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Risk‐sensitive dual control
Author(s) -
Dey Subhrakanti,
Moore John B.
Publication year - 1997
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199712)7:12<1047::aid-rnc249>3.0.co;2-#
Subject(s) - dual (grammatical number) , control (management) , computer science , control theory (sociology) , artificial intelligence , philosophy , linguistics
In this paper, we develop new results concerning the risk‐sensitive dual control problem for output feedback nonlinear systems, with unknown time‐varying parameters. These results are not merely immediate specializations of known risk‐sensitive control theory for nonlinear systems, but rather, are new formulations which are of interest in their own right. A dynamic programming equation solution is given to an optimal risk‐sensitive dual control problem penalizing outputs, rather than the states, for a reasonably general class of nonlinear signal models. This equation, in contrast to earlier formulations in the literature, clearly shows the dual aspects of the risk‐sensitive controller regarding control and estimation. The computational task to solve this equation, as has been seen for the risk‐neutral dual control problem, suffers from the so‐called ‘curse of dimensionality’. This motivates our study of the risk‐sensitive version for a suboptimal risk‐sensitive dual controller. Explicit controllers are derived for a minimum phase single‐input, single‐output auto‐regressive model with exogenous input and unknown time‐varying parameters. Also, simulation studies are carried out for an integrator with a time‐varying gain. They show that the risk‐sensitive suboptimal dual controller is more robust to uncertain noise environments compared with its risk‐neutral counterpart. © 1997 by John Wiley & Sons, Ltd.