多变量离散时间系统的自适应LQ控制(英文)

Discrete-Time Adaptive LQ Control for Multivariable Systems

考虑了多变量离散系统的自适应LQ(线性二次型 )控制问题 .利用LS(最小二乘 )算法和WLS(加权最小二乘 )算法的自收敛性和随机正则化的思想[1] ,证明了修改的估计模型是几乎处处自收敛的、一致可控和一致可观的 .基于上面的估计 ,提出了两种自适应LQ控制律 ,证明了闭环系统是稳定的和最优的 .

Discrete time adaptive LQ (linear quadratic) control for multivariable systems is considered. Using self convergence of LS (least squares) algorithm, WLS (weighted least squares) algorithm and the idea of random regularization [1] , we first prove that the modified estimated model is almost surely self convergent, uniformly controllable and observable. Then we prove that two adaptive LQ control laws are stable and optimal.\;