华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (1): 1-14.

• 数学 统计学 •    下一篇

具有未知阶数和系数的线性随机系统的自适应控制

杨昌利1,2, 阮荣耀1, 龚妙昆1   

  1. 1.华东师范大学数学系，上海200062; 2.华东师范大学信息学院，上海200062
  • 收稿日期:2001-12-21 修回日期:2003-06-16 出版日期:2004-03-25 发布日期:2004-03-25
  • 通讯作者: 杨昌利

Adaptive- Control for Linear Stochastic Systems with Unknown Orders and Coefficients

YANG Chang-li 1,2, RUAN Rong-yao 1, GONG Miao-kung 1   

  1. 1. Department of Mathematics，East China Normal University，Shanghai 200062，China;2. School of Information Science and Technology', East China Normal University, Shanghai 200062, China
  • Received:2001-12-21 Revised:2003-06-16 Online:2004-03-25 Published:2004-03-25
  • Contact: YANG Chang-li

摘要： 该文考虑具有未知阶数和系数的离散时间线性随机控制系统(ARMAX模型)，提出一种便于在线实施的自适应控制新算法。在一定的条件下，该算法能保证所建立的闭环系统全局稳定和输出跟踪渐进最优，而且阶数和系数的估计都具有强一致性，同时还给出系数估计的收敛速度。仿真结果表明所提出的自适应控制的新算法是有效的和可行的，且控制量在容许控制的范围之内。

关键词: ARMAX模型, 阶数估计, 参数估计, 强一致性, 自适应控制, 全局稳定性, ARMAX模型, 阶数估计, 参数估计, 强一致性, 自适应控制, 全局稳定性

Abstract: This paper considers single-input single-output linear discrete-time stochastic feed-back control systems(ARMAX model) with unknown orders and coefficients, and propose a new adaptive control algorithm, which is easily implemented on-line. The algorithm can guarantee the global stability of the resulting closed-loop system and the asymptotic optimality of the adaptive tracking. And the estimates of the orders and coefficients are all strongly consistent in the closed-loop identification. Simultaneously, the convergent rate of coefficient estimates to their true values is also given. The simulation results given in this paper show that the new algorithm of the adaptive control we developed here are effective and feasible, besides the control quantities are in the range of the admissible control.

Key words: order estimation, parameter estimation, strong consistency, adaptive control, global stability, ARMAX model, order estimation, parameter estimation, strong consistency, adaptive control, global stability

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