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线性二次型调节问题(LQ 问题)的综合方法已有了很多研究。综合过程的一个核心步骤是要求解一个矩阵 Riccati 方程。一般来说,这个方程只能采用数值方法进行求解。当系统维数较高时,计算过程变得十分复杂,而且会面临严重的数值问题,如计算精度、内存容量、收敛速度等。此文主要对一类在控制工程中有一定适用范围的 LQ 问题,给出一种实用的综合方法。其最优控制律的计算公式具有闭合形式,
Much research has been done on the synthesis of linear quadratic adjustment problems (LQ problems). A core step in the synthesis process is to solve a matrix Riccati equation. In general, this equation can only be solved numerically. When the system dimension is high, the calculation process becomes very complicated, and will face serious numerical problems, such as calculation accuracy, memory capacity, convergence speed and so on. This paper mainly presents a practical and comprehensive method for a class of LQ problems that have certain scope of application in control engineering. The optimal control law of the formula has a closed form,