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