Abstract
An adaptive control problem is formulated and solved for a completely observed, continuous-time, linear stochastic system with an ergodic quadratic cost criterion. The linear transformationsA of the state,B of the control, andC of the noise are assumed to be unknown. Assuming only thatA is stable and that the pair (A, C) is controllable and using a diminishing excitation control that is asymptotically negligible for an ergodic, quadratic cost criterion it is shown that a family of least-squares estimates is strongly consistent. Furthermore, an adaptive control is given using switchings that is self-optimizing for an ergodic, quadratic cost criterion.
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