Time optimal swing-up control of single pendulum

Swing-up of a rotating type pendulum from the pendant to the inverted state is known to be one of most difficult control problems, since the system is nonlinear, underactuated, and has uncontrollable states. This paper studie s a time optimal swing-up control of the pendulum using bounded input. Time optimal control of a nonlinear system can be formulated by Pontryagin's Ma ximum Principle, which is, however, hard to compute practically. In this pa per, a new computational approach is presented to attain a numerical soluti on of the time optimal swing-up problem. Time optimal control problem is de scribed as minimization of the achievable time to attain the terminal state under the bounded input amplitude, although algorithms to solve this probl em are known to be complicated., Therefore, in this paper, it is shown how the optimal time swing-up control is formulated as an auxiliary problem in that the minimal input amplitude is searched so that the terminal state sat isfies a specification at a given time. Through the proposed approach,, tim e optimal control can be solved by nonlinear optimization. Its approach is evaluated by numerical simulations of a simplified pendulum model, is check ed satisfying the necessary condition of Maximum Principle, and is experime ntally verified using the rotating type pendulum.