Simultaneous Optimization of Continuous Control Inputs and Discrete State Waypoints

2006 ◽  
pp. 302-317 ◽  
Author(s):  
Jun-ichi Imura ◽  
Hiromichi Matsushima
Keyword(s):  
Simultaneous Optimization ◽  
Continuous Control ◽  
Discrete State

scholarly journals Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations

2021 ◽  
Author(s):  
Eduardo Casas ◽  
Mariano Mateos ◽  
Arnd Rösch
Keyword(s):  
Control Problem ◽  
Error Estimates ◽  
Numerical Approximation ◽  
Discrete Equation ◽  
Element Approximation ◽  
Continuous Control ◽  
Optimal Controls ◽  
Discrete State ◽  
Semilinear Elliptic ◽  
Continuous Problem

AbstractWe analyze the numerical approximation of a control problem governed by a non-monotone and non-coercive semilinear elliptic equation. The lack of monotonicity and coercivity is due to the presence of a convection term. First, we study the finite element approximation of the partial differential equation. While we can prove existence of a solution for the discrete equation when the discretization parameter is small enough, the uniqueness is an open problem for us if the nonlinearity is not globally Lipschitz. Nevertheless, we prove the existence and uniqueness of a sequence of solutions bounded in $$L^\infty (\varOmega )$$ L ∞ ( Ω ) and converging to the solution of the continuous problem. Error estimates for these solutions are obtained. Next, we discretize the control problem. Existence of discrete optimal controls is proved, as well as their convergence to solutions of the continuous problem. The analysis of error estimates is quite involved due to the possible non-uniqueness of the discrete state for a given control. To overcome this difficulty we define an appropriate discrete control-to-state mapping in a neighbourhood of a strict solution of the continuous control problem. This allows us to introduce a reduced functional and obtain first order optimality conditions as well as error estimates. Some numerical experiments are included to illustrate the theoretical results.

Method and Technology for Continuous Control of Performance and Operating Quality of Automotive and Combine Machinery

2020 ◽  
Vol 14 (3) ◽  
pp. 160
Author(s):  
Ildar Gabitov ◽  
Samat Insafuddinov ◽  
Ildar Badretdinov ◽  
Viktor Pavlenko ◽  
Filyus Safin
Keyword(s):  
Continuous Control

Determination of Combined and Second Order Factor Effects for Simultaneous Optimization of Physical and Mechanical Properties of NR/BR Blend System

2014 ◽  
Vol 42 (4) ◽  
pp. 290-304
Author(s):  
Rajarajan Aiyengar ◽  
Jyoti Divecha
Keyword(s):  
Physical And Mechanical Properties ◽  
Second Order ◽  
Simultaneous Optimization ◽  
Order Effects ◽  
Elongation At Break ◽  
Five Factors ◽  
Rubber Compounds ◽  
Polybutadiene Rubber ◽  
Contour Plots

ABSTRACT The blends of natural rubber (NR), polybutadiene rubber (BR), and other forms of rubbers are widely used for enhancing the mechanical and physical properties of rubber compounds. Lots of work has been done in conditioning and mixing of NR/BR blends to improve the properties of its rubber compounds and end products such as tire tread. This article employs response surface methodology designed experiments in five factors; high abrasion furnace carbon black (N 330), aromatic oil, NR/BR ratio, sulfur, and N-oxydiethylene-2-benzothiazole sulfenamide for determination of combined and second order effects of the significant factors leading to simultaneous optimization of the NR/BR blend system. One of the overall optimum of eight properties existed at carbon 44 phr, oil 6.1 phr, NR/BR 78/22 phr with the following values of properties: tensile strength (22 MPa), elongation at break (528%), tear resistance (30 kg/mm), rebound resilience (67%), moderate hardness (68 International rubber hardness degrees) with low heat buildup (17 °C), permanent set (12%), and abrasion loss (57 mm3). More optimum combinations can easily be determined from the NR/BR blend system models contour plots.

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