On energy-optimal controls for a second-order nonlinear system

1969 ◽  
Vol 12 (7) ◽  
pp. 835-838
Author(s):  
V. P. Savel'ev
Keyword(s):  
Nonlinear System ◽  
Second Order ◽  
Optimal Controls

scholarly journals First and second order optimality conditions for the control of Fokker-Planck equations

2021 ◽  
Vol 27 ◽  
pp. 15
Author(s):  
M. Soledad Aronna ◽  
Fredi Tröltzsch
Keyword(s):  
Control Variable ◽  
Sufficient Conditions ◽  
Planck Equation ◽  
Second Order ◽  
Optimal Controls ◽  
Main Emphasis ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Fokker Planck Equations ◽  
Fokker Planck

In this article we study an optimal control problem subject to the Fokker-Planck equation ∂tρ − ν∆ρ − div(ρB[u]) = 0 The control variable u is time-dependent and possibly multidimensional, and the function B depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.

scholarly journals A High-Order Numerical Method for a Nonlinear System of Second-Order Boundary Value Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Minqiang Xu ◽  
Jing Niu ◽  
Li Guo
Keyword(s):  
Nonlinear System ◽  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Boundary Value ◽  
Linear Equations ◽  
Second Order ◽  
High Order ◽  
Reproducing Kernel Method

This paper is concerned with a high-order numerical scheme for nonlinear systems of second-order boundary value problems (BVPs). First, by utilizing quasi-Newton’s method (QNM), the nonlinear system can be transformed into linear ones. Based on the standard Lobatto orthogonal polynomials, we introduce a high-order Lobatto reproducing kernel method (LRKM) to solve these linear equations. Numerical experiments are performed to investigate the reliability and efficiency of the presented method.

Research on Bifurcation of Asymmetric System Based on Second-Order Averaging Method

2015 ◽  
Vol 713-715 ◽  
pp. 1835-1838
Author(s):  
An Kang Hu ◽  
Ya Chong Liu ◽  
Yu Lu ◽  
Feng Lei Han
Keyword(s):  
Nonlinear System ◽  
Averaging Method ◽  
Second Order ◽  
Local Bifurcation ◽  
Saddle Node Bifurcation ◽  
Asymmetric System ◽  
Saddle Node ◽  
Basic Characteristics

Bifurcation which may lead to chaos is the typical character of nonlinear system, and an asymmetric system with asymmetric parameter is adopted in this paper. The basic characteristics which vary with the asymmetric parameter are investigated firstly, and then, the second-order averaging method is used to investigate the local bifurcation of the asymmetric system. The super and sub critical saddle-node bifurcation curves of both left center and right center of the system are solved analytically. The results show that the degree of asymmetric is influenced by the value of asymmetric parameter and the two bifurcation curves of the same center are intersected at the point which also depends on the asymmetric parameter value.

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