生存理论和价格调整

Viability Theory and Price Regulation

本文介绍法国数学家J.P.Aubin提出的大系統的生存理论。在这一理论中,为刻划系统的非决定性,用微分包含代替通常的微分方程来描述系统。同时,系统将不再追求最优性,而只求在某一范围内生存。系统的轨线则由生存性和惯性原理来形成。生存理论看来将在经济系统、生物系统、生态系统、社会系统等大系统的问题中得到应用。本文以价格调整问題作为例子,来说明这种理论与经典的系统最优控制理论的不同。

This paper presents the viability theory of macro-systems, created by French mathematician J.P. Aubin.In this theory,for characterizing the non-determinism of systems,a system is described by differential inclusons, instead of differential equations. Morever, the system does not seek an optimality,and merely requires the viability in a certain domain. The trajectories of system is so determined by the viability and the inertia principle.The viability theory appears to have applications in problems of macro-systems such as economic systems, biological systems, eclogical systems,sociological systeams and others.This paper considers a problem of price regulation as an example for explaining the drffenence between the classical optimal control theory of systems and this one.