Application of positional solutions to piecewise linear quadratic problems for damping and stabilizing a pendulum

The problem of damping vibrations (rotations) about a stable lower nonlinear equilibrium position and the problem of stabilizing the unstable upper state are considered for a nonlinear model of a pendulum. A bounded damping (stabilizing) feedback is constructed by using the realizations of positional solutions to special constrained optimal control problems with a quadratic performance index. Auxiliary problems involve a piecewise linear approximation of source nonlinear equations. Some results of numerical experiments are presented.