Advertisement

S.O.C.R.A.t.E.S. Simultaneous Optimal Control by Recursive and Adaptive Estimation System: Problem Formulation and Computational Results

  • Giacomo Patrizi
Conference paper

Abstract

The algorithm to be presented determines at the same time an accurate estimation and the optimal control policy for a dynamic process, by solving one optimization problem. For general dynamic nonlinear systems, the traditional two stage approach may entail severe suboptimization and the application of inefficient controls. This is avoided in the approach suggested. All the statistical conditions that the estimates must fulfill are formulated as inequality constraints, as well as the general specification conditions of the dynamic system. Thus a single optimization problem is solved in the identification parameters and in the control variables, which is highly nonlinear and non convex in all its parts. This will determine a sufficiently precise optimal control, as desired, if one exists.

Keywords

Period Forecast Mib30 Index Optimal Control Policy Single Optimization Problem Optimal Dynamic Portfolio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kumar, P., R. P. Varaya, (1986) Stochastic Systems, Estimation, Identification and Adaptive Control, Prentice Hall, Englwood Cliffs, N.J..Google Scholar
  2. 2.
    Amemiya, T., (1985), Advanced Econometrics, Blackwell, Oxford.Google Scholar
  3. 3.
    Lazzarini, K., G. Patrizi, (1995), Identificazione ed Ottimizzazione Simultanea di Sistemi Dinamici, Sugitalia’95: Atti del Convegno, SAS User Group Italia, XI Convegno Utenti Italiani di SAS System, Firenze, 25–27 ottobre 1995, SAS User Group Italia, Milano, pp. 311–324.Google Scholar
  4. 4.
    Patrizi, G., (1999), Se.N.E.C.A. Sequential Nonlinear Estimation by a Constrained Algorithm, submitted for pubblication.Google Scholar
  5. 5.
    Patrizi, G. (1999), S.O.C.R.A.t.E.S. Simultaneous Optimal Control by Recursive and AdapTive Estimation System, SEUGI 17 Proceedings, SAS Institute Inc. Cary, NC.Google Scholar
  6. 6.
    Lobo, M., S., S. Boyd, Policies for Simultaneous Estimation and Optimization, Stanford University Report, http://www.stanford.edu/boyd/groupindex.html
  7. 7.
    Kalman, R. E., P. L. Falb, M. A. Arbib, (1969), Topics in Mathematical System Theory, McGraw-Hill, New York.Google Scholar
  8. 8.
    Söderström, T., P. Stoica, (1989), System Identification , Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  9. 9.
    Cannon, M. D., C. D. Cullum Jr., E. Polak, (1970), Theory of Optimal Control and Mathematical Programming, McGraw-Hill, New York.Google Scholar
  10. 10.
    Bunke, H., O. Bunke, (1986), Statistical Inference in Linear Models, Wiley, New York.Google Scholar
  11. 11.
    Breusch, T. S., A. R. Pagan, (1979), A Simple Test for Heteroschedasticity and Random coefficient Variation, Econometrica, vol. 47, pp. 1287–1294.CrossRefGoogle Scholar
  12. 12.
    Jennrich, R., I., (1969) Asymptotic Properties of Non-Linear Least Squares Estimators, The Annals of Mathematical Statisitcs, vol. 40, pp. 633–643.CrossRefGoogle Scholar
  13. 13.
    Patrizi, G., (1998), A New Algorithm for General Nonlinear Constrained Optimization: Convergence and Experimental Results, submitted for pubblication.Google Scholar
  14. 14.
    Patrizi, G., (1999), S.O.C.R.A.t.E.S. Simultaneous Optimal Control by Recursive and AdapTive Estimation System, Optimality Conditions and Convergence Results, in preparation.Google Scholar
  15. 15.
    Moran, P. A. P., (1953), The Statistical Analysis of the Canadian Lynx Cycle, I: Structure and Prediction, Australian Journal of Zoology, vol. 1, pp. 163–173.CrossRefGoogle Scholar
  16. 16.
    Cox, D. R., (1977), Discussion of papers by Campbell and Walker, Tong and Morris, J. Royal Statistical Soc., vol A140, pp. 453–4.Google Scholar
  17. 17.
    Ozaki, T., (1982), The Statistical Analysis of Perturbed Limit Cycles Processes using Nonlinear Time Series Models, J. of Time Series Analysis, vol. 3 pp. 2941.Google Scholar
  18. 18.
    Tong, H., (1990), Non-Linear Time Series: A Dynamical System Approach, Clarendon Press, Oxford.Google Scholar
  19. 19.
    SAS Institute, SAS Language, SAS Institute, Cary NC. 1996.Google Scholar
  20. 20.
    Bartolozzi, F., A. De Gaetano, E. Di Lena, S. Marino, L. Nieddu, G. Patrizi,(2000), Operational Research Techniques in Medical Treatment and Dio-gnosis: A Review, European Journal Of Operational Research, vol.120, n.3 (February).Google Scholar
  21. 21.
    Bardati, F., F. Bartolozzi, G. Patrizi, (1998) A Constrained Optimization Approach to the Control of a Phased Array Radiofrequency Hyperthermia System, Ricerca Operativa vol. 28 n. 85–86, pp.63–94.Google Scholar
  22. 22.
    Ugolini, C., (1999), Generalizzazione della Selezione di Portafoglio mediante Sistemi Dinamici, Tesi di Laurea, Facoltà di Scienze Statistiche, Università di Roma “La Sapienza” a.a.1997–1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Giacomo Patrizi
    • 1
  1. 1.Dipartimento di Statistica, Probabilità e Statistiche ApplicateUniversità di Roma “La Sapienza”Italy

Personalised recommendations