Sensitivity of optimal control to final state specification by a combined continuation and nonlinear programming approach

Rosen, Oscar; Luus, Rein

doi:10.1016/0009-2509(89)85196-6

Cited by 16 publications

(7 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…NPSOL uses a sequential quadratic programming procedure for solving nonlinear optimization problems and is considered to be the most effective method for NLP problems (Gill et al, 1985). The use of nonlinear programming provides a reliable means of obtaining optimal control (Rosen and Luus, 1989).…”

Section: Solution By Nonlinear Programming (Nlp)mentioning

confidence: 99%

Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor

1992

Self Cite

View full text Add to dashboard Cite

The reaction scheme for the isomerization and hydrogenation of methylcyclopentane using bifunctional catalyst is considered in a tubular reactor. The aim is to maximize the concentration of benzene at the outlet of the reactor by choosing the optimal blend of the catalyst along the reactor. When the problem was attempted by nonlinear programming employing sequential quadratic programming, twenty‐five local optima were obtained from 100 random starting conditions. By using iterative dynamic programming in addition to the best two local optima obtained by nonlinear programming, the global optimum was also obtained.

show abstract

Section: Solution By Nonlinear Programming (Nlp)mentioning

confidence: 99%

Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor

1992

Self Cite

View full text Add to dashboard Cite

show abstract

“…To enable tightly constrained optimal control problems to be solved and to examine the sensitivity of the constraints, Rosen and Luus (1989) used homotopic continuation. The goal of this paper is to investigate the use of continuation to enlarge the search region in optimization problems where it is difficult to find a feasible solution, to identify active inequality constraints and then to use these active inequalities as equality constraints to obtain the optimum accurately.…”

Section: Introductionmentioning

confidence: 99%

Handling inequality constraints in direct search optimization

Luus

Sabaliauskas

Harapyn

2006

Engineering Optimization

Self Cite

View full text Add to dashboard Cite

The use of homotopic continuation, where the constraints are relaxed initially by a constraint relaxation parameter δ, can overcome the difficulty of obtaining feasible solutions for highly constrained optimization problems. During optimization, δ is systematically reduced in size until finally δ is put equal to zero. This then corresponds to the original optimization problem and an approximate optimal solution is now available. For refinement of this approximate solution, the active inequalities are identified and the optimization problem is reformulated so that the active inequalities are used as equalities. This simplifies the optimization problem and enables the optimal solution to be obtained very accurately. The viability of this two-step procedure is tested with several problems.

show abstract

“…The gradient-dependent method based on Pontryagin's maximum principle may have the convergent problem; a good initial estimate is usually relevant to the "nal solution [2]. On the other hand, the major disadvantage of DP is known as the curse of dimensionality which discourages the use of DP on dynamic systems with more than three or four state variables [3].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of time-delayed optimal control problems by iterative dynamic programming

Chen

Sun

Chang

2000

Optim. Control Appl. Meth.

View full text Add to dashboard Cite

This work presents a numerical method to solve the optimal control problem with time‐delayed arguments and a fixed terminal time. A series of auxiliary states obtained from the linearly truncated Taylor series expansion are used to represent the status of a time‐delayed state at different time intervals. The backward iterative dynamic programming (IDP) technique can thus be directly employed to solve the delay‐free optimal control problem with augmented states. Five numerical examples are provided, demonstrating the proposed method's effectiveness in solving the time‐delayed optimal control problems. Copyright © 2000 John Wiley & Sons, Ltd.

show abstract

Sensitivity of optimal control to final state specification by a combined continuation and nonlinear programming approach

Cited by 16 publications

References 18 publications

Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor

Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor

Handling inequality constraints in direct search optimization

Numerical solution of time-delayed optimal control problems by iterative dynamic programming

Contact Info

Product

Resources

About