This project addresses the qualitative structure of small-time reachable sets and piecewise regularity properties of optimal controls for nonlinear systems. For single-input systems it is known that optimal trajectories can exhibit undesirable features such as chattering bang-bang arcs if the dimension of the system becomes too large. This may be due to a lack of possibility to influence the system via the control vector field. To explore that scenario this project seeks to analyze the local structure of small-time reachable sets in dimension n for increasing values of n, in particular, to develop tests for optimality of complex concatenations of bang and singular arcs, and ii) to investigate multi-input systems using higher-order approximating cones which take into account specific structures of trajectories under consideration. The underlying technical framework is provided by differential-geometric descriptions and Lie-algebraic computational techniques. The long term aim of this work is to achieve a qualitative understanding of the local behavior of nonlinear control systems. Aside from its evident theoretical relevance, such a knowledge might also be practically of interest for any possible future approach to design involving nonlinear components.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8820413
Program Officer
Michael H. Steuerwalt
Project Start
Project End
Budget Start
1989-06-01
Budget End
1991-11-30
Support Year
Fiscal Year
1988
Total Cost
$44,284
Indirect Cost
Name
Washington University
Department
Type
DUNS #
City
Saint Louis
State
MO
Country
United States
Zip Code
63130