This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
为实现沿海区域的海上风电场、海上采气平台和陆上热电联供燃气电厂等多种能源生产子单元的协同化运行,考虑可再生能源出力和氢负荷的随机波动,提出沿海区域综合能源生产单元(coastal integrated energy production units,CIEPU)随机优...为实现沿海区域的海上风电场、海上采气平台和陆上热电联供燃气电厂等多种能源生产子单元的协同化运行,考虑可再生能源出力和氢负荷的随机波动,提出沿海区域综合能源生产单元(coastal integrated energy production units,CIEPU)随机优化调度模型。采用参数化代价函数近似(parametric cost function approximation,PCFA)的动态规划算法求解随机优化调度模型。通过一种基于梯度下降的求解方法--Adadelta法,获得策略函数的一阶信息,并计算梯度平方的指数衰减平均值,以更新策略函数的迭代步长;对随机优化调度模型进行策略参数逼近,从而得到近似最优的策略参数,并逐一时段求解出CIEPU的最优调度计划。最后,以某个CIEPU为例,分析计算结果表明,所提出方法获得的优化调度方案可以提高CIEPU运行的经济性并降低碳排放量,验证了所提方法的准确性和高效性。展开更多
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
文摘为实现沿海区域的海上风电场、海上采气平台和陆上热电联供燃气电厂等多种能源生产子单元的协同化运行,考虑可再生能源出力和氢负荷的随机波动,提出沿海区域综合能源生产单元(coastal integrated energy production units,CIEPU)随机优化调度模型。采用参数化代价函数近似(parametric cost function approximation,PCFA)的动态规划算法求解随机优化调度模型。通过一种基于梯度下降的求解方法--Adadelta法,获得策略函数的一阶信息,并计算梯度平方的指数衰减平均值,以更新策略函数的迭代步长;对随机优化调度模型进行策略参数逼近,从而得到近似最优的策略参数,并逐一时段求解出CIEPU的最优调度计划。最后,以某个CIEPU为例,分析计算结果表明,所提出方法获得的优化调度方案可以提高CIEPU运行的经济性并降低碳排放量,验证了所提方法的准确性和高效性。
