This research monograph gives a complete discussion of the theory of the discrete-time hyperbolic map. Both scalar and matrix representations are considered. The dynamics of the map are analyzed and discussions of stability, quasiperiodicity, and chaos are included. Several applications are discusssed, the most important being the discrete-time linear time-invariant quadratic regulator. The results obtained from this analysis are then extended to the continuous-time linear regulator. A discussion of the linear quadratic regulator with negative state weighting provides some important insights into the general regulator theory. The results contained in this monograph should be accessible to the first year graduate student or advanced senior undergraduate. Interested readers should also have a background in ODE's, difference equations, optimization theory, and/or digital control theory.
The Hyperbolic Map and Applications to the Linear Quadratic Regulator
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Description
This research monograph gives a complete discussion of the theory of the discrete-time hyperbolic map. Both scalar and matrix representations are considered. The dynamics of the map are analyzed and discussions of stability, quasiperiodicity, and chaos are included. Several applications are discusssed, the most important being the discrete-time linear time-invariant quadratic regulator. The results obtained from this analysis are then extended to the continuous-time linear regulator. A discussion of the linear quadratic regulator with negative state weighting provides some important insights into the general regulator theory. The results contained in this monograph should be accessible to the first year graduate student or advanced senior undergraduate. Interested readers should also have a background in ODE's, difference equations, optimization theory, and/or digital control theory.
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory...
Surveys.- Multiples of forms.- On Saltman's p-Adic Curves Papers.- Serre's Conjecture II: A Survey.- Field Patching, Factorization, and Local-Global Principles.- Deformation Theory and Rational...
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