一类无穷时区上的时间不一致最优控制问题的均衡控制

Equilibrium control of a class of time-inconsistent optimal control problems with infinite horizon

本文研究了一类无穷时区上的时间不一致最优控制问题,其中的目标泛函含有贴现函数,且贴现率充分大.在此类问题中,贴现率不保持恒定使得问题具有时间不一致性,从而局部最优不再等价于整体最优,本文考虑问题的均衡控制而非最优控制.运用针状变分方法,本文推导了容许控制成为均衡控制的充要条件.当贴现函数为指数型时,该结果便退化为无穷时区上的Pontryagin最大值原理.最后我们给出该结果在经济学中的一个应用.

We study time-inconsistent optimal control problems with infinite horizon and dominating discount.In this problem,the non-constant discount rate results in the time inconsistency,thus local optimization is not equal to overall optimization anymore.Hence we study the equilibrium control instead of the optimal control.By using the needle variation method,we deduce some sufficient and necessary conditions for the equilibrium control.When the discount function has exponential form,our results degenerate to the Pontryagin maximum principle with infinite horizon.Finally,we give an example in economy.