Studying various optimal control problems in biodiesel production in a batch reactor under uncertainty

The optimal control problem encountered in biodiesel production can be formulated using various performance indices, namely, maximum concentration, minimum time, and maximum profit. The problems involve determining optimal temperature profile so as to maximize these performance indices. This paper presents the formulations of these optimal control problems and analyzes the solutions. Optimal control problems involve the solution of partial or second order differential equation depending on the method used, resulting in difficult tasks to solve due to their mathematical representation. This difficulty becomes more challenging when uncertainty in any parameter is considered. It has been shown that the application of maximum principle in optimal control problems provides the same results but its formulation avoids the solution of second order or partial differential equations. In this work, we use the maximum principle to solve the problems in the deterministic case. Further, we consider uncertainty in the feed composition and their effects on the optimal control solution.