Blade Design of Axial-Flow Compressors by the Method of Optimal Control Theory—Application of Pontryagin’s Maximum Principles, a Sample Calculation and Its Results

1987 ◽  
Vol 109 (1) ◽  
pp. 103-107 ◽  
Author(s):  
Chuan-gang Gu ◽  
Yong-miao Miao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Function Method ◽  
Axial Flow ◽  
Maximum Principles ◽  
Penalty Function Method ◽  
Blade Design ◽  
Transformation Technique ◽  
Theory Application

Using the continual transformation technique [3] and the augmented penalty function method, the typical optimal control problem with various constraints proposed in the paper [2] has been converted to a new equivalent optimal control problem with no constraint. This enables the application of Pontryagin ’s maximum principle. Further, by means of the conjugate gradient method an example of the calculation is shown and the corresponding program is developed. A satisfactory optimal diffusion factor distribution has been obtained.

scholarly journals A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xiangyu Gao ◽  
Xian Zhang ◽  
Yantao Wang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Function Method ◽  
Optimal Control Problems ◽  
Optimal Parameter ◽  
Inequality Constraints ◽  
Terminal State ◽  
Control Problems ◽  
Penalty Function Method

We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact penalty function method is used to transform the constrained optimal parameter selection problem into a sequence of approximate unconstrained optimal control problems. It is shown that, if the penalty parameter is sufficiently large, the locally optimal solutions of these approximate unconstrained optimal control problems converge to the solution of the original optimal control problem. Finally, numerical simulations on two examples demonstrate the effectiveness of the proposed method.

scholarly journals Applications of the penalty function method in constrained optimal control problems

1989 ◽  
Vol 2 (4) ◽  
pp. 251-265 ◽  
Author(s):  
An-qing Xing
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Penalty Function ◽  
Function Method ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Penalty Function Method ◽  
Constrained Optimal Control ◽  
Numerical Examples ◽  
Constrained Optimal Control Problem

This paper uses the penalty function method to solve constrained optimal control problems. Under suitable assumptions, we can solve a constrained optimal control problem by solving a sequence of unconstrained optimal control problems. In turn, the constrained solution to the main problem can be obtained as the limit of the solutions of the sequence. In using the penalty function method to solve constrained optimal control problems, it is usually assumed that each of the modified unconstrained optimal control problems has at least one solution. Here we establish an existence theorem for those problems. Two numerical examples are presented to demonstrate the findings.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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