Adaptive Predictive Control: A Data-Driven Closed-Loop Subspace Identification Approach

Algorithm 1

Summary of the proposed method.

(1) Construct the block Hankel matrices from the closed-loop data.

(2) Obtain the intermediate subspace matrices 𝐿_𝑤 and 𝐿_𝑢 by solving the least squares problem (24).

(3) Compute the closed-loop subspace matrices 𝐿_𝑤 and 𝐿_𝑢 using (25).

(4) Derive the predictor 𝑦_𝑓 of predictive controller with (26).

(5) Implement the control input 𝑢 using (27) and (28).

(6) At the next time, when new data arrives, implement the data inspection strategy. If the data

is harmful (or useless), keep the 𝑢 constant. Otherwise, implement the following steps.

(7) Build the new input-output Hankel matrix 𝐷^∗ and the new R matrix is the QR decomposition

results of 𝐷^∗ with (35).

(8) Recursively computer the elements 𝑅₁₁, 𝑅₂₁, 𝑅₂₂, 𝑅₃₁, 𝑅₃₂ of R matrix using (38) and (39).

(9) Calculate the new subspace matrices using (40) and computer the control input by

repeating steps 4-5. Then, back to step 6.