Title :
Controllability distributions and systems approximations: a geometric approach
Author :
Ruiz, A.C. ; Nijmeijer, H.
Author_Institution :
Dept. of Appl. Math., Twente Univ., Enschede, Netherlands
Abstract :
Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the results
Keywords :
controllability; geometry; nonlinear control systems; Taylor series approximation; control synthesis; controllability distributions; controlled invariant distributions; geometric approach; nonlinear control theory; nonlinear system; solvability conditions; systems approximations; Control system analysis; Control system synthesis; Control systems; Control theory; Controllability; Linear approximation; Mathematics; Nonlinear control systems; Nonlinear systems; Taylor series;
Conference_Titel :
Decision and Control, 1992., Proceedings of the 31st IEEE Conference on
Conference_Location :
Tucson, AZ
Print_ISBN :
0-7803-0872-7
DOI :
10.1109/CDC.1992.371784
