Optimal control of unknown parameter systems
Optimal control of unknown parameter systems
复制标题
未知参数系统的最优控制
DOI：
10.1109/9.35284
复制
发表时间：
1989
影响因子：
6.8
通讯作者：
K. Loparo
中科院分区：
文献类型：
--
作者：
F. Casiello;K. Loparo
问题是讨论找到一个成本功能的自适应控制律是最佳的。所考虑的系统是一个未知参数的部分可观测线性随机系统。众所周知，当参数属于有限集时，可以导出此问题的最优有限维滤波器。由于最优滤波器涉及对给定观测值的每个参数值的后验概率的有限集合的评估，因此自然的自适应控制方案是：（i）在给定每个参数的情况下开发最优线性反馈律;（ii）使用后验概率来形成加权平均。（凸组合）的各个控制策略;和（iii）使用加权平均值作为控制律。在一般情况下，设计了一个二次成本泛函，使得该策略是最优的，并且表明，与双重控制问题相一致的探测效应是具有参数不确定性的标准线性二次高斯问题所固有的。>
The problem is discussed of finding a cost functional for which an adaptive control law is optimal. The system under consideration is a partially observed linear stochastic system with unknown parameters. It is well known that an optimal finite-dimensional filter for this problem can be derived when the parameters belong to a finite set. Since the optimal filter involves the evaluation of a finite set of a posteriori probabilities for each of the parameter values given the observations, a natural adaptive control scheme is: (i) develop the optimal linear feedback law given each parameter; (ii) use the a posteriori probabilities to form the weighted average (convex combination) of the individual control policies; and (iii) use the weighted average as the control law. A quadratic cost functional is devised for which this strategy is optimal, in a general case, and it is shown that the probing effect identified with dual control problems is inherent in the standard linear-quadratic-Gaussian problem with parameter uncertainty. >