Real-Time Optimal Control Using TransWORHP and WORHP Zen

In many industrial applications solutions of optimal control problems are used, where the need for low computational times outweighs the need for absolute optimality. For solutions of fully discretized optimal control problems we propose two methods to approximate the solutions of problems with modified parameter values in real-time by using sensitivity derivatives. We use TransWORHP to transcribe an optimal control problem to a sparse nonlinear programming problem, which will be solved using our NLP solver WORHP. For this nominal solution sensitivity derivatives can be computed with respect to any system parameter using WORHP Zen. On NLP level, the sensitivity derivatives allow to perform correction steps for changes in the system parameters. This concept can be transferred to discretized optimal control problems using, e.g., the sensitivity derivatives of the boundary condition or of the discretized differential equations. The quality and applicability of both methods are illustrated by a trajectory planning problem in the context of the planar restricted problem of three bodies. In both methods the sensitivity derivatives can be used to give numerical validations of the theoretically expected convergence behaviour.