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Adaptive continuous-time linear quadratic Gaussian control
Duncan, Tyrone E. Guo, L. Pasik-Duncan, Bozenna
Duncan, Tyrone E.
Guo, L.
Pasik-Duncan, Bozenna
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Abstract
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, Q(1)(1/2)) 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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©1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Date
1999-09
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Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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Keywords
Adaptive control, Least-squares, Linear-quadratic-gaussian, Linear stochastic systems, Optimality
Citation
Duncan, TE; Guo, L; Pasik-Duncan, B. Adaptive continuous-time linear quadratic Gaussian control. IEEE TRANSACTIONS ON AUTOMATIC CONTROL. September 1999. 44(9) : 1653-1662