Optimal control of singular systems with a cost on changing control

In this paper, we consider a class of optimal control problems with a cost on changing control, where the system dynamics are described by singular differential equations. Using a constraint transcription coupled with a local smoothing technique, a penalty function, and the control parametrization technique, an efficient computational method is developed for solving this optimal control problem sequentially. The convergence performance of the proposed method is also established. For illustration, this method is used to find the optimal feeding policy for a fed-batch fermentation process.