Based on frequency response and convex optimization,a novel optimal control system was developed for chemical processes.The feedforward control is designed to improve the tracking performance of closed loop chemical s...Based on frequency response and convex optimization,a novel optimal control system was developed for chemical processes.The feedforward control is designed to improve the tracking performance of closed loop chemical systems.The parametric model is not required because the system directly utilizes the frequency response of the loop transfer function,which can be measured accurately.In particular,the extremal values of magnitude and phase can be solved according to constrained quadratic programming optimizer and convex optimization.Simulation examples show the effectiveness of the method.The design method is simple and easily adopted in chemical industry.展开更多
In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measu...In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.展开更多
In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved ...In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.展开更多
A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemi...A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemical machining are different from traditional electrochemical machining.An equivalent kinematic model is established to analyze the novel electrodes motion,since the anode and cathode rotate in the same direction while the cathode simultaneously feeds along the line of centres.According to the kinematic equations of the electrodes and Faraday’s law,a material removal model is established to simulate the evolution of the anode profile in co-rotating electrochemical machining.The simulation results indicate that the machining accuracy of the convex structure is strongly affected by the angular velocity ratio and the radius of the cathode tool.An increase of the angular velocity ratio can improve the machining accuracy of a convex structure.A small difference in the radius of the cathode tool will cause changes in the shape of the sidewalls of the convex structure.The width of the cathode window affects only the width of the convex structure and the inclination a of the sidewall.A relation between the width of the cathode window and the width of the convex structure was obtained.The formation process for a convex structure under electrochemical dissolution was revealed.Based on the simulation results,the optimal angular velocity ratio and cathode radius were selected for an experimental verification,and 12 convex structures were simultaneously fabricated on the inner surface of a thin-walled revolving part.The experimental results are in good agreement with the simulation results,which verifies the correctness of the theoretical analysis.Therefore,inner surface co-rotating electrochemical machining is an effective method for fabricating convex structures on the inner surface of a revolving part.展开更多
基金Supported by the National Natural Science Foundation of China（51205133） Natural Science Foundation of Shanghai（11ZR1409000） Ph.D.Programs Foundation of Ministry of Education of China（20110074120007）
文摘Based on frequency response and convex optimization,a novel optimal control system was developed for chemical processes.The feedforward control is designed to improve the tracking performance of closed loop chemical systems.The parametric model is not required because the system directly utilizes the frequency response of the loop transfer function,which can be measured accurately.In particular,the extremal values of magnitude and phase can be solved according to constrained quadratic programming optimizer and convex optimization.Simulation examples show the effectiveness of the method.The design method is simple and easily adopted in chemical industry.
文摘In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.
基金National Natural Science Foundation of China(1 9971 0 72 )
文摘In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.
基金supported by the National Natural Science Foundation of China(No.52175414)National Natural Science Foundation of China for Creative Research Groups(No.51921003)the China Postdoctoral Science Foundation(No.2019M661833).
文摘A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemical machining are different from traditional electrochemical machining.An equivalent kinematic model is established to analyze the novel electrodes motion,since the anode and cathode rotate in the same direction while the cathode simultaneously feeds along the line of centres.According to the kinematic equations of the electrodes and Faraday’s law,a material removal model is established to simulate the evolution of the anode profile in co-rotating electrochemical machining.The simulation results indicate that the machining accuracy of the convex structure is strongly affected by the angular velocity ratio and the radius of the cathode tool.An increase of the angular velocity ratio can improve the machining accuracy of a convex structure.A small difference in the radius of the cathode tool will cause changes in the shape of the sidewalls of the convex structure.The width of the cathode window affects only the width of the convex structure and the inclination a of the sidewall.A relation between the width of the cathode window and the width of the convex structure was obtained.The formation process for a convex structure under electrochemical dissolution was revealed.Based on the simulation results,the optimal angular velocity ratio and cathode radius were selected for an experimental verification,and 12 convex structures were simultaneously fabricated on the inner surface of a thin-walled revolving part.The experimental results are in good agreement with the simulation results,which verifies the correctness of the theoretical analysis.Therefore,inner surface co-rotating electrochemical machining is an effective method for fabricating convex structures on the inner surface of a revolving part.
