Optimal control of a switched autonomous system with time delay arising in fed-batch processes

Abstract

In this paper, we propose a switched autonomous system with time delay to model the 1,3-propanediol (1,3-PD) production in a fed-batch process. Taking the switching instants and the terminal time as the control variables, we formulate a constrained time-delayed optimal control (CTOC) problem to optimize the 1,3-PD production process. Using a time-scaling transformation and parametrizing the switching instants into new parameters, an equivalent CTOC problem is investigated. A numerical solution method is then developed to seek the optimal control strategy. This method is based on the constraint transcription technique and the gradients of the cost functional together with those of the constraints. Numerical simulation results show that the mass of 1,3-PD per unit time at the terminal time is increased considerably compared with the experiment results.