Optimal Adaptive Control Methods for Structurally Varying Systems

78 Pages Posted: 13 Dec 2006 Last revised: 28 Jul 2022

See all articles by Alexander H. Sarris

Alexander H. Sarris

National and Kapodistrian University of Athens - Faculty of Economics; National Bureau of Economic Research (NBER)

Michael Athans

Massachusetts Institute of Technology (MIT); National Bureau of Economic Research (NBER)

Date Written: December 1973

Abstract

The problem of simultaneously identifying and controlling a time-varying, perfectly-observed linear system is posed. The parameters are assumed to obey a Markov structure and are estimated with a Kalman filter. The problem can be solved conceptually by dynamic programming, but even with a quadratic loss function the analytical computations cannot be carried out for more than one step because of the dual nature of the optimal control law. All approximations to the solution that have been proposed in the literature, and two approximations that are presented here for the first time are analyzed. They are classified into dual and non-dual methods. Analytical comparison is untractable; hence Monte Carlo simulations are used. A set of experiments is presented in which five non-dual methods are compared. The numerical results indicate a possible ordering among these approximations.

Suggested Citation

Sarris, Alexander and Athans, Michael, Optimal Adaptive Control Methods for Structurally Varying Systems (December 1973). NBER Working Paper No. w0024, Available at SSRN: https://ssrn.com/abstract=259339

Alexander Sarris (Contact Author)

National and Kapodistrian University of Athens - Faculty of Economics ( email )

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Michael Athans

Massachusetts Institute of Technology (MIT) ( email )

Cambridge, MA 02139
United States
(617) 253-6173 (Phone)
(617) 258-8553 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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