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Adaptive continuous-time linear quadratic Gaussian control

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3 Author(s)
Duncan, T.E. ; Dept. of Math., Kansas Univ., Lawrence, KS, USA ; Guo, L. ; Pasik-Duncan, B.

The adaptive linear quadratic Gaussian control problem, where the linear transformation of the state A and the linear transformation of the control B are unknown, is solved assuming only that (A, B) is controllable and (A, Q11/2) is observable, where Q 1 determines the quadratic form for the state in the integrand of the cost functional. A weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable and observable. A diminishing excitation is used with the adaptive control to ensure that the family of estimates is strongly consistent. A lagged certainty equivalence control using this family of estimates is shown to be self-optimizing for an ergodic, quadratic cost functional

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Automatic Control, IEEE Transactions on  (Volume:44 ,  Issue: 9 )