Perspectives in Control Theory pp 75-88 | Cite as

# Singular Optimal Problems

Chapter

## Abstract

Much of the content for this paper is motivated by the following variational problem. Suppose that the state space .

*M*is a real, analytic manifold of dimension*m*, and that*X*_{0}, ...,*X*_{ c }are real analytic vector fields on*M*. Consider the following differential system on*M*defined by this data:$$
\frac{{dx(t)}}{{dt}} = {X_0}(x(t)) + \sum\limits_{i = 1}^c {{u_i}{X_i}(x(t))}
$$

## Keywords

Vector Field Poisson Bracket Optimal Trajectory Integral Curve Poisson Algebra
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## Copyright information

© Springer Science+Business Media New York 1990