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On constrained stochastic optimal parameter selection problems

Published online by Cambridge University Press:  17 April 2009

C.J. Goh  and
K.L. Teo
C.J. Goh
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia
K.L. Teo
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia
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This paper considers a special class of stochastic optimal parameter selection problem subject to probability constraints on the state. The system dynamics are governed by a linear Ito stochastic differential equation with controllable parameters appearing nonlinearly in the dynamics. The problem seeks to optimise a cost functional which is quadratic in the state with weighting matrices being time invariant but depending nonlinearly on the parameters. Although the inclusion of the probability state constraints renders the problem insolvable by the conventional LQG theory, we show that the problem can in fact be transformed into an equivalent deterministic optimal parameter selection problem solvable by an existing software MISER. Numerical examples are presented to demonstrate the feasibility and efficiency of the proposed approach.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 393 - 405
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Ahmed, N.U., Elements of Finite–dimensional Systems and Control Theory (Longman Scientific & Technical, Harlow, 1988).Google Scholar
[2]Ahmed, N.U. and Georgenas, N.D., ‘On optimal parameter selection’, IEEE Trans. Automat. Control AC–18 (1973), 313–314.Google Scholar
[3]Anderson, B.D.D. and Moore, J.B., Linear Optimal Control (Prentice-Hall, Englewood Cliffs, 1971).CrossRefGoogle Scholar
[4]Cesari, L., Optimization Theory and Applications (Springer-Verlag, Berlin, Heidelberg, New York, 1983).Google Scholar
[5]Craven, B.D., Mathematical Programming and Control Theory (Chapman and Hall, London, 1978).Google Scholar
[6]Dolezal, J., ‘On the solution of optimal control problems involving parameters and general boundary conditions’, Kybernetika 17 (1981), 71–81.Google Scholar
[7]Goh, C.J. and Teo, K.L., MISER: An Optimal Control Software (Applied Rsearch Corporation, National University of Singapore, 1987).Google Scholar
[8]Goh, C.J. and Teo, K.L., ‘Control parametrization: A unified approach to optimal control problems with general constraints’, Automatica 24 (1988), 3–18.CrossRefGoogle Scholar
[9]Goh, C.J. and Teo, K.L., ‘MISER: A Fortran program for solving optimal control problems’, Adv. Engrg. Software 10 (1988), 90–98.CrossRefGoogle Scholar
[10]Jennings, L.S. and Teo, K.L., ‘A computational algorithm for functional inequality constrained optimization problems’, Automatica (1990) (to appear).CrossRefGoogle Scholar
[11]Kwakernaak, H. and Sivan, R., Linear Optimal Control System (Wiley-Interscience, New York, 1972).Google Scholar
[12] ‘Linear–Quadratic–Gaussian Problems’, Special Issue, IEEE Trans. Automat. Control AC–16 (1971).Google Scholar
[13]Reid, D.W. and Teo, K.L., ‘Optimal parameter selection of parabolic systems’, Math. Oper. Res. 5 (1980), 467–474.CrossRefGoogle Scholar
[14]Russell, D.L., Mathematics of Finite–Dimensional Control Systems (Marcel Dekker, New York, 1979).Google Scholar
[15]Schittkowski, K., ‘NLPQL: A Fortran subroutine for solving constrained nonlinear programming problems’, Oper. Res. Ann. 5 (1985), 485–500.CrossRefGoogle Scholar
[16]Teo, K.L. and Ahmed, N.U., ‘Optimal feedback control for a class of stochastic systems’, Internat. J. Systems Sci. 5 (1974), 357–365.Google Scholar
[17]Teo, K.L. and Goh, C.J., ‘A simple computational procedure for optimization problems with functional inequality constraints’, IEEE Trans. Automat. Control. AC-32 (1987), 940–941.CrossRefGoogle Scholar
[18]Teo, K.L. and Goh, C.J., ‘A computational method for combined optimal parameter selection and optimal control problems with general constraints’, J. Austral. Math. Soc. Ser. B 30 (1989), 350–364.Google Scholar
[19]Van Mellaert, L.J. and Dorato, P., ‘Numerical solution of an optimal control problem with a probability criterion’, IEEE Trans. Automat. Control AC-17 (1972), 543–546.Google Scholar