Iterative dynamic programming

The use of time stages of varying lengths in iterative dynamic programming (Luus, 2000) may indeed provide a computationally acceptable solution. Actually, such an approach may prove to be feasible particularly for model discrimination purposes. In model discrimination we seek the optimal inputs, u(t), that will maximize the overall divergence among r rival models given by Equation 12.23. 

Luus, R Iterative Dynamic Programming, Chapman Hall, CRC, London, UK, 2000. 

Luus, R. Optimization of Fed-batch Fermentors by Iterative Dynamic Programming. Biotechnol Bioeng 41 599-602 (1992). 

The third requirement is a scoring scheme to identify optimal dynamic programming alignments used in the above iterative multiple alignment... 

B. Bojkov, R. Luus, 1992, Use of Random Admissible Values for Control in Iterative Dynamic Programming, Ind. Eng. Chem. Res., vol. 31, p.l308 B. Bojkov, R. Luus, 1993, Evaluation of the Parameters Used in Iterative Dynamic Programming, Can. J. Chem. Eng., vol. 71. p. 451... 

I. Development of the Mathematical Model and Algorithm, Rev. Chim., vol. 37, p. 697 A. Woinaroschy, 2007, Time-Optimal Control of Distillation Columns by Iterative Dynamic Programming, Chem. Eng. Trans., vol. 11, p. 253... 

As methods based on dynamic programming cannot account for pairwise-interaction potentials the so-called frozen approximation approach [189] has been proposed. This method performs several iterations of profile environments. In the first iteration, the chemical environment is defined via the contact partners of the template. In subsequent rounds the aligned residues from the previous iteration replace the residues of the template. The idea is that target and template structure are similar enough such that the iterative process converges towards the optimal assignment. 

Taylor W. R., Protein structure comparison using iterated double dynamic programming. Protein Sci, 1999. 8(3) p. 654-65. 

A numerical technique that has become very popular in the control field for optimization of dynamic problems is the IDP (iterative dynamic programming) technique. For application of the IDP procedure, the dynamic trajectory is divided first into NS piecewise constant discrete trajectories. Then, the Bellman s theory of dynamic programming [175] is used to divide the optimization problem into NS smaller optimization problems, which are solved iteratively backwards from the desired target values to the initial conditions. Both SQP and RSA can be used for optimization of the NS smaller optimization problems. IDP has been used for computation of optimum solutions in different problems for different purposes. For example, it was used to minimize energy consumption and byproduct formation in poly(ethylene terephthalate) processes [ 176]. It was also used to develop optimum feed rate policies for the simultaneous control of copolymer composition and MWDs in emulsion reactions [36, 37]. 

Convergence of the multiloop optimization method that is based on iterative apphcation of dynamic programming has a strict physical explanation. The stationary flow distribution... 

Luus, R. (2000). Iterative dynamic programming, CRC Press, Boca Raton. 

One important class of nonlinear programming techniques is called quadratic programming (QP), where the objective function is quadratic and the constraints are hnear. While the solution is iterative, it can be obtained qmckly as in linear programming. This is the basis for the newest type of constrained multivariable control algorithms called model predic tive control. The dominant method used in the refining industiy utilizes the solution of a QP and is called dynamic matrix con-... 

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