Computation of time optimal swing up control of single pendulum

Time optimal control under bounded input has been studied. This paper presents a computational strategy to obtain the time optimal control for nonlinear systems, and discrete time control under input bound is considered. The swing up control of a single pendulum from pendant stable equilibrium to upright unstable equilibrium is used to illustrate our approaches. For a simplified model of the single pendulum, which is a second-order system, an approach based on the linear programming method is introduced, while for the actual single pendulum, an approach based on nonlinear optimization is introduced. Simulation results show that our computational approaches are feasible