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 Adaptive Finite-Time Stabilization of High-Order Nonlinear Systems with Dynamic and Parametric Uncertainties

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Meng-Meng Jiang ◽  
Xue-Jun Xie
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Finite Time ◽  
State Feedback ◽  
High Order ◽  
Parametric Uncertainties ◽  
Nonlinear Functions ◽  
Sign Function ◽  
Dynamic Uncertainty ◽  
Finite Time Stabilization

Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.

scholarly journals Transformation of CLF to ISS-CLF for Nonlinear Systems with Disturbance and Construction of Nonlinear Robust Controller withL2Gain Performance

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Keizo Okano ◽  
Kojiro Hagino ◽  
Hidetoshi Oya
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Linearization ◽  
Feedback System ◽  
Stability Control ◽  
Control Law ◽  
Robust Controller ◽  
Control Lyapunov Function ◽  
Nonlinear Control Law ◽  
Nonlinear Robust

A new nonlinear control law for a class of nonlinear systems with disturbance is proposed. A control law is designed by transforming control Lyapunov function (CLF) to input-to-state stability control Lyapunov function (ISS-CLF). The transformed CLF satisfies a Hamilton-Jacobi-Isaacs (HJI) equation. The feedback system by the proposed control law has characteristics ofL2gain. Finally, it is shown by a numerical example that the proposed control law makes a controller by feedback linearization robust against disturbance.

State Feedback and Output Feedback Control of Polynomial Nonlinear Systems Using Fractional Lyapunov Functions

2007 ◽  
Author(s):  
Qian Zheng ◽  
Fen Wu
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Output Feedback ◽  
Lyapunov Functions ◽  
State Feedback ◽  
The State ◽  
State Feedback Control ◽  
Feedback Gain ◽  
Variation Rate

In this paper, we will study the state feedback control problem of polynomial nonlinear systems using fractional Lyapunov functions. By adding constraints to bound the variation rate of each state, the general difficulty of calculating derivative of nonquadratic Lyapunov function is effectively overcome. As a result, the state feedback conditions are simplified as a set of Linear Matrix Inequalities (LMIs) with polynomial entries. Computationally tractable solution is obtained by Sum-of-Squares (SOS) decomposition. And it turns out that both of the Lyapunov matrix and the state feedback gain are state dependent fractional matrix functions, where the numerator as well as the denominator can be polynomials with flexible forms and higher nonlinearities involved in. Same idea is extended to a class of output dependent nonlinear systems and the stabilizing output feedback controller is specified as polynomial of output. Synthesis conditions are similarly derived as using constant Lyapunov function except that all entries in LMIs are polynomials of output with derivative of output involved in. By bounding the variation rate of output and gridding on the bounded interval, the LMIs are solvable by SOS decomposition. Finally, two examples are used to materialize the design scheme and clarify the various choices on state boundaries.

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.

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