On singular extremals in the time minimal control problem in \({\mathbb{R}}^ 3\). (English) Zbl 0602.49027

Bonnard, Bernard

SIAM J. Control Optimization 23, 794-802 (1985).

The author studies the time minimal control problem of a single-input generic system in \(E^ 3\) given by \(dx/dt=X(x)+uY(x)\) where X and Y are analytic and the singular controls are defined by a feedback of the form \(u(x)=\Delta '(x)/\Delta (x).\) The author classifies the local behaviour of singular trajectories near points x such that \(\Delta (x)=0\) when X is quadratic and Y a constant. The analysis is applicable to the Euler equation of a rigid body control problem.

Reviewer: E.Chukwu

MSC:

93B99	Controllability, observability, and system structure
49K15	Optimality conditions for problems involving ordinary differential equations
58C25	Differentiable maps on manifolds
58K99	Theory of singularities and catastrophe theory
70E15	Free motion of a rigid body
70Q05	Control of mechanical systems
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

polynomial systems; time minimal control; singular controls; feedback; Euler equation; rigid body control