摘要: This document considers stochastic differential equations of Ito type. This problem is a fundamental one in the field of stochastic control. The theory of stochastic control has been successfully applied to a wide variety of pract... 展开 This document considers stochastic differential equations of Ito type. This problem is a fundamental one in the field of stochastic control. The theory of stochastic control has been successfully applied to a wide variety of practical problems as demonstrated in Maybeck, including problems involving the tracking of objects with imaging sensors. The problem of tracking aircraft with infrared sensors has been addressed in this mathematical framework by Kendrick, Maybeck, and Reid and by Maybeck, Jensen, and Harnley. The specific problem which gave impetus to this research involves real time control of the orientation of the optical axis of an infrared imaging sensor. The problem of choosing a good control for a system modeled in this framework involves the property of stability of solutions of the stochastic differential equation representing the system. Stability of these solutions is established by constructing a Liapunov function for the equation. In this way, the construction of a Liapuinov function for the equation is of great value in choosing controls. This and other background material are explained in Kushner. In his recent monograph, Mees remarked that there is no good general method for constructing Liapunov functions for systems represented by ordinary differential equations. 收起