Expressing optimal control problems as differential algebraic equations

England, Roland; Gómez, Susana; Lamour, René

doi:10.1016/j.compchemeng.2005.02.040

Cited by 10 publications

(12 citation statements)

References 17 publications

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“…1. This is consistent with the result obtained by England [15]. The optimal objective function value is J * (12) ≈ 0.477712020050041, rather than the value 0.476946 obtained in [7].…”

Section: Global Optimumsupporting

confidence: 92%

Comments on “Optimal Use of Mixed Catalysts for Two Successive Chemical Reactions”

Liu

2014

J Optim Theory Appl

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The paper "Optimal use of mixed catalysts for two successive chemical reactions" by Jackson was first presenting an analytical solution for the plug flow reactor catalyst blend problem. However, the exact optimal value of the problem was not given, which has caused confusion and inaccuracies in the subsequent literatures. As a supplement and correction, this study gives the optimal solutions and optimal objective values analytically for the cases when the reactor length equals 1 and 12. These results are also verified numerically using the time-scaling method.

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“…1. This is consistent with the result obtained by England [15]. The optimal objective function value is J * (12) ≈ 0.477712020050041, rather than the value 0.476946 obtained in [7].…”

Section: Global Optimumsupporting

confidence: 92%

Comments on “Optimal Use of Mixed Catalysts for Two Successive Chemical Reactions”

Liu

2014

J Optim Theory Appl

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“…The second example is the catalyst mixing problem [4,7]; this problem has index 1 or 3, depending on the initial data. If we start at t 0 = 1/2 and use α = (0.9, 0.07, −0.002, −.24, 0.227, −0.227, 0.773) T andx 0 = α as the initial approximation, we obtain an index one problem.…”

Section: Examplementioning

confidence: 99%

Computation of consistent initial values for properly stated index 3 DAEs

Lamour

Mazzia

2009

Bit Numer Math

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The computation of consistent initial values is one of the basic problems when solving initial or boundary value problems of DAEs. For a given DAE it is, in fact, not obvious how to formulate the initial conditions that lead to a uniquely solvable IVP. The existing algorithms for the solution of this problem are either designed for fixed index, or they require a special structure of the DAE or they need more than the given data (e.g. additional differentiations). In this paper, combining the results concerning the solvability of DAEs with properly stated leading terms with an appropriate method for the approximation of the derivative, we propose an algorithm that provides the necessary data to formulate the initial conditions and which works at least for nonlinear DAEs up to index 3. Illustrative examples are given.

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“…Most of this derivation has been presented elsewhere ( [6,7]), but the outline is given here for completeness.…”

Section: Calculus Of Variationsmentioning

confidence: 99%

“…In Section 2 we give an outline of the methodology to transform an optimal control problem into a system of DAEs (for a detailed presentation see [6,7]). In Section 3, the tractability index is introduced and applied to the DAEs obtained before.…”

Section: Introductionmentioning

confidence: 99%

The properties of differential-algebraic equations representing optimal control problems

England

Gómez

Lamour

2009

Applied Numerical Mathematics

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A procedure is described for transforming a general optimal control problem to a system of Differential-Algebraic Equations (DAEs). The Kuhn-Tucker conditions consist of differential equations, complementarity conditions and corresponding inequalities. The latter are converted to equalities by adding a new variable combining the slack variable and the corresponding Lagrange multiplier.We investigate the properties of the resulting DAEs. The index of a system of DAEs determines the well-conditioning of the problem. The concept of the tractability index is used to investigate the index in a systematic way, and during this process, it indicates which components of the system of equations must be differentiated to reduce the index. For an index-3 problem, the index is reduced without increasing the number of equations, and a numerical procedure is used to determine the index.In the examples used here, the DAEs can be solved analytically. The examples are tested by the numerical determination of the index, and the results confirm the previously known properties of these examples.The reformulation proposed here, as well as the index determination, might be used in the future, to develop a methodology to solve optimal control problems.

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Expressing optimal control problems as differential algebraic equations

Cited by 10 publications

References 17 publications

Comments on “Optimal Use of Mixed Catalysts for Two Successive Chemical Reactions”

Comments on “Optimal Use of Mixed Catalysts for Two Successive Chemical Reactions”

Computation of consistent initial values for properly stated index 3 DAEs

The properties of differential-algebraic equations representing optimal control problems

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