Optimal Adaptive Controller for Stochastic Systems Based on Weighted Least-squares Algorithm
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摘要: 普通的最小二乘算法LS，并不能保证它的收敛性，而加权的最小二乘算法WLS，却有很好的收敛性，采用这种算法进行随机系统的辨识，能够保证算法所得的参数收敛于某一个向量，而且这种算法在很多方面具有同普通最小二乘算法一样的性质，采用这种算法对随机系统进行适应控制，能够保证系统是闭环全局稳定的，而且这种适应控制还能收敛于“一步超前”最优控制。
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关键词:
- WLS算法 /
- “一步超前”最优适应控制器 /
- 闭环全局稳定
Abstract: In general, we can not guarantee the convergence of the common LS method. A recursive least-squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self-convergence property, i.e., it converges to a certain random vector almost surely irrespective of the control law design. Such algorithms enjoy almost the same nice asymptotic properties as the standard least-squares. With adaptive control, the closed-loop system is globally stable and the adaptive controller may converge to the one-step-ahead optimal controller. -
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