arXiv 1503.001612015-03math.OC

关于无限视界问题中作为极限梯度的Hamilton量

On Hamiltonian as limiting gradient in infinite horizon problem

Dmitry Khlopin

备注：: for Journal of Dynamical and Control Systems

摘要：

对右端为自由的Bolza型折扣问题，导出了最优性的必要条件，其形式为Pontryagin最大值原理.最优性是在一致超越最优性的意义上理解的。假设存在这样的过程，并假设最优过程的相应收益（以反常积分的形式表示）在黎曼意义下收敛。不需要对轨迹或伴随变量的渐进行为进行其他假设。本文证明了Pontryagin最大值原理存在一个满足Michel横截条件的极限解，特别是证明了最大化Hamilton量的平稳性条件和最大化Hamilton量在无穷远处为零的事实.证明了这一条件与支付函数沿最优过程在无穷远处的极限次微分的关系。还考虑了支付没有折扣乘数的情况。

英文摘要：

Necessary conditions of optimality in the form of the Pontryagin Maximum Principle are derived for the Bolza-type discounted problem with free right end. The optimality is understood in the sense of the uniformly overtaking optimality. Such process is assumed to exist, and the corresponding payoff of the optimal process (expressed in the form of improper integral) is assumed to converge in the Riemann sense. No other assumptions on the asymptotic behaviour of trajectories or adjoint variables are required. In this paper, we prove that there exists a corresponding limiting solution of the Pontryagin Maximum Principle that satisfies the Michel transversality condition; in particular, the stationarity condition of the maximized Hamiltonian and the fact that the maximized Hamiltonian vanishes at infinity are proved. The connection of this condition with the limiting subdifferentials of payoff function along the optimal process at infinity is showed. The case of payoff without discount multiplier is also considered.

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摘要：

英文摘要：

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