Abstract
The problem of optimal control is considered for the system ˙x=Ax + Bu; x(0)= c, where A is subject to random change, u is restricted to a closed, bounded region U, and a quadratic performance index is used. A general formulation of the problem is given and results are obtained for a particular, simple behaviour of A The optimal system shows adaptive behaviour of an elementary kind, and uses the whole of the available control effort at each instant. It is not known whether the last property would persist for less simple behaviour of A, or for systems disturbed by noise.

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