Tight reachability bounds for constrained nonlinear systems using mean value differential inequalities

Automatica ◽  
2021 ◽  
Vol 134 ◽  
pp. 109911
Author(s):  
Kai Shen ◽  
Dillard L. Robertson ◽  
Joseph K. Scott
Keyword(s):  
Nonlinear Systems ◽  
Mean Value ◽  
Differential Inequalities ◽  
Constrained Nonlinear Systems

Dynamics of large constrained nonlinear systems-a taxonomy theory [power system stability]

1995 ◽  
Vol 83 (11) ◽  
pp. 1530-1561 ◽  
Author(s):  
V. Venkatasubramanian ◽  
H. Schattler ◽  
J. Zaborsky
Keyword(s):  
Nonlinear Systems ◽  
Power System ◽  
Power System Stability ◽  
System Stability ◽  
Constrained Nonlinear Systems

Calculation of Nonlinear Systems Under Narrow Band Excitation Using Equivalent Linearization and Path Continuation

2021 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt
Keyword(s):  
Nonlinear Systems ◽  
Narrow Band ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Mean Value ◽  
Equivalent Linearization ◽  
Efficient Procedure ◽  
Stochastic Excitations ◽  
Wide Range ◽  
The One

Abstract Turbomachines experience a wide range of different types of excitation during operation. On the structural mechanics side, periodic or even harmonic excitations are usually assumed. For this type of excitation there are a variety of methods, both for linear and nonlinear systems. Stochastic excitation, whether in the form of Gaussian white noise or narrow band excitation, is rarely considered. As in the deterministic case, the calculations of the vibrational behavior due to stochastic excitations are even more complicated by nonlinearities, which can either be unintentionally present in the system or can be used intentionally for vibration mitigation. Regardless the origin of the nonlinearity, there are some methods in the literature, which are suitable for the calculation of the vibration response of nonlinear systems under random excitation. In this paper, the method of equivalent linearization is used to determine a linear equivalent system, whose response can be calculated instead of the one of the nonlinear system. The method is applied to different multi-degree of freedom nonlinear systems that experience narrow band random excitation, including an academic turbine blade model. In order to identify multiple and possibly ambiguous solutions, an efficient procedure is shown to integrate the mentioned method into a path continuation scheme. With this approach, it is possible to track jump phenomena or the influence of parameter variations even in case of narrow band excitation. The results of the performed calculations are the stochastic moments, i.e. mean value and variance.

scholarly journals On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach

Automatica ◽  
2005 ◽  
Vol 41 (9) ◽  
pp. 1583-1589 ◽  
Author(s):  
J.M. Bravo ◽  
D. Limon ◽  
T. Alamo ◽  
E.F. Camacho
Keyword(s):  
Nonlinear Systems ◽  
Interval Arithmetic ◽  
Invariant Sets ◽  
Constrained Nonlinear Systems
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