Analysis of approximations to dual control

B. Lindoff, J. Holst and B. Wittenmark

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

The dual control problem for time-varying or non-linear stochastic systems is inherently analytically and computationally untractable due to the demand of alternating minimizations and mean value computations.
Hence, it has to be approached using approximations, leading to suboptimal dual control. The core of the successful approximative controller is its ability to be able to consider future changes in the development of the parameters.
This paper presents an analysis of the dual control concept, and a comparison between a number of suboptimal controllers. The analytical comparisons are based on a reformulation of the dual control problem. This reformulation
makes it possible to interpret and understand the nature of different approximations to dual control, in particular the Adaptive Predictive Controller (APC) and the Active Suboptimal Dual Controller (ASOD). Furthermore it makes the origin of the computational problems encountered more clear, and suggests new alternatives for approximation. The analysis is carried through on relatively simple examples and is illustrated with simulations. The performance of the controllers when applied to more complicated time-varying systems is illustrated with simulations as well.
Key words:
dual control, adaptive control, stochastic control, time-varying systems, stochastic systems