Adaptive continuous-time linear quadratic Gaussian control
- 1 September 1999
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 44 (9) , 1653-1662
- https://doi.org/10.1109/9.788532
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/sub 1//sup 1/2/) is observable, where Q/sub 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.Keywords
This publication has 11 references indexed in Scilit:
- Stochastic linear quadratic adaptive control for continuous-time first-order systemsSystems & Control Letters, 1997
- Stochastic Adaptive Control for Continuous-Time Linear Systems with Quadratic CostApplied Mathematics & Optimization, 1996
- Self-convergence of weighted least-squares with applications to stochastic adaptive controlIEEE Transactions on Automatic Control, 1996
- Adaptive pole placement without excitation probing signalsIEEE Transactions on Automatic Control, 1994
- Continuous time stochastic adaptive control: non-explosion, ϵ-consistency and stabilitySystems & Control Letters, 1992
- Identification and Stochastic Adaptive ControlPublished by Springer Nature ,1991
- Adaptive control of continuous-time linear stochastic systemsMathematics of Control, Signals, and Systems, 1990
- Will the self-tuning approach work for general cost criteria?Systems & Control Letters, 1985
- Optimal Adaptive Control of Linear-Quadratic-Gaussian SystemsSIAM Journal on Control and Optimization, 1983
- Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic SystemsThe Annals of Statistics, 1982