
There exists a very broad class of industrial devices which
need to change their position in a minimum time. Dynamics of
the above devices, called position mechanisms, depends
essentially on the motion resistance and may be defined by planar
nonlinear and discontinuous differential equation. Timeoptimal
problem of this system will be understood as a transfer of any
two dimensional initial state to any two dimensional target state
in a minimum time. Timeoptimality of the controlled processes
of that controlled object may be ensured only in a closedloop
system which attributes to each of the state a time optimal value
of the control function u. Thus, the open controlled system by
a feedback system in which the control function depends on state
of system. In real closedloop system such as mentioned above
both the internal uncertainty and external perturbations may appear.
So, the created feedback system becomes a nontimeoptimal one.
We create two spetial factors p and r those may be usefull
in identification of divergent and convergent oscilatory process.
It has been shown that if the function, created by controller,
h differs from the time optimal one and 0 < p < 1 then the
closedloop system induces the convergent nonlinear oscillations,
i.e. state trajectory goes around the target state and reaches it
in finite time after performing undefined number of encirclements.
Instead, if the factor r > 1 then the closedloop system induces
the divergent nonlinear oscillations, i.e. state trajectory goes
around the target state divergently and tends to form the limit
curve with the target state in its interior.
