最速控制问题中的Ляпунов方法

The second method of lyapunov applied to the design of time-optimal control

本文讨论了Ляпунов第二法在最速控制中的应用。从理论上分析了一类线性定常系统存在Ляпунов意义下最速控制解的条件,从工程实现角度讨论了Ляпунов意义下最佳开关面的问题,并以一个3阶伺服系统的模拟装置为例,对经典控制理论、极大值原理和Ляпунов方法等3种设计方案的实验研究结果作出了比较。

The second method of Lyapunov applied to the design of time-optimal control is dis-cussed. The conditions are discussed theoretically whose satisfaction assures that there isthe solution of time-optimal control in Lyapunov meaning for a class of time-invariantlinear systems. The problems of optimal switching surfaces in Lyapunov meaning to the en-gineering realization are dealt with. The classical control experiment and the time-optimalcontrol experiments in Lyapunov meaning and maximum principle upon the simulatingplant with 3 orders for a typical radar servomechanism are made. The comparison of theexperimental results is given.