This paper investigates the problem of implementing rate constraints when solving
nonlinear optimal control problems with direct transcription methods. We generalize the
approach of directly implementing rate constraints on the discretization mesh to all types
of collocation methods (
h
,
p
and
hp
), for both state and input variables. This “on mesh”
implementation replaces the additional dynamic equations and nonlinear path constraints in
classical implementations with linear equations. Thus, there is no contribution to the Hessian
and the contribution to the Jacobian can be precomputed, enabling faster iterations. Through
an example, the benefits of the proposed approach are demonstrated, both in terms of obtaining
singular arc-free solutions, as well as reductions in computation time of more than 20%.