多通道动力系统中平衡测度的熵与对策论平衡反馈算子
On the entropy of equilibrium measures and game-theoretic equilibrium feedback operators in multi-channel dynamical systems
摘要：
研究了多通道动力系统中平衡测度的熵与博弈论平衡反馈算子之间的关系。具体来说，我们表明，存在一个平衡测度，它最大化的自由能（即，熵和对势的积分之和）与由一组反馈算子组成的多通道动力系统的平衡或“最大熵“状态有关。此外，我们观察到，这样的连接是有意义的，当这组反馈算子的战略相互作用在无限的地平线上，在博弈论的意义上，使用当前的系统状态信息。最后，我们简要地评论了当系统中存在随机扰动时，我们的结果对平衡反馈算子的弹性行为的影响。
英文摘要：
We investigate the connection between the entropy of equilibrium measures and game-theoretic equilibrium feedback operators in a multi-channel dynamical system. Specifically, we show that the existence of an equilibrium measure, which maximizes the free energy (i.e., the sum of the entropy and the integral over a potential), is related to an equilibrium or "maximum entropy" state for the multi-channel dynamical system that is composed with a set of feedback operators. Further, we observe that such a connection makes sense when this set of feedback operators strategically interacts over an infinite-horizon, in a game-theoretic sense, using the current state-information of the system. Finally, we briefly comment on the implication of our result to the resilient behavior of the equilibrium feedback operators, when there is a random perturbation in the system.
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