An exact penalty method for solving optimal control problems

Feiring, Bruce R.

doi:10.1016/0096-3003(85)90002-5

Cited by 5 publications

(5 citation statements)

References 3 publications

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“…Further, this and (10) Since, by assumption, r(t) 2 p ( t ) , it follows that Therefore P ( U , r ) -P ( B , r) 2 6…”

Section: O R -I T H Dr+xt(t)= Hh D T + ( L X ( X ( T ) ) ) T H ( T )mentioning

confidence: 75%

“…By direct calculations and from (14) and (8) for any u in some neighbourhood B ( a ) of U, where a is a positive number and x in p ( u , r) (see (6)) is the response corresponding to u. Therefore B ( t ) is a local optimal solution to problem (6)'' and the theorem is proved.…”

Section: O R -I T H Dr+xt(t)= Hh D T + ( L X ( X ( T ) ) ) T H ( T )mentioning

confidence: 89%

“…This discussion above has attempted to do two things: first, to use the exact penalty function method to solve the constrained optimal control problem (3); and secondly, to prove that the solution of problem (3) may be obtained by solving the modified unconstrained optimal control problem (6). An example is presented to illustrate the findings.…”

Section: Discussionmentioning

confidence: 99%

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Exact penalty function approach to constrained optimal control problems

Xing

Chen²,

Wang

et al. 1989

Optim Control Appl Methods

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Given the well known concept that optimal control problems may be solved either by the maximum principle or by the dynamic programming technique which employs many numerical algorithms, this paper attempts to show that the exact penalty function method may be used to transform a constrained optimal control problem into an unconstrained optimal control problem. Under certain conditions the constrained optimal control problem is shown to be equivalent to an unconstrained optimal control problem, which can be easily solved by a numerical technique.

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“…Further, this and (10) Since, by assumption, r(t) 2 p ( t ) , it follows that Therefore P ( U , r ) -P ( B , r) 2 6…”

Section: O R -I T H Dr+xt(t)= Hh D T + ( L X ( X ( T ) ) ) T H ( T )mentioning

confidence: 75%

Section: O R -I T H Dr+xt(t)= Hh D T + ( L X ( X ( T ) ) ) T H ( T )mentioning

confidence: 89%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Exact penalty function approach to constrained optimal control problems

Xing

Chen²,

Wang

et al. 1989

Optim Control Appl Methods

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show abstract

“…Exact penalty methods seem to be more attractive for chemical engineering applications. Some exact penalty functions have been proposed in the OC literature with interesting computational properties both in the indirect and direct frameworks 184–186 . One disadvantage of these functions is that they usually give rise to nonsmoothness.…”

Section: Current Challenges and Perspectivesmentioning

confidence: 99%

“…Some exact penalty functions have been proposed in the OC literature with interesting computational properties both in the indirect and direct frameworks. [184][185][186] One disadvantage of these functions is that they usually give rise to nonsmoothness. Therefore, further research is needed to solve efficiently the associated penalty problem.…”

Section: Uncertaintymentioning

confidence: 99%

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

2022

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In the mid‐1950s, Pontryagin et al. published a principle that became a fundamental concept in optimal control (OC) theory. The principle provides theoretical and practical methods to find the solution of OC problems, in particular, open‐loop control problems. In chemical engineering, the principle has played an important role as a decision making framework for more than 60 years. This study gathers the main contributions on the application of the Pontryagin's principle to the dynamic optimization of chemical processes. A concise overview of the optimality conditions for a wide class of constrained OC problems is provided. Numerical methods to solve the necessary conditions and strategies to address inequality constraints are summarized. The information and illustrative case study presented in this work can be used as a guide to implement the principle in different settings. Opportunities for further application of the principle in relevant chemical engineering problems are also discussed.

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Applications of the exterior penalty method in constrained optimal control problems

Xing

Wang

1989

Optim Control Appl Methods

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SUMMARYThis paper gives a theoretical analysis of the applications of the exterior penalty method in continuoustime non-linear programs and constrained optimal control problems. As an example, the Cauchy Inequality in the continuous case is proved. Also, the exterior penalty method is used to treat constrained optimal control problems. It is proved, under suitable assumptions, that a constrained optimal control problem can be solved by performing a sequence of unconstrained optimal control problems, and the constrained solution to the constrained optimal control problem can be obtained as the limit of the solutions to the sequence of unconstrained optimal control problems. In using the exterior penalty 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. An existence theorem for these problems is also given.

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An exact penalty method for solving optimal control problems

Cited by 5 publications

References 3 publications

Exact penalty function approach to constrained optimal control problems

Exact penalty function approach to constrained optimal control problems

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

Applications of the exterior penalty method in constrained optimal control problems

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