A time-optimal control that steers the phase point for a third-order linear
system to the origin is constructed in an explicit analytical form. It is
assumed that the characteristic exponents are zero, and the constraints on
the control function are non-symmetric. The system simulates the dynamics o
f a point mass driven by a force whose rate of change can be regulated. An
optimal control is constructed both in the feedback and open-loop forms. In
the latter case, the optimal control is a function of time. Relations are
derived for the switching curve and surface and for the time intervals of t
he motion; optimal phase trajectories are constructed; the feedback control
portrait is investigated. The influence of a parameter characterizing the
degree of asymmetry of the constraints is studied. "Near-optimal" control m
odes, which are much simpler to implement, are constructed. (C) 2000 Elsevi
er Science Ltd. All rights reserved.