On the stability of sliding mode control for a class of underactuated nonlinear systems

2010 ◽  
Author(s):  
S G Nersesov ◽  
H Ashrafiuon ◽  
P Ghorbanian
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Mode Control ◽  
The Stability

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

scholarly journals Nonlinear Backstepping Control Design for Coupled Nonlinear Systems under External Disturbances

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Wonhee Kim ◽  
Chang Mook Kang ◽  
Young Seop Son ◽  
Chung Choo Chung
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Backstepping Control ◽  
State Variables ◽  
External Disturbances ◽  
Mode Control ◽  
Disturbance Cancellation ◽  
The Stability ◽  
Nonlinear Backstepping Control

A nonlinear backstepping control is proposed for the coupled normal form of nonlinear systems. The proposed method is designed by combining the sliding-mode control and backstepping control with a disturbance observer (DOB). The key idea behind the proposed method is that the linear terms of state variables of the second subsystem are lumped into the virtual input in the first subsystem. A DOB is developed to estimate the external disturbances. Auxiliary state variables are used to avoid amplification of the measurement noise in the DOB. For output tracking and unmatched disturbance cancellation in the first subsystem, the desired virtual input is derived via the backstepping procedure. The actual input in the second subsystem is developed to guarantee the convergence of the virtual input to the desired virtual input by using a sliding-mode control. The stability of the closed-loop is verified by using the input-to-state stable (ISS) property. The performance of the proposed method is validated via numerical simulations and an application to a vehicle system based on CarSim platform.

scholarly journals Sliding Mode Control and Geometrization Conjecture in Seismic Response

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 353
Author(s):  
Ligia Munteanu ◽  
Dan Dumitriu ◽  
Cornel Brisan ◽  
Mircea Bara ◽  
Veturia Chiroiu ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Ricci Flow ◽  
Lyapunov Functions ◽  
Seismic Waves ◽  
Sliding Mode ◽  
Flow Process ◽  
Mode Control ◽  
Finite Period ◽  
The Stability ◽  
Story Building

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

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