Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach |
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基金项目: | supported in part by the NSF grant DMS-1007514 |
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摘 要: | A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N -person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.
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关 键 词: | 最优控制问题 收敛时间 非合作 常微分方程 平衡控制 价值函数 纳什均衡 极限问题 |
Deterministic time-inconsistent optimal control problems — an essentially cooperative approach |
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Authors: | Jiong-min Yong |
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Affiliation: | Jiong-min YONG Department of Mathematics, University of Central Florida, Orlando, FL 32816 |
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Abstract: | A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find
a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative
N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved
that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the
value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent
limit problem is a time-consistent equilibrium control of the original problem. |
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Keywords: | time-inconsistency pre-committed optimal control time-consistent equilibrium control multi-level hierarchical differential games |
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