The First Order Necessary Conditions for Nonsmooth Variational and Control Problems

1984 ◽  
Vol 22 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Halina Frankowska
Keyword(s):  
Necessary Conditions ◽  
Control Problems ◽  
First Order ◽  
And Control

Parameter Normalization in Multibody Dynamics

2008 ◽  
Author(s):  
Saeed Ebrahimi ◽  
Jo´zsef Ko¨vecses
Keyword(s):  
Parameter Estimation ◽  
Multibody Dynamics ◽  
Eigenvalue Problems ◽  
Physical Structure ◽  
Control Problems ◽  
Inertial Parameters ◽  
Parametric Studies ◽  
Novel Concept ◽  
And Control

In this paper, we introduce a novel concept for parametric studies in multibody dynamics. This is based on a technique that makes it possible to perform a natural normalization of the dynamics in terms of inertial parameters. This normalization technique rises out from the underlying physical structure of the system, which is mathematically expressed in the form of eigenvalue problems. It leads to the introduction of the concept of dimensionless inertial parameters. This, in turn, makes the decomposition of the array of parameters possible for studying design and control problems where parameter estimation and sensitivity is of importance.

On Measures of Coupling Between the Artifact and Controller Optimal Design Problems

2009 ◽  
Author(s):  
Diane L. Peters ◽  
Panos Y. Papalambros ◽  
A. Galip Ulsoy
Keyword(s):  
System Optimization ◽  
Optimization Method ◽  
Ease Of Use ◽  
Control Problems ◽  
Design Problems ◽  
Sensitivity Equations ◽  
Smart Products ◽  
Two Measures ◽  
And Control ◽  
Artifact Design

Optimization of smart products requires optimizing both the artifact design and its controller. The presence of coupling between the design and control problems is an important consideration in choosing the system optimization method. Several measures of coupling have been proposed based on different viewpoints of the system. In this paper, two measures of coupling, a vector based on optimality conditions and a matrix derived from an extension of the global sensitivity equations, are shown to be related under certain conditions and to be consistent in their coupling determination. The measures’ physical interpretation and relative ease of use are discussed using the example of a positioning gantry. A further relation is derived between one measure and a modified sequential formulation that would give results sufficiently close to the true solutions.

scholarly journals A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

1995 ◽  
Vol 36 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Mohammad A. Kazemi
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Fréchet Derivative ◽  
Necessary Condition ◽  
Control Problems ◽  
Partial Differential ◽  
Frechet Derivative ◽  
First Order

AbstractIn this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

Sign in / Sign up

Export Citation Format

Share Document