A framework for global stabilization of nonlinear systems by continuous state feedback

2003 ◽  
Author(s):  
Chunjiang Qian ◽  
Wei Lin
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Global Stabilization ◽  
Continuous State

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.

scholarly journals Learning Output Reference Model Tracking for Higher-Order Nonlinear Systems with Unknown Dynamics

Algorithms ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 121 ◽  
Author(s):  
Mircea-Bogdan Radac ◽  
Timotei Lala
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Reference Model ◽  
The State ◽  
State Transitions ◽  
Practical Implementation ◽  
General Function ◽  
State Action ◽  
Model Free ◽  
Continuous State

This work suggests a solution for the output reference model (ORM) tracking control problem, based on approximate dynamic programming. General nonlinear systems are included in a control system (CS) and subjected to state feedback. By linear ORM selection, indirect CS feedback linearization is obtained, leading to favorable linear behavior of the CS. The Value Iteration (VI) algorithm ensures model-free nonlinear state feedback controller learning, without relying on the process dynamics. From linear to nonlinear parameterizations, a reliable approximate VI implementation in continuous state-action spaces depends on several key parameters such as problem dimension, exploration of the state-action space, the state-transitions dataset size, and a suitable selection of the function approximators. Herein, we find that, given a transition sample dataset and a general linear parameterization of the Q-function, the ORM tracking performance obtained with an approximate VI scheme can reach the performance level of a more general implementation using neural networks (NNs). Although the NN-based implementation takes more time to learn due to its higher complexity (more parameters), it is less sensitive to exploration settings, number of transition samples, and to the selected hyper-parameters, hence it is recommending as the de facto practical implementation. Contributions of this work include the following: VI convergence is guaranteed under general function approximators; a case study for a low-order linear system in order to generalize the more complex ORM tracking validation on a real-world nonlinear multivariable aerodynamic process; comparisons with an offline deep deterministic policy gradient solution; implementation details and further discussions on the obtained results.

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 A Note on Stabilization of Discrete Nonlinear Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
Fengjun Tang ◽  
Rong Yuan
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
State Feedback ◽  
New Method ◽  
Stabilization Problem ◽  
Control Lyapunov Function ◽  
Continuous State ◽  
Discrete Nonlinear Systems

We deal with the stabilization problem of discrete nonlinear systems. We construct a control Lyapunov function on discrete nonlinear systems. Then, we present a new method to construct a continuous state feedback law.

scholarly journals Global Finite-Time Stabilization for a Class of Uncertain High-Order Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jian Wang ◽  
Jing Xie ◽  
Fangzheng Gao
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
High Order ◽  
Finite Time Stability ◽  
Adding A Power Integrator ◽  
System A ◽  
Continuous State ◽  
Finite Time Stabilization ◽  
Power Integrator

This paper addresses the problem of global finite-time stabilization by state feedback for a class of high-order nonlinear systems under weaker condition. By using the methods of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee the global finite-time stability of the resulting closed-loop system. A simulation example is provided to illustrate the effectiveness of the proposed approach.

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