Risk - Sensitive Dual Control

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 risksensitive 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.