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Feedback{invariant Optimal Control Theory and Di erential Geometry, II. Jacobi Curves
 

Summary: Feedback{invariant Optimal Control Theory
and Di erential Geometry, II. Jacobi Curves
for Singular Extremals
A. A. Agrachev 
Abstract
This is the second article in the series opened by the paper [4].
Jacobi curves were de ned, computed, and studied in that paper for
regular extremals of smooth control systems. Here we do the same for
singular extremals. The last section contains a feedback classi cation
and normal forms of generic single{input aĆne in control systems on
a 3-dimensional manifold.
Introduction
This paper is a continuation of [4]. Jacobi curves were de ned, computed,
and studied in [4] for regular extremals of smooth control systems. Here we
do the same for singular extremals.
The points of the Jacobi curves are the L-derivatives of endpoint map-
pings. The notion of L-derivative was introduced in [4]; in section 1 of the
present paper we prove a general existence theorem for the L-derivatives of
smooth mappings and indicate a way to compute them. In section 2 we ac-
tually compute the L-derivatives of the endpoint mappings and the Jacobi

  

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 

Collections: Engineering; Mathematics