The uncoupled microbial fed-batch fermentation optimization based on state-dependent switched system

In the actual microbial fermentation process, excessive or insufficient substrate can produce inhibitory effects on cells growth. The artificial substrate feeding rules by past experiences have great blindness to keep substrate concentration in a given appropriate range. This paper considers that alkali feed depends on pH value of the solution and glycerol feed depends on glycerol concentration of the solution in the uncoupled microbial fed-batch fermentation process, and establishes a state-dependent switched system in which the flow rates of glycerol and alkali, the number of mode switches, the mode sequence and the switching times are prior unknown. To maximize the yield of target product 1,3-Propanediol (1,3-PD), we formulate a switching optimal control problem with the flow rates of glycerol and alkali, the number of mode switches, the mode sequence and the switching times as decision variables, which is a mixed-integer dynamic programming problem. For solving the mixed-integer dynamic programming problem, the control parametrization technique, the time scaling transformation and the embedded system technology are used to obtain an approximate parameter optimization problem. By using a parallel optimization algorithm, we obtain the optimal control strategies. Under the obtained optimal control strategies, the 1,3-PD yield at the terminal time is increased significantly compared with the previous results.