Estimation and control with bounded data uncertainties

The paper describes estimation and control strategies for models with bounded data uncertainties. We shall refer to them as BDU estimation and BDU control methods, for brevity. They are based on constrained game-type formulations that allow the designer to explicitly incorporate into the problem statement a priori information about bounds on the sizes of the uncertainties. In this way, the effect of uncertainties is not unnecessarily over-emphasized beyond what is implied by the a priori bounds; consequently, overly conservative designs, as well as overly sensitive designs, are avoided. A feature of these new formulations is that geometric insights and recursive techniques, which are widely known and appreciated for classical quadratic-cost designs, can also be pursued in this new framework. Also, algorithms for computing the optimal solutions with the same computational effort as standard least-squares solutions exist, thus making the new formulations attractive for practical use. Moreover, the framework is broad enough to encompass applications across several disciplines, not just estimation and control. Examples will be given of a quadratic control design, an H∞ control design, a total-least-square design, image restoration, image separation, and co-channel interference cancellation. A major theme in this paper is the emphasis on geometric and linear algebraic arguments, which lead to useful insights about the nature of the new formulations. Despite the interesting results that will be discussed, several issues remain open and indicate potential future developments; these will be briefly discussed.

Published in:
Linear Algebra and its Applications, 284, 1-3, 259-306

 Record created 2017-12-19, last modified 2018-03-17

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