离散时滞系统的线性二次最优控制与仿真

The optimal control and simulation of linear quadratic for discrete systems with delays

研究单输入两时滞的离散系统的线性二次最优控制问题。将所研究的问题等价地转化成一个带约束条件的时滞问题,再转化成一个无时滞问题,最后通过一系列的等价转化,变成一个易求解的条件极值问题。通过求解该条件极值问题得到了系统的最优控制输入序列,并对所提出的方法进行了仿真模拟,结果表明该方法是正确的,具有很好的效果。

The linear quadratic optimal control problem for discrete-time systems with single-input and two input delays is considered. The problem is first converted to a problem with constraint and delays, and then is converted to a problem without delays. Finally, by some equivalent conversion, the problem is converted to an easily solved conditional extreme value problem. The optimal control input sequences are successfully derived by solving the conditional extreme value problem. Digital simulation is carried out, and its results show that the approach is right and very effective.