A Time-Optimal Control Synthesis for a Nonlinear Pendulum

摘要

A time-optimal control synthesis is obtained that steers a nonlinear pendulum to the bottom stable equilibrium position. The solution is based on the maximum principle and involves the analytical investigation in combination with numerical calculations. As a result, for different values of the maximum admissible control torque, switching curves and dispersal curves (or separation curves), which confine domains in the phase space that correspond to different values of the bang-bang optimal control, are constructed. The investigated patterns of synthesis reveal the mechanism of generation of numerous breaks on switching curves for small control torques.