ANNSA: a hybrid artificial neural network/simulated annealing algorithm for optimal control problems

This paper introduces a numerical technique for solving nonlinear optimal control problems. The universal function approximation capability of a three-layer feedforward neural network has been combined with a simulated annealing algorithm to develop a simple yet efficient hybrid optimisation algorithm to determine optimal control profiles. The applicability of the technique is illustrated by solving various optimal control problems including multivariable nonlinear problems and free final time problems. Results obtained for the different case studies considered agree well with those reported in the literature.

[1]  R. Luus,et al.  Optimal control by iterative dynamic programming with deterministic and random candidates for control , 2000 .

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

[3]  Bong Hyun Chung,et al.  Adaptive optimization of fed-batch culture of yeast by using genetic algorithms , 2002 .

[4]  L. Bittner L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishechenko, The Mathematical Theory of Optimal Processes. VIII + 360 S. New York/London 1962. John Wiley & Sons. Preis 90/– , 1963 .

[5]  Pavan K. Shukla,et al.  Optimisation of biochemical reactors : an analysis of different approximations of fed-batch operation , 1998 .

[6]  Costas J. Spanos,et al.  Advanced process control , 1989 .

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

[8]  V. K. Jayaraman,et al.  Dynamic Optimization of Fed‐Batch Bioreactors Using the Ant Algorithm , 2001, Biotechnology progress.

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

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

[11]  D. R. Baughman,et al.  Neural Networks in Bioprocessing and Chemical Engineering , 1992 .

[12]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[13]  Rein Luus,et al.  Iterative dynamic programming , 2019, Iterative Dynamic Programming.

[14]  Rimvydas Simutis,et al.  A comparative study on random search algorithms for biotechnical process optimization , 1997 .

[15]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

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

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[18]  R. Luus,et al.  Evaluation and improvement of control vector iteration procedures for optimal control , 1972 .

[19]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[20]  Pu Li,et al.  Simulated annealing for the optimization of batch distillation processes , 2000 .

[21]  Serge Domenech,et al.  Separation sequence synthesis how to use simulated annealing procedure , 1993 .

[22]  H. J. Oberle,et al.  Numerical Computation of Optimal Feed Rates for a Fed-Batch Fermentation Model , 1999 .

[23]  Domingos Barbosa,et al.  Optimization of reactive distillation processes with simulated annealing , 2000 .

[24]  Peter T. Cummings,et al.  Process optimization via simulated annealing: Application to network design , 1989 .

[25]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[26]  J. Banga,et al.  Dynamic Optimization of Batch Reactors Using Adaptive Stochastic Algorithms , 1997 .

[27]  H. Lim,et al.  Optimization of biphasic growth of Saccharomyces carlsbergensis in fed‐batch culture , 1989, Biotechnology and bioengineering.

[28]  Johannes Andries Roubos,et al.  An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance , 1999 .

[29]  William L. Goffe,et al.  SIMANN: FORTRAN module to perform Global Optimization of Statistical Functions with Simulated Annealing , 1992 .