scholarly journals A New Approach to Adaptive Stabilization of Stochastic High-Order Nonholonomic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Guangju Li ◽  
Kemei Zhang
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Nonholonomic Systems ◽  
High Order ◽  
Function Technique ◽  
Adaptive Stabilization ◽  
Closed Loop System ◽  
Sign Function ◽  
New Approach ◽  
Asymptotic Stability In Probability

This paper studies the problem of adaptive stabilization for a class of stochastic high-order nonholonomic systems. Under the weaker assumptions, by constructing the appropriate Lyapunov function and combining sign function technique, an adaptive state feedback controller is designed to guarantee global asymptotic stability in probability of the closed-loop system. The effectiveness of the controller is demonstrated by a mechanical system.

Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity

2018 ◽  
Vol 41 (7) ◽  
pp. 1888-1895
Author(s):  
Fangzheng Gao ◽  
Yanling Shang ◽  
Yuqiang Wu ◽  
Yanhong Liu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Dead Zone ◽  
Fixed Time ◽  
High Order ◽  
Closed Loop System ◽  
Sign Function ◽  
Input Nonlinearity ◽  
Power Integrator

This paper considers the problem of global fixed-time stabilization for a class of uncertain high-order nonlinear systems. One distinct characteristic of this work is that the system under consideration possesses the dead-zone input nonlinearity. By delicately combining the sign function with a power integrator technique, a state feedback controller is designed such that the states of the resulting closed-loop system converge to the origin within a fixed time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

scholarly journals Adaptive Exponential Stabilization for a Class of Stochastic Nonholonomic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaoyan Qin
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Nonholonomic Systems ◽  
Input State ◽  
Stabilization Problem ◽  
Adaptive Stabilization ◽  
Closed Loop System ◽  
Scaling Technique ◽  
Switching Strategy ◽  
Parameter Separation

This paper investigates the adaptive stabilization problem for a class of stochastic nonholonomic systems with strong drifts. By using input-state-scaling technique, backstepping recursive approach, and a parameter separation technique, we design an adaptive state feedback controller. Based on the switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the states of closed-loop system are global bounded in probability.

scholarly journals Adaptive State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems Driven by Noise of Unknown Covariance

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Cong-Ran Zhao ◽  
Xue-Jun Xie ◽  
Na Duan
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
High Order ◽  
Feedback Stabilization ◽  
Stochastic Nonlinear Systems ◽  
Closed Loop System ◽  
Stochastic Nonlinear System ◽  
Unknown Covariance ◽  
Globally Stable ◽  
Smooth State

This paper further considers more general high-order stochastic nonlinear system driven by noise of unknown covariance and its adaptive state-feedback stabilization problem. A smooth state-feedback controller is designed to guarantee that the origin of the closed-loop system is globally stable in probability.

scholarly journals Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Nengwei Zhang ◽  
Enbin Zhang ◽  
Fangzheng Gao
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Design Procedure ◽  
High Order ◽  
Global Stabilization ◽  
Closed Loop System ◽  
System A ◽  
Continuous State ◽  
High Order Time

Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

A Digital Algorithm for Near-Minimum-Time Control of Robot Manipulators

1987 ◽  
Vol 109 (4) ◽  
pp. 320-327 ◽  
Author(s):  
C. K. Kao ◽  
A. Sinha ◽  
A. K. Mahalanabis
Keyword(s):  
Control Algorithm ◽  
State Feedback ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Minimum Time ◽  
State Feedback Control ◽  
Final States ◽  
Closed Loop System ◽  
Time Control ◽  
Digital Algorithm

A digital state feedback control algorithm has been developed to obtain the near-minimum-time trajectory for the end-effector of a robot manipulator. In this algorithm, the poles of the linearized closed loop system are judiciously placed in the Z-plane to permit near-minimum-time response without violating the constraints on the actuator torques. The validity of this algorithm has been established using numerical simulations. A three-link manipulator is chosen for this purpose and the results are discussed for three different combinations of initial and final states.

scholarly journals The Adaptive Neural Control for a Class of High-Order Uncertain Stochastic Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xiaoyan Qin
Keyword(s):  
Nonlinear Systems ◽  
Neural Control ◽  
Closed Loop ◽  
Control Method ◽  
High Order ◽  
Stochastic Nonlinear Systems ◽  
Closed Loop System ◽  
Adaptive Neural Control ◽  
Control Scheme ◽  
Approximation Capability

This paper studies the problem of the adaptive neural control for a class of high-order uncertain stochastic nonlinear systems. By using some techniques such as the backstepping recursive technique, Young’s inequality, and approximation capability, a novel adaptive neural control scheme is constructed. The proposed control method can guarantee that the signals of the closed-loop system are bounded in probability, and only one parameter needs to be updated online. One example is given to show the effectiveness of the proposed control method.

Sliding Mode Output Feedback Control of Vibration in a Flexible Structure

2007 ◽  
Vol 129 (6) ◽  
pp. 851-855 ◽  
Author(s):  
M. C. Pai ◽  
A. Sinha
Keyword(s):  
Output Feedback ◽  
Control Algorithm ◽  
Closed Loop ◽  
Sliding Mode ◽  
Output Feedback Control ◽  
Flexible Structure ◽  
Numerical Verification ◽  
Closed Loop System ◽  
New Approach ◽  
Small Gain

This paper presents a new approach for the robust control of vibration in a flexible structure in the presence of uncertain parameters and residual modes. The technique is based on the sliding mode control algorithm using direct output feedback and assumes that actuators and sensors are not collocated. The uncertainty matrix need not satisfy the invariance or matching conditions. The small gain theorem/μ analysis is applied to analyze the asymptotic behavior of the closed-loop system with parametric uncertainties inside boundary layers. The model of a flexible tetrahedral truss structure is used to conduct numerical verification of the theoretical analysis.

Adaptive Feedback Control of Stochastic Nonholonomic Systems with Uncertainties

2015 ◽  
Vol 727-728 ◽  
pp. 692-696
Author(s):  
Gui Ling Ju ◽  
Wei Hai Sun
Keyword(s):  
Closed Loop ◽  
Nonholonomic System ◽  
Nonholonomic Systems ◽  
The State ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Output Measurement ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Switching Control Strategy

This paper deals with the adaptive control design of stochastic nonholonomic system with uncertainties. The state-input scaling technique, stochastic Lyapunov-like theorem and back-stepping approach are used to design the feedback controller. The controllers guarantee all states of the closed-loop system are largely asymptotically stable in probability, In order to make the state scaling effective, a new switching control strategy based on the output measurement of the first subsystem is employed.

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