Dynamic optimization of chemical and biochemical processes using restricted second order information

Abstract The extension of a recently developed method for the dynamic optimization of chemical and biochemical processes is presented. This method is based on the control vector parameterization approach and makes use of the calculation of first- and second-order sensitivities to obtain exact gradient and projected Hessian information. In order to achieve high discretization levels of the control variables with a moderate computational cost, a mesh refining technique is also presented here. The robustness and efficiency of this strategy is illustrated with the solution of several challenging case studies.

[1]  Vassilios Vassiliadis,et al.  Computational solution of dynamic optimization problems with general differential-algebraic constraints , 1993 .

[2]  Julio R. Banga,et al.  Stochastic optimization for optimal and model-predictive control , 1998 .

[3]  R. Luus Application of dynamic programming to high-dimensional non-linear optimal control problems , 1990 .

[4]  Julio R. Banga,et al.  Stochastic Dynamic Optimization of Batch and Semicontinuous Bioprocesses , 1997 .

[5]  Margaret H. Wright,et al.  Direct search methods: Once scorned, now respectable , 1996 .

[6]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[7]  P. Pardalos,et al.  State of the art in global optimization: computational methods and applications , 1996 .

[8]  S. A. Dadebo,et al.  Dynamic optimization of constrained chemical engineering problems using dynamic programming , 1995 .

[9]  R. Luus Optimal control by dynamic programming using systematic reduction in grid size , 1990 .

[10]  S. Shioya,et al.  Optimization and control in fed-batch bioreactors , 1992 .

[11]  S. Nash Newton-Type Minimization via the Lanczos Method , 1984 .

[12]  J Hong,et al.  Optimal substrate feeding policy for a fed batch fermentation with substrate and product inhibition kinetics , 1986, Biotechnology and bioengineering.

[13]  Mark A. Kramer,et al.  Sensitivity analysis of systems of differential and algebraic equations , 1985 .

[14]  V. Vassiliadis,et al.  Second-order sensitivities of general dynamic systems with application to optimal control problems , 1999 .

[15]  M. Guay,et al.  Optimization and sensitivity analysis for multiresponse parameter estimation in systems of ordinary , 1995 .

[16]  Julio R. Banga,et al.  Global Optimization of Chemical Processes using Stochastic Algorithms , 1996 .

[17]  R. Luus On the application of iterative dynamic programming to singular optimal control problems , 1992 .

[18]  Rein Luus,et al.  Evaluation of gradients for piecewise constant optimal control , 1991 .

[19]  W. Fred Ramirez,et al.  Optimal fed‐batch control of induced foreign protein production by recombinant bacteria , 1994 .

[20]  Jayant M. Modak,et al.  AN IMPROVED COMPUTATIONAL ALGORITHM FOR SINGULAR CONTROL PROBLEMS IN CHEMICAL REACTION ENGINEERING , 1989 .

[21]  G Stephanopoulos,et al.  A note on the optimality criteria for maximum biomass production in a fed‐batch fermentor , 1984, Biotechnology and bioengineering.

[22]  Barnett F. Dodge,et al.  Deviation from the inverse‐thickness relation in gas‐metal permeation , 1963 .

[23]  J. E. Cuthrell,et al.  Simultaneous optimization and solution methods for batch reactor control profiles , 1989 .

[24]  W. Ramirez,et al.  Optimal production of secreted protein in fed‐batch reactors , 1988 .

[25]  W. Ramirez,et al.  Obtaining smoother singular arc policies using a modified iterative dynamic programming algorithm , 1997 .

[26]  Ji-Pyng Chiou,et al.  Optimal control and optimal time location problems of differential-algebraic systems by differential evolution , 1997 .

[27]  H. Lim,et al.  Computational algorithms for optimal feed rates for a class of fed‐batch fermentation: Numerical results for penicillin and cell mass production , 1986, Biotechnology and bioengineering.

[28]  Julio R. Banga,et al.  A hybrid method for the optimal control of chemical processes , 1998 .

[29]  G Stephanopoulos,et al.  Optimization of fed‐batch penicillin fermentation: A case of singular optimal control with state constraints , 1989, Biotechnology and bioengineering.