Series Solutions to Static Team Control Problems

Abstract
The concept of infinite second guessing is known to play a role in the consideration of multi-person control problems. By considering the problem in its appropriate Hilbert space context we formalize this concept and show that it does in fact play a vital part in the structure of those solutions that are available. We give an explicit series solution to the constant coefficient quadratic cost team problem. This solution is valid for any distribution of noise, which is square integrable. The well-known linearity of optimal control in the Gaussian case is immediately apparent. An important special case is given further consideration and other applications are indicated. Finally a theorem characterising the limit behaviour of the series in terms of the information common to all players is presented.

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