Penalty Function Method and Necessary Optimum Conditions in Optimal Control Problems with Bounded State Variables

1975 ◽  
pp. 128-133
Author(s):  
Yu. M. Volin
Keyword(s):  
Optimal Control ◽  
Penalty Function ◽  
Function Method ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Penalty Function Method ◽  
State Variables ◽  
Optimum Conditions ◽  
Bounded State

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.

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.

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