Simultaneous Iterative Solution Technique for Time-Optimal Control Using Dynamic Programming

Dadebo, S. A.; McAuley, Kimberley B.

doi:10.1021/ie00045a016

Cited by 14 publications

(9 citation statements)

References 15 publications

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“…In this case, by a simple variable transformation, the problem was converted to one of combined optimal parameter selection and optimal control. The independent time variable was normalized and the final time became a decision variable only at the final stage of the IDP algorithm (Dadebo and McAuley, 1995b). Optimization results were similar to the fixed-end time studies, although the IDP algorithm appeared to have more difficulty in reaching the optimum for the variable end time approach.…”

Section: Variable End Time Approachmentioning

confidence: 75%

Dynamic modeling and optimal fed-batch feeding strategies for a two-phase partitioning bioreactor

Cruickshank

McLellan

2000

Biotechnol. Bioeng.

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A dynamic model for the degradation of phenol in a two‐phase partitioning bioreactor has been developed based on mechanistic balances around the bioreactor. The key process characteristics including substrate transfer between the organic and aqueous phases, substrate inhibition, oxygen limitation, and cell entrainment were incorporated into the model. The model predictions were validated against existing experimental data obtained for a 2‐L bioreactor, and good correlation was observed for the time frames of the simulations, as well as for trends in cell and substrate concentrations. Optimal fed‐batch, phenol feeding strategies were then developed based on two approaches: (1) maximization of phenol consumption in a fixed time interval and (2) consumption of a fixed amount of phenol in minimal time. The optimal feeding policies, determined using the Iterative Dynamic Programming algorithm, provided substantial improvements in the amount of phenol consumed when compared to a typical experimental heuristic approach. For example, 45.73 g of phenol was predicted to be consumed in 50 h (not including lag phase) using the optimal feeding profile compared to 10.26 g of phenol consumed in the simulated experimental approach. Oxygen limitation was predicted to be a recurring operational challenge in the partitioning bioreactor, and had a strong impact on the optimization results. © 2000 John Wiley & Sons, Inc. Biotechnol Bioeng 67: 224–233, 2000.

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Section: Variable End Time Approachmentioning

confidence: 75%

Dynamic modeling and optimal fed-batch feeding strategies for a two-phase partitioning bioreactor

Cruickshank

McLellan

2000

Biotechnol. Bioeng.

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“…The importance of satisfying the state constraint throughout the time interval is evident from the results given in Table . It is unlikely that the piecewise constant control policy for the constrained arc used by Dadebo and McAuley can give better results than the ones obtained by the continuous control policy used in this work. For all the cases, the results are very close to the ones obtained by Maurer and Weigand .…”

Section: Numerical Examplesmentioning

confidence: 70%

“…The second example is a time-optimal control problem introduced by Bell and Katusiime and solved, among others, by Maurer and Wiegand, Dadebo and McAuley, and Maurer and Vossen . The system equations are given by The states x 1 and x 2 represent the concentrations of unbound warfarin and phenylbutazone, respectively.…”

Section: Numerical Examplesmentioning

confidence: 99%

Two-Step Method for Dynamic Optimization of Inequality State Constrained Systems Using Iterative Dynamic Programming

Sundaralingam¹

2015

Ind. Eng. Chem. Res.

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A two step method for the solution of dynamic optimization problems with state inequality constraints using Iterative dynamic programming (IDP) is presented. In the first step, a preliminary control policy along with approximate values for the start and end points of the state constrained arc is obtained. The final solution is obtained in the second step by using the preliminary control policy as an input along with an analytical expression for the control during the constrained portion of the state trajectory. The use of flexible stage lengths in IDP helps in locating the start and end points of the state constrained arc accurately. For the examples considered, the method results in better values of the performance index than previously reported in the literature. It also results in a significant reduction in computation time as compared to the existing method, for the solution of problems with a single active state constraint and a single control, using IDP.

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“…By contracting the control region for each time stage after each cycle of dynamic programming computation, the IDP finally obtains an optimal control profile. Due to the advantages of being easily implemented on a personal computer and having greater possibility to obtain a globally optimal solution than a nonlinear programming method, the original IDP method and some of the improved versions (Lin and Hwang, 1996b;Hwang and Lin, 1998) have been successfully applied to solve various optimal control problems of nonlinear processes Luus, 1994a,b, 1996;Dadebo and McAuley, 1995b;Keil, 1993a, 1994;Hartig et al, 1996;Keil et al, 1996;Luus, 1990cLuus, , 1991Luus, , 1993aLuus and Bojkov, 1994;Luus et al, 1992;Luus and Galli, 1991;Mekarapiruk and Luus, 1997), including time-delay systems (Dadebo and Luus, 1992;Dadebo and McAuley, 1995a;Lin and Hwang, 1996a) and systems with a large number of state and control variables (Bojkov and Luus, 1992a,b, 1993Hartig and Keil, 1993b;Luus, 1990bLuus, , 1993dLuus and Smith, 1991).…”

Section: Introductionmentioning

confidence: 99%

Enhancement of the Global Convergence of Using Iterative Dynamic Programming To Solve Optimal Control Problems

Lin

Hwang

1998

Ind. Eng. Chem. Res.

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Although iterative dynamic programming (IDP) has been well recognized as a powerful method for finding the true optimal solution to a nonlinear dynamic optimization problem, the global optimality of the IDP solution is still not guaranteed completely. This paper explores enhancing the global convergence of using iterative dynamic programming to solve optimal control problems. Two approaches are employed to enhance the possibility of obtaining the true optimum while reducing the required computation efforts. One approach employs Sobol's quasi-random sequence generator to generate allowable controls and the other utilizes multipass computation. Numerical examples show that the use of multipass IDP computation with small numbers of state grid points and allowable control values can indeed enhance the possibility of obtaining a true optimum. This is particularly true when the allowable control values are generated by using Sobol's quasi-random sequence generator.

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Simultaneous Iterative Solution Technique for Time-Optimal Control Using Dynamic Programming

Cited by 14 publications

References 15 publications

Dynamic modeling and optimal fed-batch feeding strategies for a two-phase partitioning bioreactor

Dynamic modeling and optimal fed-batch feeding strategies for a two-phase partitioning bioreactor

Two-Step Method for Dynamic Optimization of Inequality State Constrained Systems Using Iterative Dynamic Programming

Enhancement of the Global Convergence of Using Iterative Dynamic Programming To Solve Optimal Control Problems

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