The time-dependent solution of reduced air-sea coupling stochastic-dynamicmodel is accurately obtained by using the Fokker-Planck equation and the quantum mechanical method.The analysis of the time-dependent solution ...The time-dependent solution of reduced air-sea coupling stochastic-dynamicmodel is accurately obtained by using the Fokker-Planck equation and the quantum mechanical method.The analysis of the time-dependent solution suggests that when the climate system is in the groundstate, the behavior of the system appears to be a Brownian movement, thus reasoning the foothold ofHasselmann's stochastic climatic model; when the system is in the first excitation state, the motionof the system exhibits a form of time-decaying, or under certain condition a periodic oscillationwith the main period being 2.3 yr. At last, the results are used to discuss the impact of thedoubling of carbon dioxide on climate.展开更多
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic...This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.展开更多
The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the n...The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.展开更多
基金Project supported jointly by the National Natural Science Foundation of China under Grant Nos. 40275031 and 40231006 andthe State Key Development Program for Basic Research of China under Grant No. 2006CB400503.
文摘The time-dependent solution of reduced air-sea coupling stochastic-dynamicmodel is accurately obtained by using the Fokker-Planck equation and the quantum mechanical method.The analysis of the time-dependent solution suggests that when the climate system is in the groundstate, the behavior of the system appears to be a Brownian movement, thus reasoning the foothold ofHasselmann's stochastic climatic model; when the system is in the first excitation state, the motionof the system exhibits a form of time-decaying, or under certain condition a periodic oscillationwith the main period being 2.3 yr. At last, the results are used to discuss the impact of thedoubling of carbon dioxide on climate.
基金supported by National Natural Science Foundation of China (No. 60774010, 10971256, and 60974028)Jiangsu"Six Top Talents" (No. 07-A-020)+2 种基金Natural Science Foundation of Jiangsu Province (No. BK2009083)Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province(No.07KJB510114)Natural Science Foundation of Xuzhou Normal University (No. 08XLB20)
文摘This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
文摘The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.
