A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under whi...A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.展开更多
Platinum-based material is the most efficient and durable electrocatalyst for motivating the hydrogen evolution reaction(HER)in an acidic electrolyte;however,its low abundance and high cost limit its further applicati...Platinum-based material is the most efficient and durable electrocatalyst for motivating the hydrogen evolution reaction(HER)in an acidic electrolyte;however,its low abundance and high cost limit its further application in proton-exchange membrane water electrolysis(PEMWE)technology.Therefore,minimizing the Pt amount while retaining high activity would be desirable.Herein,we use defect-rich W_(18)O_(49)nanowires to anchor well-dispersed,ultrafine Pt species(Pt-W_(18)O_(49))via a freeze-drying method to avoid aggregation,further mediating an efficient and durable HER in acidic water.Density functional theory analyses also demonstrate that the strong electronic interaction between the Pt species and W_(18)O_(49)support greatly improves the HER performance.With a 1/10 Pt loading amount of the commercial 20 wt%Pt/C,the Pt-W_(18)O_(49)catalyst requires the overpotentials of 116 and 743 mV to achieve high current densities of 100 and 1000 mA cm^(−2)in 0.5 mol L^(−1)H_(2)SO_(4),outperforming those of the 20 wt%Pt/C benchmark.More importantly,the Pt-W_(18)O_(49)catalyst can sustain a high-currentdensity HER at 500 mA cm^(−2)for more than 38 h without obvious degradation.This work paves a new avenue for synergistically reducing the Pt amount and retaining high activity for real-world PEMWE.展开更多
基金Project supported by the National Natural Science Foundation ofChina (No. 10332030), the Special Fund for Doctor Programs inInstitutions of Higher Learning of China (No. 20020335092), andthe Zhejiang Provincial Natural Science Foundation (No. 101046),China
文摘A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
基金the National Natural Science Foundation of China(21866028)the Development and Innovation Program of Bingtuan(2012QY13)+1 种基金the Program of Science and Technology Innovation Team in Bingtuan(2020CB006)the Achievement Transformation and Technique Popularization Project of Shihezi University(CGZH201910).
文摘Platinum-based material is the most efficient and durable electrocatalyst for motivating the hydrogen evolution reaction(HER)in an acidic electrolyte;however,its low abundance and high cost limit its further application in proton-exchange membrane water electrolysis(PEMWE)technology.Therefore,minimizing the Pt amount while retaining high activity would be desirable.Herein,we use defect-rich W_(18)O_(49)nanowires to anchor well-dispersed,ultrafine Pt species(Pt-W_(18)O_(49))via a freeze-drying method to avoid aggregation,further mediating an efficient and durable HER in acidic water.Density functional theory analyses also demonstrate that the strong electronic interaction between the Pt species and W_(18)O_(49)support greatly improves the HER performance.With a 1/10 Pt loading amount of the commercial 20 wt%Pt/C,the Pt-W_(18)O_(49)catalyst requires the overpotentials of 116 and 743 mV to achieve high current densities of 100 and 1000 mA cm^(−2)in 0.5 mol L^(−1)H_(2)SO_(4),outperforming those of the 20 wt%Pt/C benchmark.More importantly,the Pt-W_(18)O_(49)catalyst can sustain a high-currentdensity HER at 500 mA cm^(−2)for more than 38 h without obvious degradation.This work paves a new avenue for synergistically reducing the Pt amount and retaining high activity for real-world PEMWE.
