# Estimating Real Process Derivatives in on-Line Optimization - A Review

### M. Mansour

#### Abstract

The solution of the Integrated System Optimization and Parameter Estimation (ISOPE) problem necessitates the calculus of real process output derivatives with respect to the inputs. This information is needed in order to satisfy first and second order optimality conditions. Several methods exist and have been developed for calculating these derivatives. In this paper a review of most of the existing methods is presented, in which the Finite Difference Approximation, Dual Control Optimization, Broydonâ€™s method, Dynamic Model Identification, with both linear and nonlinear models, together with a neural networks scheme are presented and applied, under simulation, to a cascade Continuous Stirred Tank Reactor (CSTR) system. The results are then discussed and compared to identify the advantages and disadvantages of using each method.

#### References

- Brdys, M. A. and Tatjewski, P., 1994. An algorithm for steady-state optimizing dual control of uncertain plants, paper presented at the 1st IFAC Workshop on new trends in design of control systems, September 7 - 10, Smolenice, Slovak Republic, pp 249-254.
- Ellis, J. E., Kambhampati, C., Sheng, G. and Roberts, P.D., 1988. Approaches to the optimizing control problem, Int. J. of Systems Science, Vol. 19, No. 10, pp 1969-1985.
- Fletcher, R., 1980. Practical Methods of Optimization, Vol.1, A. Wiley-Interscience Publication.
- Garcia, C. E. and Morari, M., 1981. Optimal operation of integrated processing Systems, AICHE Journal, Vol. 27, No. 6, pp 960-968.
- Mansour, M. and Ellis, J. E., 2003. Comparison of methods for estimating real process derivatives in online optimisation, Applied Mathematical Modeling, Vol. 27, pp 275-291.
- Mansour, M. and Ellis, J. E., 2008. Methodology of online optimization applied to a chemical process, Applied Mathematical Modeling, Vol. 32, pp 170-184.
- Roberts, P. D., 1979. An algorithm for steady-state system optimization and parameter estimation, Int. J. of Systems Science, Vol. 10, pp 719-734.
- Roberts, P. D, and Williams. T. W. C., 1981. On an algorithm for combined system optimisation and parameter estimation, Automatica, Vol. 17, pp 199- 209.
- Zhang, H. and Roberts, P.D., 1990. On-line steady-state optimisation of nonlinear constrained processes with slow dynamics, Trans Ins MC, Vol. 12, No 5, pp 251- 261.

#### Paper Citation

#### in Harvard Style

Mansour M. (2012). **Estimating Real Process Derivatives in on-Line Optimization - A Review** . In *Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-8565-20-4, pages 120-124. DOI: 10.5220/0004059101200124

#### in Bibtex Style

@conference{simultech12,

author={M. Mansour},

title={Estimating Real Process Derivatives in on-Line Optimization - A Review},

booktitle={Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2012},

pages={120-124},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004059101200124},

isbn={978-989-8565-20-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - Estimating Real Process Derivatives in on-Line Optimization - A Review

SN - 978-989-8565-20-4

AU - Mansour M.

PY - 2012

SP - 120

EP - 124

DO - 10.5220/0004059101200124