Single Species Dynamic System Impulse Optimal Control

Many systems in the real world may suffer disturbances whose duration is very short relative to the entire process. Continuous differential equations can not reflect the dynamic change appearing in the system accurately. But impulsive differential equations can describe this situation exactly.First, we introduce the single species Logistic and Gompertz impulsive capture models. Then, utilizing the theories of optimization problems on impulsive differential equations, we solve the optimization problems for the two models to maximize the profit function, which is taken as the performance index. Further, we get the optimal impulsive capture time and the corresponding capture quantity. We design several algorithms that can be used in the two impulsive capture models to realize the optimal control for decision variables by MATLAB7.10, and use the optimal impulsive capture time and the corresponding profit function analytic solution of Logistic impulsive capture model to verify their effectiveness and validity. Finally, comparing the error between the simulation results and the analytic results, we find out the most suitable algorithm, by which the numerical solution is worked out on the optimal capture time and the optimal capture amount for Gompertz model. This algorithm is verified also suitable for an improved profit function.This paper obtains the optimal capture strategy by introducing optimal control method of impulsive differential systems into single species dynamic model, and gets numerical results for the optimal decision variables and performance index by computer simulation.