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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
non-linear and discontinuous differential equation. Time-optimal
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. Time-optimality of the controlled processes
of that controlled object may be ensured only in a closed-loop
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 closed-loop system such as mentioned above
both the internal uncertainty and external perturbations may appear.
So, the created feedback system becomes a non-time-optimal 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
closed-loop system induces the convergent non-linear 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 closed-loop system induces
the divergent non-linear 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.
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