Abstract
An adaptive control problem is described and its solution for a completely observed, continuous time, linear stochastic system with an ergodic quadratic cost criterion is given. The linear transformations A of the state and B of the control are assumed to be unknown. Assuming only that A is stable, and that the pair, A and the linear transformation of the noise, is controllable, and using a diminishing excitation control, it is shown that a family of least squares estimates is strongly consistent. An adaptive control using switches that is self optimizing for an ergodic, quadratic cost criterion is presented. >
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