Adaptive Linear Quadratic Gaussian Control: The Cost-Biased Approach Revisited
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The research of this author was supported by MURST under the 60% project "Adaptive identification, prediction and control" and the 40% project "Model identification, system control and signal processing." This research was conducted while M. C. Campi was visiting the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign in the summer of 1995 2 Department of Electrical and Computer Engineering, and the Coordinated Science Laboratory, University of Illinois, 1308 West Main Street, Urbana, IL 61801 prkumar@decision.csl.uiuc.edu The research of this author was supported by U.S. Army Research Office contract DAAH-04-95-1-0090 and Joint Service Electronics Program contract N00014-96-1-0129 In adaptive control, a standard approach is to resort to the so-called certainty equivalence principle which consists of generating some standard parameter estimate and then using it in the control law as if it were the true parameter. As a consequence of this philosophy, the estimation problem is decoupled from the control problem and this substantially simplifies the corresponding adaptive control scheme. On the other hand, the complete absence of dual properties makes certainty equivalent controllers run into an identifiability problem which generally leads to a strictly suboptimal performance. In this paper, we introduce a cost-biased parameter estimator to overcome this difficulty. This estimator is applied to a linear quadratic Gaussian controller. The corresponding adaptive scheme is proven to be stable and optimal when the unknown system parameter lies in an infinite, yet compact, parameter set. adaptive control, linear quadratic Gaussian control, self-optimizing control, cost-biased approach, certainty equivalence.
