Team-optimal closed-loop Stackelberg strategies for systems with slow and fast modest†
Team-optimal closed-loop Stackelberg strategies for systems with slow and fast modest†
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DOI：
10.1080/00207178308933053
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发表时间：
1983-06
影响因子：
2.1
通讯作者：
M. Salman;J. Cruz
中科院分区：
文献类型：
--
作者：
M. Salman;J. Cruz
讨论了具有慢模式和快模式的系统的团队最优闭环Stackelberg策略。证明了当小奇异摄动参数趋于零时，纯慢速博弈和全序博弈的代价函数在极限上具有相同的值。结果表明，如果领导者的近似策略设计基于慢子系统，而跟随者的设计基于全阶系统，则所得到的解是不适定的。此外，如果在领导者的近似策略中加入快速信息，则通过组合慢策略和快策略来构造近似策略的奇异摄动技术是不适定的，不能用于该问题。提出了一种新的设计方法，通过求解与全阶问题具有相同信息结构的降阶问题来构造近似Stackelberg策略。证明了存在的条件和……
This paper discusses team-optimal closed-loop Stackelberg strategies for systems with slow and fast modes. It is established that the cost functions of the players in the pure slow and the full-order games have the same value in the limit as the small singular perturbation parameters tends to zero. It is shown that if the leader bases the design of his approximate strategy on the slow subsystem, while the follower bases his design on the full-order system, then the resulting solution is ill-posed. Moreover, if the fast information is incorporated in the approximate strategy of the leader, then it is shown that the singular perturbation technique of constructing approximate strategies by composing the slow and fast strategies is ill-posed and cannot be used in this problem. A new design methodology to construct approximate Stackelberg strategies by solving reduced-order problems, which have the same information structure as the full-order one, is presented. It is shown that the conditions for existenco and...