We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter.Assuming the convexity of the control domain,we...We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter.Assuming the convexity of the control domain,we obtain the stochastic maximum principle as the necessary condition for an optimal control,and we also prove its sufficiency under proper conditions.The stochastic linear quadratic problem in this setting is also discussed.展开更多
Since the knotters on the Chinese rectangular balers are imported from outside of the country, Chinese knotters with independent intellectual property rights is far away from being closed. In order to harvest a large ...Since the knotters on the Chinese rectangular balers are imported from outside of the country, Chinese knotters with independent intellectual property rights is far away from being closed. In order to harvest a large quantity of straw in a short period on the small-scale lands of China, basic requirements on the knotters are summarized. Mathematical model of the knotter is also determined uniquely. Furthermore, the ^-type-knots knotter equipped on the Chinese square baler to form the ~ type knots is designed. Knotting rate experiments of the qb-type-knots knotter on the test bench and in the wheat/maize straws covered fields are carried out to check the knotting performances of the knotter. The parameters of the formed knots are also tested. The experiments results show that the knotting rate of the qb-type-knots knotter reaches 100.0% on the test bench without straws, while reaches 99.6% in the wheat straws covered field and 100.0% in the maize straws covered field. The average maximum force in the knotting process is 194.7 N in the lab experiment. The length out of the knots formed in lab is 15.9%-20.6% lower than the knots formed in the field experiment. The breaking force of the knots formed in the field is 115.9%-167.2% higher than the knots formed in lab due to the higher preload and interactions with the compacted bales. Highly relevant relationships exist between the breaking force of the formed knots and the maximum force in the forming process of the knots in the lab experiment. The designed knotter breaks out the embarrassing situation of the domestic knotters which don＇t have independent intellectual property rights, and promotes the development of Chinese knotter technology, and the mathematical model is helpful for designing new type of knotters.展开更多
基金The authors are also grateful to the two anonymous referees for their valuable comments.J.Song is partially supported by Shandong University(Grant No.11140089963041)the National Natural Science Foundation of China(Grant No.12071256).
文摘We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter.Assuming the convexity of the control domain,we obtain the stochastic maximum principle as the necessary condition for an optimal control,and we also prove its sufficiency under proper conditions.The stochastic linear quadratic problem in this setting is also discussed.
基金supported by Program for Changjiang Scholars and Innovative Research Team in University of China(Grant No.IRT13039)National Natural Science Foundation of China(Grant No.51175499)+1 种基金Beijing Municipal Natural Science Foundation of China(Grant No.6112015)Chinese Universities Scientific Fund(Grant No.2012YJ091)
文摘Since the knotters on the Chinese rectangular balers are imported from outside of the country, Chinese knotters with independent intellectual property rights is far away from being closed. In order to harvest a large quantity of straw in a short period on the small-scale lands of China, basic requirements on the knotters are summarized. Mathematical model of the knotter is also determined uniquely. Furthermore, the ^-type-knots knotter equipped on the Chinese square baler to form the ~ type knots is designed. Knotting rate experiments of the qb-type-knots knotter on the test bench and in the wheat/maize straws covered fields are carried out to check the knotting performances of the knotter. The parameters of the formed knots are also tested. The experiments results show that the knotting rate of the qb-type-knots knotter reaches 100.0% on the test bench without straws, while reaches 99.6% in the wheat straws covered field and 100.0% in the maize straws covered field. The average maximum force in the knotting process is 194.7 N in the lab experiment. The length out of the knots formed in lab is 15.9%-20.6% lower than the knots formed in the field experiment. The breaking force of the knots formed in the field is 115.9%-167.2% higher than the knots formed in lab due to the higher preload and interactions with the compacted bales. Highly relevant relationships exist between the breaking force of the formed knots and the maximum force in the forming process of the knots in the lab experiment. The designed knotter breaks out the embarrassing situation of the domestic knotters which don＇t have independent intellectual property rights, and promotes the development of Chinese knotter technology, and the mathematical model is helpful for designing new type of knotters.
