The convergence of self-tuning feedback control for linear stochastic systems
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We consider adaptive control of linear stochastic systems, i.e., the control of unknown linear systems subject to stochastic disturbances whose spectra are also unknown. We examine the basic convergence issues, including the convergence of adaptive controllers and parameter estimates as well as the convergence of input and output. Despite over a decade of effort, previous works in this area are very much fragmented. Relatively complete convergence results are available only for adaptive minimum variance control of unit delay systems.
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Duncan, T. E., & Pasik-Duncan, B.
Stochastic Theory and Adaptive Control