Adaptive control in the scalar linear-quadratic model in continuous time

Alain Le Breton

Statistics & Probability Letters, 1992, vol. 13, issue 3, 169-177

Abstract: We consider a one-dimensional controlled linear system in continuous time where the autoregressive parameter is unknown and the input must be chosen in order to minimize a quadratic cost. We define adaptive controls based on a least squares procedure for estimation. For these procedures it is shown that, whatever is the true value of the parameter, the estimate converges almost surely and the cost reaches its minimum.

Keywords: Adaptive; autoregressive; consistency; control; estimate; martingale; optimal (search for similar items in EconPapers)
Date: 1992
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