Ebook: The Hyperbolic Map and Applications to the Linear Quadratic Regulator

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.

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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.

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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.
Content:
Front Matter....Pages -
Introduction....Pages 1-3
Qualitative dynamics of the hyperbolic iteration map....Pages 4-23
General solution derivation for the hyperbolic iteration map....Pages 24-36
Appendix A extension to the multidimensional case....Pages 37-39
Appendix B some interesting applications of the hyperbolic map....Pages 40-45
The linear quadratic regulator — Background....Pages 46-59
The linear quadratic regulator under negative Q....Pages 60-98
Conclusion....Pages 99-100
Back Matter....Pages -

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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.
Content:
Front Matter....Pages -
Introduction....Pages 1-3
Qualitative dynamics of the hyperbolic iteration map....Pages 4-23
General solution derivation for the hyperbolic iteration map....Pages 24-36
Appendix A extension to the multidimensional case....Pages 37-39
Appendix B some interesting applications of the hyperbolic map....Pages 40-45
The linear quadratic regulator — Background....Pages 46-59
The linear quadratic regulator under negative Q....Pages 60-98
Conclusion....Pages 99-100
Back Matter....Pages -
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