参数未知随机系统的最小方差对偶自适应控制

Variance minimization dual adaptive control for stochastic systems with unknown parameters

针对参数未知随机系统的自适应控制问题,研究了最小方差对偶自适应控制。分析了由于未知参数的不确定性,使得运用动态规划原理求解最优控制律时存在着困难,转而寻求次优控制律;给出了差分方程转换成状态空间模型的方法,将未知参数在一个确定的模型集中取值,运用动态规划原理得到各模型的控制律,通过各模型后验概率加权获得次优对偶控制律。给出了算例,以验证此算法的有效性,表明所得到的控制律既有调节作用,又有学习作用。

The variance minimization dual adaptive control with the unknown parameters for stochastic systems is studied. Owing to the difficulty to solve the optimal dual control law using dynamic programming principle as a result of the uncertainty of the unknown parameters, hence the aim is transferred to find the suboptimal control law. The difference equation included the unknown parameters is transferred into the state space model, and let the unknown parameters take the values in the definite model set. To use the dynamic programming principle achieves the control law for every model, and a suboptimal dual control law is obtained through the weighted average of posterior probability of every model. An example is given to verify the effectiveness of the approach. It is shown that the control law obtained by the approach has both the adjusting feature and the learning feature.