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. 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 extensive computational burden for solving this equation motivates our study of risk-sensitive versions for one-step horizon cost indices and suboptimal risk-sensitive dual control. The idea of a more generalized optimal risk-sensitive dual controller is briefly introduced