Time-Optimal Control Problem of Two Non-Synchronous Oscillators

The time-optimal control problem for a system consisting of two non-synchronous oscillators is considered. Each oscillator controlled with shared limited scalar control. objective the to accelerate oscillatory given specific position, where first must have non-zero phase coordinates, but second one remain motionless at terminal moment. For an arbitrary number unknown switching moments that determine optimal relay control, necessary extremum conditions in form nonlinear matrix equalities are proposed. study necessary/sufficient made it possible describe reachability set space oscillator, find analytical curve corresponding two-switching class, which also separates three switching-control class. theorems proved and dependence criteria on constraints shown. Matrix different classes switchings found. All obtained results numerically validated illustrated mathematical modeling.