Control of nonlinear systems with nilpotent structure in singular problems
by
Mihai Popescu
Statistics and Applied Mathematics Institute of the Romanian Academy, Bucharest

Optimal control theory offers modern methods regarding the control of systems and thus plays an important role in linear control theory (more specifically, the linear quadratic regulator and linear quadratic Gaussian control theories. The use of the optimal control in the class of linear systems permits a substantial diminution of computation of the optimal control law. Moreover, it makes up an efficient method for solving the non-linear optimal control problems. The Lie brackets of vector fields, generating a Lie algebra that has a certain relevant sub-algebra nilpotent, have become a main mathematical tool in optimal control theory.

In this paper the minimum singular functional control problem is analyzed for a class of multi-input affine nonlinear systems in the hypothesis whose associated Lie algebra is nilpotent. The optimal control corresponding to the first, second and third order nilpotent operator is determined. We develop an algorithm for solving the singular problem that is applicable whether or not singular sub-arcs exist in the optimal control.

Date received: January 29, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakt-42.