertainties and suppress large external disturbances, doing so as effectively as sliding mode control does. The advantage of using linear control is that the control law is simple and control chattering can be avoided. Moreover, a noise-free control scheme is proposed as an improvement of the feedback control; the modified design preserves the advantages of linear control and generates a chattering-free control signal even in a noisy environment.

Tracking Control of an Uncertain MEMS Resonator via Adaptive Terminal Sliding Mode Control

2013 ◽  
Vol 302 ◽  
pp. 665-670
Author(s):  
Chi Ching Yang ◽  
Rong Hao Guo
Keyword(s):  
Sliding Mode ◽  
Reference Signal ◽  
Sufficient Conditions ◽  
Adaptive Controller ◽  
Lyapunov Theory ◽  
Time Varying ◽  
External Disturbances ◽  
Terminal Sliding Mode ◽  
Mems Resonator ◽  
System Uncertainties

The purpose of this study is to develop the adaptive terminal sliding mode scheme to control a MEMS resonator with a six-powered potential function for tracking a given reference signal in the presence of system uncertainties and external disturbances. The proposed adaptive controller includes the time-varying feedback gains can tackle the nonlinear dynamics without directly eliminating. Meanwhile, these time-varying feedback gains are adaptively updated according to the suitable updated rules without the known bounds of system uncertainties and external disturbances. Some sufficient conditions to guarantee the stability based on Lyapunov theory and numerical simulations are performed to demonstrate the effectiveness of the presented scheme.

High‐order sliding‐mode observer–based input‐output linearization

2019 ◽  
Vol 29 (10) ◽  
pp. 3183-3199 ◽  
Author(s):  
A. Ferreira de Loza ◽  
L. Fridman ◽  
L. T. Aguilar ◽  
R. Iriarte
Keyword(s):  
Sliding Mode ◽  
High Order ◽  
Sliding Mode Observer ◽  
Input Output ◽  
Input Output Linearization

scholarly journals Input–output linearization of non-linear time-varying delay systems: the single-input single-output case

2019 ◽  
Vol 37 (3) ◽  
pp. 831-854
Author(s):  
Ihab Haidar ◽  
Florentina Nicolau ◽  
Jean-Pierre Barbot ◽  
Woihida Aggoune
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Input Output ◽  
Time Varying Delay ◽  
Output Stabilization ◽  
Non Linear ◽  
Varying Delay ◽  
Input Output Linearization

Abstract This paper deals with the input–output linearization of non-linear time-varying delay systems. We introduce an extension of the Lie derivative for time-varying delay systems and derive sufficient conditions for the existence of a causal and bounded non-linear feedback linearizing the input–output behaviour of the system. Sufficient conditions ensuring the internal stability after output stabilization are also presented. Finally, several examples illustrating our main results are discussed.

Delayed Output Feedback Control for Nonlinear Systems With Fuzzy Observers

2012 ◽  
Author(s):  
Mansour Karkoub ◽  
Tzu Sung Wu
Keyword(s):  
Feedback Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Output Feedback ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
External Disturbances ◽  
Control Scheme

In this paper, the design problem of delayed output feedback control scheme using two-layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated. The Takagi-Sugeno type fuzzy linear model with an on-line update law is used to approximate the nonlinear system. Based on the fuzzy model, a two-layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices. Subsequently, a delayed output feedback adaptive fuzzy controller is developed to override the nonlinearities, time delays, and external disturbances such that the H∞ tracking performance is achieved. The linguistic information is developped by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. The filtered tracking error dynamics are designed to satisfy the Strictly Positive Realness (SPR) condition. Based on the Lyapunov stability criterion and linear matrix inequalities (LMIs), some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbances on the tracking error can be attenuated to any prescribed level and consequently an H∞ tracking control is achieved. Finally, a numerical example of a two-link robot manipulator is given to illustrate the effectiveness of the proposed control scheme.

Disturbance Rejection With Simultaneous Input-Output Linearization and Decoupling Via Restricted State Feedback

1997 ◽  
Vol 122 (1) ◽  
pp. 49-62 ◽  
Author(s):  
A. S. Tsirikos ◽  
K. G. Arvanitis
Keyword(s):  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
State Feedback Control ◽  
Systems Of Equations ◽  
Input Output ◽  
Control Laws ◽  
Simultaneous Input ◽  
Input Output Linearization

The disturbance rejection with simultaneous input-output linearization and decoupling problem of nonsquare nonlinear systems via restricted state feedback is investigated in this paper. The problem is treated on the basis of an algebraic approach whose main feature is that it reduces the determination of the admissible state feedback control laws to the solution of an algebraic and a first order partial differential systems of equations. Verifiable necessary and sufficient conditions of algebraic nature based on these systems of equations are established for the solvability of the aforementioned problem. Moreover, an explicit expression for a special admissible restricted state feedback controller is analytically derived. [S0022-0434(00)02101-8]

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