Abstract
Given a nonlinear stochastic second-order system representing a sine wave oscillator impulse control theory is applied in order to improve the performance of the oscillator. This is done in two stages. First the equations of optimal impulse control are introduced and a closed-form solution is given to the equations on the closed exterior of a circular disc in the x 1−x 2 plane. Then a finite-difference scheme is suggested for solving the equations, and they are solved numerically, for a number of cases on the inside of the disk. During both stages, the action set on which an impulse is applied by the system is obtained throughout the solution.
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