Rate limited time optimal control of a planar pendulum

Time optimal control problems often admit as solution bang–bang controls but they present several drawbacks in real applications where additional degrees of regularity are desirable. In this paper, the rate limited time optimal swing up of an inverted pendulum is considered and necessary conditions that have to be satisfied by optimal trajectories in the presence of rate constraints are derived. A comparison between this approach and the results from the standard time optimal problem is reported.