Abstract
A new class of control and optimization problems for the motions of oscillatory systems, utilizing adjustable variation of the parameters, is considered. Forms of the equations of motion are proposed suitable for the use of asymptotic methods of non-linear mechanics and optimal control. The basic control modes are investigated: by bang-bang-type variation of the acceleration, velocity or the value of a parameter within relatively narrow limits. Approximate time-optimal and time-quasi-optimal control laws are constructed for non-linear oscillatory systems with regulated relative equilibrium position and stiffness. Some interesting features of the motions are observed and discussed.
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