Legendre pseudo-spectral method for solving the optimal starting pendulum of a rotating inverted pendulum

The inverted pendulum is an underdriven system with multivariable, nonlinear and strong coupling. For the time-optimal swing problem of inverted pendulum, the mathematical model of inverted pendulum is established by generalized projection method. The optimal control problem (OCP) is transformed into a nonlinear programming problem (NLP) for solving by the pseudo-spectral method. And the steps of Legendre’s pseudo-spectral method for transforming into a Bolza-type optimal control problem are summarized. The solution of this optimal control problem is realized by the MATLAB toolbox OptimTraj. The experimental results show that the pseudo-spectral method has better computational efficiency and speed, and has good results in solving complex optimal control problems.