Global stabilization for switched stochastic nonlinear systems via unbounded time-varying scaling

2017 ◽  
Vol 40 (7) ◽  
pp. 2270-2277 ◽  
Author(s):  
Zhibao Song ◽  
Junyong Zhai ◽  
Zhengwei Zhu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Switched System ◽  
Feedback Controller ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Global Stabilization ◽  
Asymptotically Stable ◽  
Control Scheme

This paper is concerned with the problem of global stabilization for switched stochastic nonlinear systems under arbitrary switchings. Based on the unbounded time-varying scaling of states, we design a state feedback controller to render the closed-loop switched system asymptotically stable in probability. Two examples are given to demonstrate the effectiveness of the proposed control scheme.

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.

scholarly journals Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jinsheng Xing ◽  
Naizheng Shi
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Complex Systems ◽  
Closed Loop ◽  
Loop System ◽  
Asymptotically Stable ◽  
Bilinear Model ◽  
Closed Loop System ◽  
Fuzzy Modelling ◽  
Control Scheme

This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rateαare derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

scholarly journals Asymptotic Stabilization by State Feedback for a Class of Stochastic Nonlinear Systems with Time-Varying Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Wang ◽  
Wuquan Li ◽  
Xiuhong Wang
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Original System ◽  
Feedback Stabilization ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Control Coefficients

This paper investigates the problem of state-feedback stabilization for a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients. By introducing effective coordinates, the original system is transformed into an equivalent one with tunable gain. After that, by using the low gain homogeneous domination technique and choosing the low gain parameter skillfully, the closed-loop system can be proved to be globally asymptotically stable in probability. The efficiency of the state-feedback controller is demonstrated by a simulation example.

scholarly journals Sufficient Conditions of Asymptotic Stability of the Time-Varying Descriptor Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Xiaoming Su ◽  
Yali Zhi
Keyword(s):  
Asymptotic Stability ◽  
Riccati Equation ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Descriptor Systems ◽  
Sufficient Condition ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Close Loop System

We discuss the time-varying descriptor systems. Firstly, a sufficient condition of asymptotic stability and impulse-free is derived based on Riccati equation. Secondly, we design a state feedback controller to make the close-loop system asymptotically stable and impulse-free. Finally, a numerical example demonstrates the proposed results.

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.

Controller Design for See-Saw Systems

2014 ◽  
Vol 898 ◽  
pp. 680-683
Author(s):  
Hai Yan Wang
Keyword(s):  
Control Theory ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
The State ◽  
Feedback Controller ◽  
System Model ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
State Feedback Controller

The control theory has widely application in many fields such as industrial and agricultural. A class of see-saw system model will be studied in this paper. Using the theory of pole assignment, we will design the state feedback controller, such that the closed-loop system is asymptotically stable. At the same time, using the tool of MATLAB, the model of closed see-saw system will be simulated and analyzed. It reveals the state regularity of see-saw system.

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