The Hyperbolic Map and Applications to the Linear Quadratic Regulator

by Brian J. Daiuto, Tom T. Hartley, Stephen P. Chicatelli

Overview

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.

Product Details

ISBN-13:	9783540967415
Publisher:	Springer Berlin Heidelberg
Publication date:	12/01/1989
Series:	Lecture Notes in Control and Information Sciences , #110
Pages:	119
Product dimensions:	6.69(w) x 9.61(h) x 0.01(d)

Table of Contents

Qualitative dynamics of the hyperbolic iteration map.- General solution derivation for the hyperbolic iteration map.- Appendix A extension to the multidimensional case.- Appendix B some interesting applications of the hyperbolic map.- The linear quadratic regulator — Background.- The linear quadratic regulator under negative Q.- Conclusion.