Optimal Control Of A Class Of Nonlinear Switched Systems And Its Application In Biological Fermentation

The production of1,3-propanediol (1,3-PD) by fed-batch fermentation has naturalswitching characteristics. In order to increase the production, many researchers havealready established the dynamic models of fed-batch fermentation. But in terms of theoptimal control, that most algorithms need to consider the restriction on the number ofswitching and switching sequence. In view of the new kind of algorithm, this paper studiedits convergence and applied it to fed-batch fermentation optimal control problem. Theresults showed that the algorithm is effective.The main results are as follows:1.On the basis of the optimal control algorithm for a class of nonlinear switched systems,we analyzed the relation among the numerical solutions, the theoretical solutions and thepiece-wise constant functions. It is proved that the numerical solutions obtained from thealgorithm will converge to the theoretical optimal solutions as division of time intervalinfinitely such that the effectiveness of the algorithm is proved. Then, the algorithm’spractical application will be realized.2. We apply the algorithm to the glycerol fermentation production model of1,3-PD.Through solving the optimal control problems of subsystem independently with the help ofcontrol parameterization method, the paper compared the Hamilton function of thesubsystems. Then, the optimal control and optimal switching rule of the switch problem areobtained without considering the restriction on the number of switching and switchingsequence.The complex process of the original algorithm is avoided.