# Model reference adaptive control question

Hi, dear friends,
here is a question in model reference adaptive control
plant: y(t) = a*y(t-1)+u(t-1) model: y_m(t) = a_m*y_m(t-1) + u_m(t-1)
control: u(t) = -theta(t)*y(t) + u_m(t-1)
adaptation: y(t-1)*e(t) theta(t)=theta(t-1)+ ----------------- 1+y(t-1)^2 where e(t) is the equation error
the question is to show
|e(t)| ------------------------ is uniformly bounded and tends to zero (1+y(t-1)^2)^(1/2)
I dont have even a clue for this question. Plz give me a hint. Thanks
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Hi, dear friends,
here is a question in model reference adaptive control
plant: y(t) = a*y(t-1)+u(t-1) model: y_m(t) = a_m*y_m(t-1) + u_m(t-1) control: u(t) = -theta(t)*y(t) + u_m(t-1)
adaptation: y(t-1)*e(t) theta(t)=theta(t-1)+ ----------------- 1+y(t-1)^2 where e(t) is the equation error
the question is to show
|e(t)| ----------------------------- is uniformly bounded and tends to zero (1+y(t-1)^2)^(1/2)
I dont have even a clue for this question. Plz give me a hint.