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.

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.

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.

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.

Further results on adaptive state feedback stabilization for a class of stochastic feedforward nonlinear systems with time delays

2018 ◽  
Vol 41 (1) ◽  
pp. 127-134 ◽  
Author(s):  
Xiaoyan Qin ◽  
Huifang Min
Keyword(s):  
Nonlinear Systems ◽  
Time Delays ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Transformation Technique ◽  
Globally Asymptotically Stable ◽  
Feedforward Nonlinear Systems

This paper further discusses the state feedback stabilization for stochastic high-order feedforward nonlinear systems with input time delay. By constructing the appropriate Lyapunov–Krasovskii functional, and using the variable transformation technique and the homogeneous domination idea, a state feedback controller is designed to ensure that the closed-loop system will be globally asymptotically stable in probability. Finally, an example is given to verify the effectiveness of the obtained analytical results.

scholarly journals State-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power

2010 ◽  
Vol 15 (1) ◽  
pp. 39-53 ◽  
Author(s):  
L. Liu ◽  
N. Duan
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
High Order ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Optimal Stabilization ◽  
Adding A Power Integrator ◽  
Power Integrator ◽  
Smooth State

This paper investigates the problem of globally asymptotically stable in probability by state-feedback for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique and choosing an appropriate Lyapunov function, a linear smooth state-feedback controller is explicitly constructed to render the system globally asymptotically stable in probability. Furthermore, we address the problem of state-feedback inverse optimal stabilization in probability. A simulation example is provided to show the effectiveness of the proposed approach.

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