Optimal Steady-State Regulator Design for a Class of Nonlinear Systems With Arbitrary Relative Degree

2020 ◽  
pp. 1-13
Author(s):  
Ranran Li ◽  
Guang-Hong Yang
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Relative Degree ◽  
State Regulator

Funnel control for nonlinear systems with higher relative degree

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Thomas Berger ◽  
Huy Hoàng Lê ◽  
Timo Reis
Keyword(s):  
Nonlinear Systems ◽  
Relative Degree ◽  
Funnel Control

Weak Instability of Chen–Ricles Explicit Method for Structural Dynamics

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Shuenn-Yih Chang
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
High Frequency ◽  
Explicit Method ◽  
Order Accuracy ◽  
Practical Applications ◽  
Correction Scheme ◽  
Highly Nonlinear ◽  
Steady State Responses ◽  
State Responses

Although the Chen–Ricles (CR) explicit method (CRM) (proposed by Chen and Ricles) has been claimed to have desired numerical properties, such as unconditional stability, explicit formulation, and second-order accuracy, it also shows some unusual properties, such as a less accuracy of solving highly nonlinear systems, a high-frequency overshoot in steady-state responses, and a weak instability. A correction scheme by adjusting the displacement difference equation with a loading term can be employed to extinguish the high-frequency overshoot in steady-state responses. However, there is still no way to get rid of the weak instability and to improve the less accuracy of solving highly nonlinear systems. It is recognized that a weak instability might result in inaccurate solutions or numerical explosions. Hence, the practical applications of CRM are strictly limited.

scholarly journals Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhongwei Lin ◽  
Jizhen Liu ◽  
Yuguang Niu
Keyword(s):  
Nonlinear Systems ◽  
Control Design ◽  
Relative Degree ◽  
Backstepping Technique ◽  
Markovian Jump ◽  
Design Problems ◽  
Stabilizing Control ◽  
Full State ◽  
Degree Set ◽  
Coordinate Changes

This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree setn,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.

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