Properties of the Time-Optimal Control for Lagrangian Single-Degree-of-Freedom Systems


The number of switchings is a vital parameter characterizing the complexity of the bang-bang optimal control. A time-optimal control problem for Lagrangian single-degree-of-freedom (single-DOF) systems is taken into account. The system describes the dynamics of an inertial object below the action of a bounded control force and an external force given as a function of the coordinate. The terminal set consists of the zero point within the phase plane. We analyze the attainable motion time along the optimal trajectories with 2 switchings and obtain corresponding necessary optimality condition. Thus, we suggest a criterion (tool) for quick checking the absence of such trajectories in the section plane. In this case, the time-optimal feedback management has the simplest structure: the quantity of switchings is not larger than one for any initial conditions. The corresponding examples are presented.

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