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# Minimum Entropy H[infinity] Control

Author: D Mustafa; K Glover Berlin, Heidelberg : Springer Berlin Heidelberg, 1990. Lecture notes in control and information sciences, 146. eBook : Document : EnglishView all editions and formats This monograph is concerned with the design of feedback controllers for linear multivariable systems, which are robust to system uncertainty. System uncertainty can be realistically represented by including perturbations with bounded H?-norm, and this is the approach taken here. For a given H?-norm bound, there is a family of robustly stabilizing controllers, and the central question in this book is which of these controllers to choose. One choice to take is that which minimizes the enthropy of the resulting closed loop transfer function, and the derivation and properties of this solution occupies most of this monograph. Explicit formulae are obtained for the minimum enthropy solution, which is a precisely defined compromise between the Linear Quadratic Gaussian optimal solution and the H?-optimal solution. The book will be appropriate for graduate classes requiring only a first course in state-space methods, and some elementary knowledge of H? control and Linear Quadratic Gaussian control.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version: Document, Internet resource Internet Resource, Computer File D Mustafa; K Glover Find more information about: D Mustafa K Glover 9783540471820 3540471820 851817204 1 online resource (ix, 144 pages). The entropy of a system -- The minimum entropy $$\mathcal{H}_\infty$$ control problem -- The minimum entropy $$\mathcal{H}_\infty$$ distance problem -- Relations to combined $$\mathcal{H}_\infty$$ /LQG control -- Relations to risk-sensitive LQG control -- The normalized $$\mathcal{H}_\infty$$ control problem -- $$\mathcal{H}_\infty$$ -characteristic values -- LQG and $$\mathcal{H}_\infty$$ monotonicity. Lecture notes in control and information sciences, 146. edited by Dennis Mustafa, Keith Glover.

### Abstract:

This monograph is concerned with the design of feedback controllers for linear multivariable systems, which are robust to system uncertainty. System uncertainty can be realistically represented by including perturbations with bounded H?-norm, and this is the approach taken here. For a given H?-norm bound, there is a family of robustly stabilizing controllers, and the central question in this book is which of these controllers to choose. One choice to take is that which minimizes the enthropy of the resulting closed loop transfer function, and the derivation and properties of this solution occupies most of this monograph. Explicit formulae are obtained for the minimum enthropy solution, which is a precisely defined compromise between the Linear Quadratic Gaussian optimal solution and the H?-optimal solution. The book will be appropriate for graduate classes requiring only a first course in state-space methods, and some elementary knowledge of H? control and Linear Quadratic Gaussian control.

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