Stabilization of a chain of three integrators subject to the control and
phase constraints is discussed. The paper continues our previous work
reported at the Optima 2022 conference, where a control law based on
two nested saturators was proposed and was proved that it globally stabilizes
the system in the lack of control and phase constraints. In this
work, to meet the phase and control constraints, we apply an advanced
six-parameter feedback law in the form of three nested saturation functions.
The number of the parameters reduces to twothe control resource
and the desired exponential convergence rate near the originby turning to
dimensionless variables and taking three coefficients from a one-parameter
family. The selection of the parameters is discussed that optimizes the
performance of the controller. We define an optimal controller as that
that globally stabilizes the system while ensuring the greatest convergence
rate. The phase portrait of the closed-loop system is shown to be
very complicated. When the convergence rate exceeds an optimal value, a
bifurcation occurs resulting in an infinite number of periodic motions the
trajectories of which lie on the surface of a cylinder in the phase space. A
lower bound of the optimal convergence rate is obtained analytically, and
its approximate value is found numerically.